Quantitative patterns in constraint interaction: FRENCH
Introduction
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This document accompanies one section of a manuscript by Anonymous.
In terms of reproducibility, this document falls short in many respects. A fair amount of work was done by hand or in GUIs, before we created the present script. We have done our best to document and explain this work here, but have not gone back and reimplemented everything in script form. We hope that the partial reproducibility here will be beneficial to readers wishing to test or modify our analysis.
Pipeline to the input file for this script
Google n-grams files are downloaded from Google
grep takes these to a set of smaller files
grep -E '^CE |^Ce |^ce |^CET |^Cet |^cet ' googlebooks-fre-all-2gram-20120701-ce > ce_cet_2grams.txtgrep -E '^BEAU |^Beau |^beau |^BEL |^Bel |^bel ' googlebooks-fre-all-2gram-20120701-be > beau_bel_2grams.txtgrep -E '^NOUVEAU |^Nouveau |^nouveau |^NOUVEL |^Nouvel |^nouvel ' googlebooks-fre-all-2gram-20120701-no > nouveau_nouvel_2grams.txtgrep -E '^VIEUX |^Vieux |^vieux |^VIEIL |^Vieil |^vieil ' googlebooks-fre-all-2gram-20120701-vi > vieux_vieil_2grams.txtgrep -E '^FOU |^Fou |^fou |^FOL |^Fol |^fol ' googlebooks-fre-all-2gram-20120701-fo > fou_fol_2grams.txtgrep -E '^MOU |^Mou |^mou |^MOL |^Mol |^mol ' googlebooks-fre-all-2gram-20120701-mo > mou_mol_2grams.txtgrep -E '^LE |^Le |^le ' googlebooks-fre-all-2gram-20120701-le > le_2grams.txtgrep "^[Ll]'" googlebooks-fre-all-1gram-20120701-l > l_1grams.txtgrep "^[Ll]' " googlebooks-fre-all-2gram-20120701-l_ > l_2grams.txtgrep -E '^LA |^La |^la ' googlebooks-fre-all-2gram-20120701-la > la_2grams.txtgrep -E '^MA |^Ma |^ma ' googlebooks-fre-all-2gram-20120701-ma > ma_2grams.txtgrep -E '^MON |^Mon |^mon ' googlebooks-fre-all-2gram-20120701-mo > mon_2grams.txtgrep -E '^TA |^Ta |^ta ' googlebooks-fre-all-2gram-20120701-ta > ta_2grams.txtgrep -E '^TON |^Ton |^ton ' googlebooks-fre-all-2gram-20120701-to > ton_2grams.txtgrep -E '^SA |^Sa |^sa ' googlebooks-fre-all-2gram-20120701-sa > sa_2grams.txtgrep -E '^SON |^Son |^son ' googlebooks-fre-all-2gram-20120701-so > son_2grams.txtgrep -E '^DE |^De |^de ' googlebooks-fre-all-2gram-20120701-de > de_2grams.txtgrep "^[Dd]'" googlebooks-fre-all-1gram-20120701-d > d_1grams.txtgrep "^[Dd]' " googlebooks-fre-all-2gram-20120701-d_ > d_2grams.txtgrep -E "^QUE |^Que |^que |^QU' |^Qu' |^qu' " googlebooks-fre-all-2gram-20120701-qu > que_qu_2grams.txtgrep -E "^QUE |^Que |^que " googlebooks-fre-all-2gram-20120701-qu > que_2grams.txtgrep -E "^QU'|^Qu'|^qu'" googlebooks-fre-all-1gram-20120701-q > qu_1grams.txtgrep -E '^NE |^Ne |^ne ' googlebooks-fre-all-2gram-20120701-ne > ne_2grams.txtgrep "^[Nn]'" googlebooks-fre-all-1gram-20120701-n > n_1grams.txtgrep "^[Nn]' " googlebooks-fre-all-2gram-20120701-n_ > n_2grams.txtgrep -E '^SE |^Se |^se ' googlebooks-fre-all-2gram-20120701-se > se_2grams.txtgrep "^[Ss]'" googlebooks-fre-all-1gram-20120701-s > s_1grams.txtgrep "^[Ss]' " googlebooks-fre-all-2gram-20120701-s_ > s_2grams.txtgrep -E '^JE |^Je |^je ' googlebooks-fre-all-2gram-20120701-je > je_2grams.txtgrep "^[Jj]'" googlebooks-fre-all-1gram-20120701-j > j_1grams.txtgrep "^[Jj]' " googlebooks-fre-all-2gram-20120701-j_ > j_2grams.txtgrep "^[Cc]'" googlebooks-fre-all-1gram-20120701-c > c_1grams.txtgrep "^[Cc]' " googlebooks-fre-all-2gram-20120701-c_ > c_2grams.txtgrep -E '^ME |^Me |^me ' googlebooks-fre-all-2gram-20120701-me > me_2grams.txtgrep "^[Mm]'" googlebooks-fre-all-1gram-20120701-m > m_1grams.txtgrep "^[Mm]' " googlebooks-fre-all-2gram-20120701-m_ > m_2grams.txtgrep -E '^TE |^Te |^te ' googlebooks-fre-all-2gram-20120701-te > te_2grams.txtgrep "^[Tt]'" googlebooks-fre-all-1gram-20120701-t > t_1grams.txtgrep "^[Tt]' " googlebooks-fre-all-2gram-20120701-t_ > t_2grams.txtgrep -E '^DU |^Du |^du ' googlebooks-fre-all-2gram-20120701-du > du_2grams.txtgrep -E "^DE L' |^De l' |^de l' " googlebooks-fre-all-3gram-20120701-de > del_3grams.txtgrep -E "^DE L'|^De l'|^de l'" googlebooks-fre-all-2gram-20120701-de > del_2grams.txtgrep -E '^AU |^Au |^au ' googlebooks-fre-all-2gram-20120701-au > au_2grams.txtgrep -E "^? L' |^A L' |^? l' |^A l' |^? l' " googlebooks-fre-all-3gram-20120701-a_ > al_3grams.txtgrep -E "^? L'|^A L'|^? l'|^A l'|^? l' " googlebooks-fre-all-2gram-20120701-a_ > al_2grams.txtgrep -E '^EN |^En |^en ' googlebooks-fre-all-2gram-20120701-en > en_2grams.txtcompile_ngrams3.pytakes all of these files, in directoryNGramExtracts, tocollated_ALL.txtclassify_phonology3.pytakescollated_ALL.txttocollated_ALL_phon_and_morph.txtPartly manually, items are extracted from
collated_ALLiff they meet all 3 criteria:
part of speech (POS), gender, and pronunciation information were available through dictionary look-up
Word1 is suitable for Word2’s part of speech (POS) and gender. For example, “le_l” is not allowed with feminines. Results are put in
collated_SELECTED.txtWord2 is in the region of interest: it begins with letter ‘h’, or with a glide sound, or occurs in lists of other aspirated words (‘uhlan’, ‘ululement’, etc.)
collate_years2.pytakescollated_SELECTED.txttotable_1900_2010_Min_10_wordMin_20_SELECT3.txt. This means that results are used from them years 1900 to 2010 only, that the word1+word2 combination must have a frequency of at least 10 during that period, and word2, in all combinations, must have a frequency of at least 20 during that period.The following word2s were excluded because of too many false hits (poor OCR), or too many in wrong language, or different meanings:
- horizontale
- hure
- hie
- Hauteville
- oie
- hombre
- hast
- h`ere
- horion
- hidalgo
- ion
- Io
- le/l’, la/l’ for most person names (pragmatically unlikely, and danger of being actually L. Lastname)
…and the remainder was converted into a version with one row per word1-word2 combination (instead of one row per word1, with separate column for each word1), with apostrophes removed: table_1900_2010_Min_10_wordMin_20_SELECT3_inRows_noApostrophe.csv.
- The following columns were added: initial vowel letter, sound, and coarsely-classified sound of word2, google n-grams token frequency for voculent and consulent versions of word1+word2 combination, frequencies looked up in Lexique (lemma film/book, form file/book), random intercept for Word2 that was obtained in SAS beta regression (see below). Result is the input file for this script,
table_1900_2010_Min_10_wordMin_20_SELECT3_inRows_Oct_2013.csv.
Prepare for analysis and plotting
set.seed(1234) #just in case we do anything with random numbers
require(lme4) || install.packages("lme4") ## Loading required package: lme4
## Loading required package: Matrix
## Loading required package: Rcpp## [1] TRUErequire(lme4)
require(car) || install.packages("car") ## Loading required package: car## [1] TRUErequire(car)
require(multcomp) || install.packages("multcomp") ## Loading required package: multcomp
## Loading required package: mvtnorm
## Loading required package: survival
## Loading required package: splines
## Loading required package: TH.data## [1] TRUErequire(multcomp)
require(stringr) || install.packages("stringr") ## Loading required package: stringr## [1] TRUErequire(stringr)
require(plotrix) || install.packages("plotrix") ## Loading required package: plotrix## Warning: package 'plotrix' was built under R version 3.1.3## [1] TRUErequire(plotrix)
#set font family for plots
myFontFamily="serif"
par(font=list(family=myFontFamily)) #will work for most plots
#how much to increase resolution
myResMultiplier <- 5 #default is 72 ppi; using this in every call to png() will make it 360Read in data
Read in and inspect data, processed from Google NGrams:
french <- read.table("table_1900_2010_Min_10_wordMin_20_SELECT3_inRows_Oct_2013.csv",
header=TRUE, sep=",")
head(french)## word2 w2_begins_with w2_phon wd2_morph word1 word1.different.format
## 1 habeas V h__V M le_l le/l
## 2 habeas V h__V M du_del du/del
## 3 habeas V h__V M au_àl au/àl
## 4 habeas V h__V M ce_cet ce/cet
## 5 habeas V h__V M de_d de/d
## 6 habileté V h__V F la_l la/l
## concatenation voculence vowel_letter vowel_sound vowel_sound_coarse
## 1 le/l+habeas 0.9770 a a a
## 2 du/del+habeas 0.9539 a a a
## 3 au/àl+habeas 1.0000 a a a
## 4 ce/cet+habeas 1.0000 a a a
## 5 de/d+habeas 0.9807 a a a
## 6 la/l+habileté 1.0000 a a a
## phrase_V_count phrase_C_count phrase_frequency lemma_freq_film
## 1 1741 41 1782 NA
## 2 1201 58 1259 NA
## 3 179 0 179 NA
## 4 42 0 42 NA
## 5 7630 150 7780 NA
## 6 223505 0 223505 2.05
## lemma_freq_books form_freq_film form_freq_books random_intercept_SAS
## 1 NA NA NA 0.4348
## 2 NA NA NA 0.4348
## 3 NA NA NA 0.4348
## 4 NA NA NA 0.4348
## 5 NA NA NA 0.4348
## 6 10.88 2.03 10.54 0.3725str(french)## 'data.frame': 1741 obs. of 19 variables:
## $ word2 : Factor w/ 358 levels "habeas","habileté",..: 1 1 1 1 1 2 2 2 2 2 ...
## $ w2_begins_with : Factor w/ 3 levels "G","V","V~G": 2 2 2 2 2 2 2 2 2 2 ...
## $ w2_phon : Factor w/ 24 levels "h__aspj","h__aspV",..: 7 7 7 7 7 7 7 7 7 7 ...
## $ wd2_morph : Factor w/ 18 levels "F","M","M_Int",..: 2 2 2 2 2 1 1 1 1 1 ...
## $ word1 : Factor w/ 20 levels "au_àl","beau_bel",..: 9 5 1 3 4 8 10 15 16 18 ...
## $ word1.different.format: Factor w/ 20 levels "au/àl","beau/bel",..: 9 5 1 3 4 8 10 15 16 18 ...
## $ concatenation : Factor w/ 1741 levels "au/àl+habeas",..: 973 661 1 197 331 866 1154 1338 1510 1627 ...
## $ voculence : num 0.977 0.954 1 1 0.981 ...
## $ vowel_letter : Factor w/ 7 levels "a","C","e","i",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ vowel_sound : Factor w/ 16 levels "a","A","a_nas",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ vowel_sound_coarse : Factor w/ 6 levels "a","e","i","o",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ phrase_V_count : int 1741 1201 179 42 7630 223505 1312 363 64712 384 ...
## $ phrase_C_count : int 41 58 0 0 150 0 0 0 0 0 ...
## $ phrase_frequency : int 1782 1259 179 42 7780 223505 1312 363 64712 384 ...
## $ lemma_freq_film : num NA NA NA NA NA 2.05 2.05 2.05 2.05 2.05 ...
## $ lemma_freq_books : num NA NA NA NA NA ...
## $ form_freq_film : num NA NA NA NA NA 2.03 2.03 2.03 2.03 2.03 ...
## $ form_freq_books : num NA NA NA NA NA ...
## $ random_intercept_SAS : num 0.435 0.435 0.435 0.435 0.435 ...Descriptive statistics
What is the range of Word2 overall (raw, unweighted) voculences
sort(tapply(french$voculence, french$word2, FUN=mean))## hachette haddock hadji hallier
## 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## hamada hammam harle harmel
## 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## harpe hart hennin hennuyer
## 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## hérissant hertz hesse hlm
## 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## hotte hottentot huchet huron
## 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## huronien hurricane yang yoga
## 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## haine yacht houille héraut
## 1.708e-05 4.624e-05 7.214e-05 1.526e-04
## hâter haute honte honteuse
## 2.859e-04 3.178e-04 3.373e-04 3.512e-04
## hongrois hauteur Hesse hêtre
## 5.704e-04 7.137e-04 7.417e-04 7.467e-04
## houblon hache hérisse hile
## 8.767e-04 1.061e-03 1.133e-03 1.284e-03
## heaume hâte halte haubert
## 1.291e-03 1.350e-03 1.434e-03 1.605e-03
## héron havre Yunnan henné
## 1.717e-03 1.837e-03 1.877e-03 1.925e-03
## huit yard haïr halètement
## 2.016e-03 2.399e-03 2.489e-03 2.967e-03
## yole Hongrie harcèlement Yokohama
## 2.986e-03 3.037e-03 3.105e-03 3.287e-03
## hall hiérarchie haoussa hamster
## 3.596e-03 3.601e-03 4.528e-03 4.669e-03
## hait hollandaise hiérarchiser heurter
## 4.802e-03 5.108e-03 5.222e-03 5.244e-03
## halle hardiesse hiérarchisation halo
## 6.648e-03 7.218e-03 8.010e-03 8.036e-03
## harceler hurler hase Hainaut
## 8.175e-03 8.488e-03 8.651e-03 8.710e-03
## hasarde hiérarque honteux haricot
## 9.027e-03 9.396e-03 1.010e-02 1.015e-02
## hanneton haro hasarder hameau
## 1.121e-02 1.189e-02 1.292e-02 1.297e-02
## hideux haut harnois hussitisme
## 1.406e-02 1.425e-02 1.456e-02 1.530e-02
## hasard héros yatagan hideuse
## 1.715e-02 1.842e-02 1.851e-02 1.967e-02
## hérisson hermandad hallebarde hernie
## 2.026e-02 2.217e-02 2.285e-02 2.302e-02
## huguenote hussard hangar hibou
## 2.500e-02 2.514e-02 2.754e-02 2.805e-02
## hazard heurt yack haie
## 2.844e-02 2.860e-02 2.954e-02 2.956e-02
## haste hérisser hérissent onze
## 3.004e-02 3.094e-02 3.302e-02 3.511e-02
## Hambourg hobereau honnir haranguer
## 4.087e-02 4.229e-02 4.259e-02 4.323e-02
## hune ouolof Haguenau hautboïste
## 4.346e-02 4.365e-02 4.762e-02 4.803e-02
## humer houspiller Houssaye harassement
## 4.913e-02 5.313e-02 5.352e-02 5.392e-02
## harasser hornblende huguenot hollandais
## 5.534e-02 5.649e-02 5.968e-02 6.877e-02
## hausse Hulot hasardeux hareng
## 7.263e-02 7.560e-02 8.246e-02 8.435e-02
## yen ouistiti haïs huguenotisme
## 8.442e-02 1.024e-01 1.035e-01 1.048e-01
## Yémen haridelle Huon hiérophanie
## 1.056e-01 1.155e-01 1.196e-01 1.216e-01
## Huguet hollande handicap hardi
## 1.225e-01 1.229e-01 1.311e-01 1.429e-01
## harnacher hasardeuse Hokkaïdo Hanoï
## 1.527e-01 1.688e-01 1.735e-01 2.144e-01
## harnachement huis hiératisme henry
## 2.206e-01 2.652e-01 2.732e-01 2.800e-01
## handicape home Hugues hyaloplasme
## 2.829e-01 3.021e-01 3.139e-01 3.182e-01
## hiatus Hautmont ouï Ouadi
## 3.939e-01 4.012e-01 4.101e-01 4.231e-01
## hiérogamie Henry Hubert hyène
## 4.505e-01 4.587e-01 4.614e-01 4.756e-01
## huiler hallstattien Herbert hindi
## 4.970e-01 5.000e-01 5.113e-01 5.282e-01
## oille hiéroglyphe iota Henri
## 5.368e-01 5.759e-01 5.830e-01 6.012e-01
## Hervé hyalite huilage oint
## 6.128e-01 6.302e-01 6.388e-01 6.571e-01
## iule ouadi Harmel Huguette
## 6.629e-01 6.766e-01 7.094e-01 7.185e-01
## oye habité oil hoir
## 7.290e-01 7.679e-01 7.755e-01 7.789e-01
## hospodar Hudson oing heureux
## 7.806e-01 7.808e-01 7.815e-01 7.821e-01
## hacienda hippisme hiérogrammate Hathor
## 7.864e-01 7.872e-01 7.879e-01 7.898e-01
## hiérophante Héra humain hauterivien
## 7.979e-01 8.174e-01 8.207e-01 8.250e-01
## hickory Iéna Hécate Hadès
## 8.332e-01 8.429e-01 8.435e-01 8.534e-01
## iambe Hauterive hégélien Hérault
## 8.635e-01 8.686e-01 8.705e-01 8.778e-01
## hetman honneur huile haïtienne
## 8.840e-01 8.855e-01 8.856e-01 8.859e-01
## herbe hégélianisme huileux habit
## 8.888e-01 8.906e-01 8.913e-01 8.943e-01
## habita homme Hispaniola holmium
## 9.035e-01 9.036e-01 9.040e-01 9.071e-01
## heure hydrogène oindre haïtien
## 9.139e-01 9.195e-01 9.204e-01 9.224e-01
## Hermite hyacinthe humidité hameçon
## 9.292e-01 9.354e-01 9.372e-01 9.373e-01
## Iénisséi Hauterivien hyper Henriette
## 9.393e-01 9.394e-01 9.454e-01 9.458e-01
## hapax hallali heur Horus
## 9.464e-01 9.487e-01 9.517e-01 9.522e-01
## humiliât Iowa Himalaya hinterland
## 9.570e-01 9.571e-01 9.611e-01 9.627e-01
## honnêteté Horace habituel hérédité
## 9.642e-01 9.670e-01 9.687e-01 9.698e-01
## habitus Utica hôtel oiseau
## 9.707e-01 9.725e-01 9.725e-01 9.734e-01
## Hector hermite hôpital habiliter
## 9.743e-01 9.744e-01 9.752e-01 9.767e-01
## Héraclite Hygie homographie ouïr
## 9.783e-01 9.784e-01 9.788e-01 9.801e-01
## habiter humaine Herzégovine habeas
## 9.805e-01 9.806e-01 9.818e-01 9.823e-01
## humanité Hélène hiver haltère
## 9.825e-01 9.829e-01 9.835e-01 9.837e-01
## yeuse Hérode Hadrien hitlérisme
## 9.849e-01 9.851e-01 9.860e-01 9.861e-01
## habitation Hypérion Yonne habitude
## 9.870e-01 9.873e-01 9.876e-01 9.877e-01
## hosanna hommage hectare humanisme
## 9.878e-01 9.881e-01 9.891e-01 9.892e-01
## histoire Hérodote ionosphère habituelle
## 9.896e-01 9.900e-01 9.900e-01 9.901e-01
## habilité humilia Honorine horreur
## 9.901e-01 9.902e-01 9.903e-01 9.908e-01
## hoirie Héraclès oued habitant
## 9.910e-01 9.922e-01 9.924e-01 9.926e-01
## iodure Hippocrate harmonica harmonie
## 9.927e-01 9.930e-01 9.931e-01 9.941e-01
## Ionie hectolitre hérésie harmattan
## 9.943e-01 9.943e-01 9.944e-01 9.951e-01
## heureuse héritage hypothèse ionisation
## 9.953e-01 9.960e-01 9.962e-01 9.967e-01
## hydro haleine hypothèque honorer
## 9.969e-01 9.974e-01 9.974e-01 9.977e-01
## Oise iodate iode héritier
## 9.979e-01 9.979e-01 9.980e-01 9.984e-01
## huilerie Héloïse iodoforme historien
## 9.985e-01 9.985e-01 9.986e-01 9.987e-01
## habite humus hydrologie hématite
## 9.992e-01 9.992e-01 9.993e-01 9.993e-01
## humilie herpès hagiographie humilier
## 9.994e-01 9.994e-01 9.994e-01 9.996e-01
## oignon habitent hélice hydrolyse
## 9.996e-01 9.997e-01 9.997e-01 9.998e-01
## hésiter hypertrophie hégémonie hémoglobine
## 9.998e-01 9.998e-01 9.998e-01 9.998e-01
## hospice hélium horloge habillement
## 9.998e-01 9.998e-01 9.998e-01 9.999e-01
## hydrate habitat humilité hospitalité
## 9.999e-01 9.999e-01 9.999e-01 9.999e-01
## héroïsme humeur hébergement horizon
## 9.999e-01 9.999e-01 9.999e-01 9.999e-01
## humour hostilité héroïne habileté
## 9.999e-01 1.000e+00 1.000e+00 1.000e+00
## hygiène hésite harpagon hebdo
## 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## hélio hélion hélix herbette
## 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## hercule hermès hermine hibiscus
## 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## hindou hipparque hippo hirondelle
## 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## histologie holocauste homélie honorée
## 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## hortensia horticulture huilier humiliation
## 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## hydrographie oison
## 1.000e+00 1.000e+00dim(tapply(french$voculence, french$word2, FUN=mean)) #how many distinct Word2s## [1] 358Histograms of voculence for word1+word2 combination, and for each word2 averaging over all word1s it occurs with:
hist(french$voculence, col="grey",xlab="rate of unasp. behavior", main="word1+word2 combinations", breaks=20)
hist(tapply(french$voculence, french$word2, FUN=mean), col="grey", xlab="rate of non-alignment", ylab="number of Word2s", main="Word2s, averaging over Word1s they occur with", breaks=20)
#Since this second one will appear in the paper, also do a PNG file:
png(file="histo_Word2_voculence.png",width=myResMultiplier*460,height=myResMultiplier*300, res=myResMultiplier*72, family=myFontFamily)
par(mar=c(4,4,3,1)+0.1)
hist(tapply(french$voculence, french$word2, FUN=mean), col="grey", xlab="rate of non-alignment", ylab="number of Word2s", main="", breaks=20)
dev.off()## pdf
## 2Regression model
A regression, with “voculence” (rate of behaving as though Word2 is vowel-initial; or, as we call it in the paper, non-alignancy) as dependent variable. Uses binomial family, because voculence has a U-shaped distribution. This does produce a warning message about non-integer successes.
Some independent variables were eliminated because they made little contribution (vowel quality, V vs. glide). Result is that any idiosyncrasy of Word2 is taken care of in its random intercept value, not attributed to more general properties of Word2, such as beginning with a vowel vs. a glide.
my_formula <- "voculence ~ word1 + (1|word2) + log(phrase_frequency)"
my_data <- subset(french, french$word1 != "fou_fol" &
french$word1 != "mou_mol" &
french$word1 != "je_j" &
french$word1 != "te_t" &
french$word1 != "me_m" &
french$word1 != "ne_n" &
french$word1 != "se_s" &
french$word1 != "ce_cet" &
french$word1 != "que_qu" &
french$word1 != "ta_ton" &
french$word1 != "nouveau_nouvel" &
french$word1 != "sa_son")
french1.glmer.type <- glmer(my_formula, data=my_data, family="binomial")## Warning: non-integer #successes in a binomial glm!
## Warning: Model failed to converge with max|grad| = 0.34544 (tol = 0.001, component 3)#try to improve convergence
french2.glmer.type <- update(french1.glmer.type,start=getME(french1.glmer.type,c("theta","fixef")))## Warning: non-integer #successes in a binomial glm!
## Warning: Model failed to converge with max|grad| = 0.0207578 (tol = 0.001, component 8)french3.glmer.type <- update(french2.glmer.type,start=getME(french2.glmer.type,c("theta","fixef")))## Warning: non-integer #successes in a binomial glm!
## Warning: Model failed to converge with max|grad| = 0.0170359 (tol = 0.001, component 7)french4.glmer.type <- update(french3.glmer.type,start=getME(french3.glmer.type,c("theta","fixef")))## Warning: non-integer #successes in a binomial glm!
## Warning: Model failed to converge with max|grad| = 0.00695753 (tol = 0.001, component 2)#that's about as good as it's going to get
summary(french4.glmer.type)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: voculence ~ word1 + (1 | word2) + log(phrase_frequency)
## Data: my_data
##
## AIC BIC logLik deviance df.resid
## 925.2 975.4 -452.6 905.2 1108
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.362 -0.223 0.059 0.172 1.320
##
## Random effects:
## Groups Name Variance Std.Dev.
## word2 (Intercept) 17.6 4.2
## Number of obs: 1118, groups: word2, 345
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.3202 0.7297 -3.18 0.0015 **
## word1beau_bel 2.4568 0.9309 2.64 0.0083 **
## word1de_d 0.3090 0.4898 0.63 0.5282
## word1du_del -0.4875 0.4640 -1.05 0.2934
## word1la_l -0.1634 0.7021 -0.23 0.8159
## word1le_l -0.3680 0.5064 -0.73 0.4674
## word1ma_mon 2.3977 0.8118 2.95 0.0031 **
## word1vieux_vieil 1.7650 0.7627 2.31 0.0207 *
## log(phrase_frequency) 0.4122 0.0925 4.46 8.3e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) wrd1b_ word1d_d wrd1d_dl word1la_l word1le_l wrd1m_
## word1bea_bl -0.422
## word1de_d -0.127 0.140
## word1du_del -0.172 0.182 0.592
## word1la_l -0.015 0.045 0.687 0.448
## word1le_l -0.052 0.119 0.619 0.573 0.486
## word1ma_mon -0.454 0.237 0.408 0.260 0.397 0.226
## word1vix_vl -0.437 0.333 0.214 0.252 0.102 0.187 0.268
## lg(phrs_fr) -0.776 0.338 -0.342 -0.223 -0.395 -0.348 0.230
## wrd1v_
## word1bea_bl
## word1de_d
## word1du_del
## word1la_l
## word1le_l
## word1ma_mon
## word1vix_vl
## lg(phrs_fr) 0.306Compare to result of beta regression in SAS (why not in R? R’s betareg package doesn’t seem to allow random effects)
| Effect | Estimate | Standard Error | DF | t Value | Pr > abs(t) |
|---|---|---|---|---|---|
| Intercept | 0.5337 | 0.03140 | 344 | 16.99 | <.0001 |
| word1 = au_Ã l | -0.08175 | 0.01965 | 765 | -4.16 | <.0001 |
| word1 = beau_bel | 0.007171 | 0.02419 | 765 | 0.30 | 0.7670 |
| word1 = de_d | -0.06596 | 0.02220 | 765 | -2.97 | 0.0031 |
| word1 = du_del | -0.1114 | 0.02106 | 765 | -5.29 | <.0001 |
| word1 = la_l | -0.08278 | 0.02794 | 765 | -2.96 | 0.0031 |
| word1 = le_l | -0.1016 | 0.02280 | 765 | -4.46 | <.0001 |
| word1 = ma_mon | 0.000791 | 0.02585 | 765 | 0.03 | 0.9756 |
| word1 = vieux_vieil | 0 | . | . | . | . (reference level) |
| logphrase | 0.01291 | 0.002958 | 765 | 4.36 | <.0001 |
Check some model properties:
#Test normality of residuals
plot(density(resid(french4.glmer.type))) #A density plot of residuals--bimodal, not surprisingly
qqnorm(resid(french4.glmer.type)) # A quantile normal plot
qqline(resid(french4.glmer.type)) # Points fall pretty close to line--looks largely OK to me
#Test homogeneity
plot(french4.glmer.type) #ideally should be uniform distribution in both dimensions.
#Except for two extreme outliers, looks...OK?
#Check for independence of residuals and factors
plot(french4.glmer.type@frame$word1,resid(french4.glmer.type)) #residuals should look similar for each Word1
plot(french4.glmer.type@frame[,4],resid(french4.glmer.type), xlab="log of phrase frequency") #residuals should look similar across frequencies
Extract random intercepts
For comparison with the random intercepts from the beta regression, add random intercepts from model above as a column of dataset.
for (i in 1:length(french$word2)) {
french$random_intercept_R[i] <- ranef(french4.glmer.type)$word2[as.character(french$word2[i]),]
}Compare random intercepts from the two models–although the relationship is not linear (to be expected), it is just about monotonic.
plot(french$random_intercept_R, french$random_intercept_SAS)
List all random intercepts from the logistic model:
ranef(french4.glmer.type)## $word2
## (Intercept)
## habeas 2.47582
## habileté 1.05627
## habilité 1.59589
## habiliter 1.13797
## habillement 2.24807
## habit 1.73489
## habitant 2.07797
## habitat 1.88350
## habitation 0.90139
## habité 2.68956
## habiter 0.52921
## habitude 0.73261
## habituel 2.42502
## habituelle 1.64925
## habitus 2.20784
## hache -4.86124
## hachette -3.86189
## hacienda -0.44610
## haddock -2.72921
## Hadès 1.04652
## hadji -3.05231
## Hadrien 0.63323
## hagiographie 1.47891
## Haguenau -3.04429
## haie -4.16121
## Hainaut -4.38506
## haine -5.54273
## haïr -3.36261
## haïtien 1.88941
## haïtienne 1.46805
## haleine 1.27459
## halètement -3.34442
## hall -4.50154
## hallali 1.90177
## halle -3.66867
## hallebarde -3.57084
## hallier -3.02356
## hallstattien 0.96437
## halo -4.19705
## halte -4.20817
## haltère 2.66244
## hamada -2.94097
## Hambourg -3.81114
## hameau -4.71389
## hameçon 1.47962
## hammam -3.66294
## hamster -3.53569
## handicap -4.08589
## hangar -4.36808
## hanneton -3.18932
## Hanoï -2.35755
## haoussa -3.05605
## hapax 2.10377
## haranguer -2.19219
## harassement -2.02283
## harasser -1.39435
## harcèlement -4.23142
## harceler -3.09722
## hardi -3.57921
## hardiesse -4.76329
## hareng -3.08212
## haricot -3.83309
## haridelle -1.84517
## harle -1.95209
## harmattan 2.58251
## harmel -2.47434
## Harmel 0.14189
## harmonica 2.58131
## harmonie 1.05649
## harnachement -3.24035
## harnacher -1.10939
## harnois -3.19059
## haro -2.91667
## harpagon 3.01157
## harpe -4.59506
## hart -2.88297
## hasard -5.41993
## hasarder -2.88028
## hasardeuse -2.56223
## hasardeux -2.73530
## hase -3.56290
## haste -2.55517
## hâte -4.93658
## hâter -3.78325
## Hathor 0.49741
## haubert -3.30092
## hausse -3.82606
## haut -5.34782
## hautboïste -1.76383
## haute -5.83745
## Hauterive 0.17030
## hauterivien 2.13328
## Hauterivien 1.81309
## hauteur -5.56961
## Hautmont -0.73204
## havre -4.39937
## hazard -3.09751
## heaume -3.34039
## hebdo 3.17355
## hébergement 2.00879
## Hécate 0.95723
## hectare 1.63661
## hectolitre 2.14654
## Hector 3.13568
## hégélianisme 0.53038
## hégélien 1.85854
## hégémonie 0.95709
## Hélène 0.62641
## hélice 1.39762
## hélio 2.48481
## hélion 3.05228
## hélium 2.02232
## hélix 3.14379
## Héloïse 1.38388
## hématite 1.43941
## hémoglobine 1.13211
## henné -3.87635
## hennin -3.03772
## hennuyer -1.41976
## Henri -1.12030
## Henriette 0.41294
## henry -0.77530
## Henry -1.16198
## Héra 0.12930
## Héraclès 2.84212
## Héraclite 2.88475
## Hérault 1.12950
## héraut -3.80378
## herbe 1.10276
## Herbert -1.74527
## herbette 2.62594
## hercule 3.27467
## hérédité 1.11775
## hérésie 1.28224
## hérissant -1.33410
## hérisser -1.85024
## hérisson -3.29645
## héritage 1.63160
## héritier 2.12922
## hermandad -2.35393
## hermès 3.38805
## hermine 1.79014
## hermite 2.89549
## Hermite 2.67165
## hernie -4.30203
## Hérode 2.88032
## Hérodote 3.37763
## héroïne 1.16304
## héroïsme 2.12074
## héron -3.84958
## héros -5.31925
## herpès 2.50005
## hertz -2.80848
## Hervé -1.59697
## Herzégovine 1.20069
## hésiter 0.75554
## hesse -1.70834
## Hesse -4.14403
## hetman 1.09885
## hêtre -4.80175
## heur 2.07112
## heure 0.65967
## heureuse 1.23628
## heureux 1.88588
## heurt -3.41871
## heurter -3.48448
## hiatus -1.38486
## hibiscus 3.10429
## hibou -3.74010
## hickory 1.53526
## hideuse -2.94451
## hideux -3.38643
## hiérarchie -5.09399
## hiérarchisation -3.95129
## hiérarchiser -3.29760
## hiérarque -2.75761
## hiératisme -1.21999
## hiérogamie -0.58118
## hiéroglyphe -0.29311
## hiérogrammate 2.26696
## hiérophanie -1.71916
## hiérophante 1.08109
## hile -3.69882
## Himalaya 1.17470
## hindi -0.39295
## hindou 3.06525
## hinterland 1.80240
## hipparque 3.26132
## hippisme 1.57394
## hippo 3.35943
## Hippocrate 3.29066
## hirondelle 1.68149
## Hispaniola 1.01269
## histoire 0.44521
## histologie 1.28126
## historien 1.70426
## hitlérisme 2.09908
## hiver 1.76130
## hlm -1.99518
## hobereau -3.19252
## hoir 1.40070
## hoirie 1.66914
## Hokkaïdo -1.62560
## hollandais -3.13114
## hollandaise -2.69320
## hollande -1.96172
## holmium 2.28608
## holocauste 2.32113
## home -1.34371
## homélie 1.83412
## hommage 1.84298
## homme 0.81552
## homographie 1.71201
## Hongrie -4.78689
## hongrois -3.93742
## honnêteté 1.12021
## honneur 1.54025
## honnir -1.90284
## honorée 3.04619
## honorer 0.57890
## Honorine 1.11301
## honte -5.39774
## honteuse -3.93796
## honteux -3.56338
## hôpital 1.41554
## Horace 2.52649
## horizon 1.81161
## horloge 1.25485
## hornblende -3.23706
## horreur 0.94948
## hortensia 3.20895
## horticulture 1.13220
## Horus 2.55210
## hosanna 3.45944
## hospice 2.07655
## hospitalité 1.18800
## hospodar 0.69430
## hostilité 0.98979
## hôtel 1.38358
## hotte -4.23187
## hottentot -2.32222
## houblon -4.13273
## houille -4.79077
## houspiller -1.65355
## Houssaye -2.67500
## Hubert -1.60305
## huchet -2.34764
## Hudson 0.93888
## huguenot -2.81736
## huguenote -2.19977
## huguenotisme -0.71881
## Hugues -1.90992
## Huguet -1.72258
## Huguette -0.12896
## huilage 0.82283
## huile 0.94620
## huiler 0.04690
## huilerie 1.50299
## huileux 2.21631
## huilier 3.44064
## huis -1.68718
## huit -4.72459
## Hulot -2.05556
## humain -0.66271
## humaine 1.13064
## humanisme 1.89102
## humanité 0.79115
## humer -2.23513
## humeur 0.96512
## humidité 0.78035
## humiliation 1.18865
## humilier 0.83805
## humilité 1.12184
## humour 2.03857
## humus 2.17523
## hune -3.30803
## Huon -1.99026
## hurler -3.20283
## huron -2.65468
## huronien -1.25394
## hurricane -1.35586
## hussard -3.85179
## hussitisme -2.80258
## hyacinthe 1.32925
## hyalite 0.81747
## hyaloplasme -0.97974
## hydrate 2.27583
## hydro 2.58822
## hydrogène 1.64377
## hydrographie 1.35932
## hydrologie 1.29932
## hydrolyse 1.18153
## hyène -0.53442
## Hygie 1.29489
## hygiène 1.03058
## hyper 2.32579
## Hypérion 2.60070
## hypertrophie 1.18647
## hypothèque 1.35583
## hypothèse 0.81000
## iambe 1.83185
## Iéna 1.80603
## Iénisséi 2.34164
## iodate 2.95709
## iode 1.76400
## iodoforme 2.59348
## iodure 1.84038
## Ionie 1.51108
## ionisation 1.02853
## ionosphère 1.92435
## iota 0.10705
## Iowa 2.11501
## iule 1.17399
## oignon 2.42514
## oil 2.45779
## oille 0.46094
## oindre 1.10373
## oing 1.78488
## oint -0.08364
## Oise 1.06746
## oiseau 1.83992
## oison 3.35400
## onze -3.81962
## ouadi 0.41779
## Ouadi -0.90688
## oued 1.80133
## ouï -0.48206
## ouïr 0.91302
## ouistiti -1.45823
## ouolof -1.94655
## oye 1.98197
## Utica 2.09973
## yacht -4.49306
## yack -2.58996
## yang -3.51015
## yard -3.12323
## yatagan -2.75690
## Yémen -3.03316
## yen -4.19899
## yeuse 1.92918
## yoga -3.97894
## Yokohama -3.39922
## yole -3.53277
## Yonne 1.22757
## Yunnan -4.06532Histogram of random intercepts from logistic model:
hist(ranef(french4.glmer.type)$word2[,1], main="histogram of random intercepts", xlab="random intercept value",col="grey")
Which Word1s are significantly different?
Take a look at the results–which levels of Word1 are significantly different?
Anova(french4.glmer.type)## Analysis of Deviance Table (Type II Wald chisquare tests)
##
## Response: voculence
## Chisq Df Pr(>Chisq)
## word1 21.1 7 0.0036 **
## log(phrase_frequency) 19.9 1 8.3e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1french4.glmer.type.glht <- glht(french4.glmer.type, linfct = mcp(word1 = "Tukey"))
summary(french4.glmer.type.glht)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: glmer(formula = voculence ~ word1 + (1 | word2) + log(phrase_frequency),
## data = my_data, family = "binomial", start = getME(french3.glmer.type,
## c("theta", "fixef")))
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## beau_bel - au_àl == 0 2.4568 0.9309 2.64 0.123
## de_d - au_àl == 0 0.3090 0.4898 0.63 0.998
## du_del - au_àl == 0 -0.4875 0.4640 -1.05 0.959
## la_l - au_àl == 0 -0.1634 0.7021 -0.23 1.000
## le_l - au_àl == 0 -0.3680 0.5064 -0.73 0.995
## ma_mon - au_àl == 0 2.3977 0.8118 2.95 0.054 .
## vieux_vieil - au_àl == 0 1.7650 0.7627 2.31 0.255
## de_d - beau_bel == 0 -2.1478 0.9895 -2.17 0.335
## du_del - beau_bel == 0 -2.9443 0.9616 -3.06 0.039 *
## la_l - beau_bel == 0 -2.6202 1.1404 -2.30 0.264
## le_l - beau_bel == 0 -2.8248 1.0054 -2.81 0.080 .
## ma_mon - beau_bel == 0 -0.0591 1.0808 -0.05 1.000
## vieux_vieil - beau_bel == 0 -0.6918 0.9873 -0.70 0.996
## du_del - de_d == 0 -0.7964 0.4316 -1.85 0.550
## la_l - de_d == 0 -0.4724 0.5102 -0.93 0.980
## le_l - de_d == 0 -0.6769 0.4350 -1.56 0.746
## ma_mon - de_d == 0 2.0888 0.7580 2.76 0.092 .
## vieux_vieil - de_d == 0 1.4560 0.8136 1.79 0.589
## la_l - du_del == 0 0.3240 0.6454 0.50 1.000
## le_l - du_del == 0 0.1195 0.4502 0.27 1.000
## ma_mon - du_del == 0 2.8852 0.8236 3.50 <0.01 **
## vieux_vieil - du_del == 0 2.2524 0.7864 2.86 0.069 .
## le_l - la_l == 0 -0.2045 0.6353 -0.32 1.000
## ma_mon - la_l == 0 2.5612 0.8366 3.06 0.039 *
## vieux_vieil - la_l == 0 1.9284 0.9826 1.96 0.469
## ma_mon - le_l == 0 2.7657 0.8540 3.24 0.023 *
## vieux_vieil - le_l == 0 2.1329 0.8328 2.56 0.149
## vieux_vieil - ma_mon == 0 -0.6328 0.9535 -0.66 0.997
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)french4.glmer.type.glht.cld <- cld(french4.glmer.type.glht)
#plot(french4.glmer.type.glht)
#french.lmer.type.glht.confint <- confint(french.lmer.type.glht)Summary, taking absolute z value of 2.5 as cutoff:
- beau > au, du, le
- ma > au, de, du, la, le
- vieux > du, le
Or, using the 0.05 p-values that are now supplied (parentheses for 0.05
Plot the significantly different levels of Word1–Word1s with the same letter label at the top are not significantly different from each other.
opar <- par(mai=c(1,1,2,1))
plot(french4.glmer.type.glht.cld)
par(opar)
#sort(table(french$word1)) #just checking what all the levels are and how many items in eachCompare to SAS beta regression results:
- {beau, ma, vieux} > {au, le, du}
- ma > la
- de > {du, le}
Basically same three strata: beau/ma/vieux, au/de/la, du/le
Make the wug
Classify Word1s. Note that this is hard-coding the differences found above:
french["word1_group"] <- NA
for(i in 1:nrow(french)) {
if(french$word1[i] == "beau_bel" | french$word1[i] == "ma_mon" |
french$word1[i] == "vieux_vieil") {
french$word1_group[i] <- "A: beau/bel, ma/mon,\n vieux/vieil"
}
if(french$word1[i] == "au_àl" | french$word1[i] == "de_d" |
french$word1[i] == "la_l") {
french$word1_group[i] <- "B: au/à l', de/d', la/l'"
}
if(french$word1[i] == "du_del" | french$word1[i] == "le_l") {
french$word1_group[i] <- "C: du/de l', le/l'"
}
}Add in a column with random intercepts, from the non-beta regression model, for each word2, and a column for Word2’s aspiratedness rank:
french["aspire"] <- NA
counter <- 1
for(j in rownames(ranef(french4.glmer.type)$word2)) {
#print(j)
for(i in 1:nrow(french)) {
if(french$word2[i] == j) {
french$aspire[i] <- ranef(french4.glmer.type)$word2[,1][counter]
}
}
counter <- counter + 1
}
#Aspire-ness rank of each word2 (listed as a property of each phrase), binomial model
#We need to go down to 5 slices to get a decent number of Word2s in each slice.
french["aspire_rank_word"] <- NA
counter <- 1
for(j in rownames(ranef(french4.glmer.type)$word2)) {
#print(j)
for(i in 1:nrow(french)) {
if(french$word2[i] == j) {
french$aspire_rank_word[i] <- as.numeric(cut(ranef(french4.glmer.type)$word2[,1], breaks=5))[counter]
}
}
counter <- counter + 1
}
#table to show how many in each group
table(french$word1_group, french$aspire_rank_word)##
## 1 2 3 4 5
## A: beau/bel, ma/mon,\n vieux/vieil 33 18 9 42 50
## B: au/à l', de/d', la/l' 68 138 58 159 172
## C: du/de l', le/l' 36 98 46 40 151#what is the average alignancy rate in each aspire-rank group?
sort(tapply(french$voculence, french$aspire_rank_word, FUN=mean))## 1 2 3 4 5
## 0.01295 0.03090 0.33012 0.92409 0.96851Make an interaction plot–random intercepts from pseudo-logistic regression model:
par(mar=c(5,5,2,6))
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=voculence,
xlab="Word2 alignancy group",ylab="rate of non-alignment"
, trace.label="Word1 alignancy group", fixed=TRUE
,xpd=TRUE)
})
#Since this will appear in the paper, also do a PNG file:
png(file="Word2_Word1_interaction_plot.png",width=myResMultiplier*460,height=myResMultiplier*300, res=myResMultiplier*72, family=myFontFamily)
#par(mar=c(5,3,2,0)+0.1, mgp=c(2,1,0))
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=voculence,
xlab="Word2 alignancy group",ylab="rate of non-alignment"
, trace.label="Word1 alignancy group", fixed=TRUE)
})
dev.off()## pdf
## 2table(french$aspire_rank_word, french$word1_group) #shows how many Word2s in each bin##
## A: beau/bel, ma/mon,\n vieux/vieil B: au/à l', de/d', la/l'
## 1 33 68
## 2 18 138
## 3 9 58
## 4 42 159
## 5 50 172
##
## C: du/de l', le/l'
## 1 36
## 2 98
## 3 46
## 4 40
## 5 151List of the ranks:
french[,c("word2","aspire_rank_word")]## word2 aspire_rank_word
## 1 habeas 5
## 2 habeas 5
## 3 habeas 5
## 4 habeas 5
## 5 habeas 5
## 6 habileté 4
## 7 habileté 4
## 8 habileté 4
## 9 habileté 4
## 10 habileté 4
## 11 habileté 4
## 12 habilité 4
## 13 habilité 4
## 14 habilité 4
## 15 habilité 4
## 16 habilité 4
## 17 habiliter 4
## 18 habiliter 4
## 19 habiliter 4
## 20 habiliter 4
## 21 habiliter 4
## 22 habillement 5
## 23 habillement 5
## 24 habillement 5
## 25 habillement 5
## 26 habillement 5
## 27 habillement 5
## 28 habillement 5
## 29 habillement 5
## 30 habillement 5
## 31 habit 5
## 32 habit 5
## 33 habit 5
## 34 habit 5
## 35 habit 5
## 36 habit 5
## 37 habit 5
## 38 habit 5
## 39 habit 5
## 40 habit 5
## 41 habita NA
## 42 habita NA
## 43 habita NA
## 44 habitant 5
## 45 habitant 5
## 46 habitant 5
## 47 habitant 5
## 48 habitant 5
## 49 habitant 5
## 50 habitant 5
## 51 habitant 5
## 52 habitant 5
## 53 habitat 5
## 54 habitat 5
## 55 habitat 5
## 56 habitat 5
## 57 habitat 5
## 58 habitat 5
## 59 habitat 5
## 60 habitat 5
## 61 habitat 5
## 62 habitation 4
## 63 habitation 4
## 64 habitation 4
## 65 habitation 4
## 66 habitation 4
## 67 habitation 4
## 68 habite NA
## 69 habite NA
## 70 habite NA
## 71 habite NA
## 72 habite NA
## 73 habite NA
## 74 habité 5
## 75 habité 5
## 76 habité 5
## 77 habité 5
## 78 habité 5
## 79 habitent NA
## 80 habitent NA
## 81 habitent NA
## 82 habitent NA
## 83 habitent NA
## 84 habiter 4
## 85 habiter 4
## 86 habiter 4
## 87 habiter 4
## 88 habiter 4
## 89 habiter 4
## 90 habitude 4
## 91 habitude 4
## 92 habitude 4
## 93 habitude 4
## 94 habitude 4
## 95 habitude 4
## 96 habituel 5
## 97 habituel 5
## 98 habituel 5
## 99 habituel 5
## 100 habituel 5
## 101 habituel 5
## 102 habituelle 5
## 103 habituelle 5
## 104 habituelle 5
## 105 habituelle 5
## 106 habituelle 5
## 107 habituelle 5
## 108 habitus 5
## 109 habitus 5
## 110 habitus 5
## 111 habitus 5
## 112 habitus 5
## 113 habitus 5
## 114 habitus 5
## 115 hache 1
## 116 hache 1
## 117 hache 1
## 118 hache 1
## 119 hache 1
## 120 hache 1
## 121 hachette 2
## 122 hachette 2
## 123 hachette 2
## 124 hachette 2
## 125 hacienda 3
## 126 hacienda 3
## 127 hacienda 3
## 128 hacienda 3
## 129 haddock 2
## 130 haddock 2
## 131 haddock 2
## 132 Hadès 4
## 133 Hadès 4
## 134 Hadès 4
## 135 Hadès 4
## 136 Hadès 4
## 137 hadji 2
## 138 hadji 2
## 139 hadji 2
## 140 hadji 2
## 141 Hadrien 4
## 142 Hadrien 4
## 143 Hadrien 4
## 144 hagiographie 4
## 145 hagiographie 4
## 146 hagiographie 4
## 147 Haguenau 2
## 148 Haguenau 2
## 149 Haguenau 2
## 150 haie 1
## 151 haie 1
## 152 haie 1
## 153 haie 1
## 154 haie 1
## 155 haie 1
## 156 Hainaut 1
## 157 Hainaut 1
## 158 Hainaut 1
## 159 Hainaut 1
## 160 Hainaut 1
## 161 haine 1
## 162 haine 1
## 163 haine 1
## 164 haine 1
## 165 haine 1
## 166 haine 1
## 167 haïr 2
## 168 haïr 2
## 169 haïr 2
## 170 haïr 2
## 171 haïr 2
## 172 haïs NA
## 173 haïs NA
## 174 haïs NA
## 175 haïs NA
## 176 hait NA
## 177 hait NA
## 178 hait NA
## 179 hait NA
## 180 haïtien 5
## 181 haïtien 5
## 182 haïtien 5
## 183 haïtien 5
## 184 haïtienne 4
## 185 haïtienne 4
## 186 haleine 4
## 187 haleine 4
## 188 haleine 4
## 189 haleine 4
## 190 haleine 4
## 191 halètement 2
## 192 halètement 2
## 193 halètement 2
## 194 halètement 2
## 195 halètement 2
## 196 hall 1
## 197 hall 1
## 198 hall 1
## 199 hall 1
## 200 hall 1
## 201 hall 1
## 202 hall 1
## 203 hall 1
## 204 hallali 5
## 205 hallali 5
## 206 hallali 5
## 207 hallali 5
## 208 hallali 5
## 209 halle 2
## 210 halle 2
## 211 halle 2
## 212 halle 2
## 213 halle 2
## 214 hallebarde 2
## 215 hallebarde 2
## 216 hallebarde 2
## 217 hallebarde 2
## 218 hallier 2
## 219 hallier 2
## 220 hallier 2
## 221 hallier 2
## 222 hallier 2
## 223 hallstattien 4
## 224 hallstattien 4
## 225 halo 1
## 226 halo 1
## 227 halo 1
## 228 halo 1
## 229 halo 1
## 230 halo 1
## 231 halte 1
## 232 halte 1
## 233 halte 1
## 234 halte 1
## 235 halte 1
## 236 halte 1
## 237 haltère 5
## 238 haltère 5
## 239 haltère 5
## 240 hamada 2
## 241 hamada 2
## 242 Hambourg 2
## 243 Hambourg 2
## 244 Hambourg 2
## 245 Hambourg 2
## 246 Hambourg 2
## 247 hameau 1
## 248 hameau 1
## 249 hameau 1
## 250 hameau 1
## 251 hameau 1
## 252 hameau 1
## 253 hameau 1
## 254 hameau 1
## 255 hameau 1
## 256 hameçon 4
## 257 hameçon 4
## 258 hameçon 4
## 259 hameçon 4
## 260 hameçon 4
## 261 hammam 2
## 262 hammam 2
## 263 hammam 2
## 264 hammam 2
## 265 hammam 2
## 266 hamster 2
## 267 hamster 2
## 268 hamster 2
## 269 hamster 2
## 270 handicap 1
## 271 handicap 1
## 272 handicap 1
## 273 handicap 1
## 274 handicap 1
## 275 handicap 1
## 276 handicap 1
## 277 handicape NA
## 278 handicape NA
## 279 hangar 1
## 280 hangar 1
## 281 hangar 1
## 282 hangar 1
## 283 hangar 1
## 284 hangar 1
## 285 hangar 1
## 286 hangar 1
## 287 hanneton 2
## 288 hanneton 2
## 289 hanneton 2
## 290 hanneton 2
## 291 hanneton 2
## 292 Hanoï 2
## 293 Hanoï 2
## 294 Hanoï 2
## 295 Hanoï 2
## 296 haoussa 2
## 297 haoussa 2
## 298 haoussa 2
## 299 haoussa 2
## 300 hapax 5
## 301 hapax 5
## 302 hapax 5
## 303 hapax 5
## 304 haranguer 2
## 305 haranguer 2
## 306 haranguer 2
## 307 haranguer 2
## 308 harassement 3
## 309 harassement 3
## 310 harassement 3
## 311 harassement 3
## 312 harassement 3
## 313 harasser 3
## 314 harasser 3
## 315 harasser 3
## 316 harcèlement 1
## 317 harcèlement 1
## 318 harcèlement 1
## 319 harcèlement 1
## 320 harcèlement 1
## 321 harceler 2
## 322 harceler 2
## 323 harceler 2
## 324 harceler 2
## 325 hardi 2
## 326 hardi 2
## 327 hardi 2
## 328 hardi 2
## 329 hardi 2
## 330 hardi 2
## 331 hardi 2
## 332 hardiesse 1
## 333 hardiesse 1
## 334 hardiesse 1
## 335 hardiesse 1
## 336 hardiesse 1
## 337 hardiesse 1
## 338 hareng 2
## 339 hareng 2
## 340 hareng 2
## 341 hareng 2
## 342 hareng 2
## 343 hareng 2
## 344 hareng 2
## 345 haricot 2
## 346 haricot 2
## 347 haricot 2
## 348 haricot 2
## 349 haricot 2
## 350 haricot 2
## 351 haridelle 3
## 352 haridelle 3
## 353 haridelle 3
## 354 harle 3
## 355 harle 3
## 356 harmattan 5
## 357 harmattan 5
## 358 harmattan 5
## 359 harmattan 5
## 360 Harmel 4
## 361 harmel 2
## 362 harmel 2
## 363 harmel 2
## 364 Harmel 4
## 365 harmonica 5
## 366 harmonica 5
## 367 harmonica 5
## 368 harmonica 5
## 369 harmonica 5
## 370 harmonica 5
## 371 harmonie 4
## 372 harmonie 4
## 373 harmonie 4
## 374 harmonie 4
## 375 harmonie 4
## 376 harmonie 4
## 377 harnachement 2
## 378 harnachement 2
## 379 harnachement 2
## 380 harnachement 2
## 381 harnachement 2
## 382 harnachement 2
## 383 harnacher 3
## 384 harnacher 3
## 385 harnois 2
## 386 harnois 2
## 387 harnois 2
## 388 harnois 2
## 389 harnois 2
## 390 harnois 2
## 391 haro 2
## 392 haro 2
## 393 haro 2
## 394 haro 2
## 395 haro 2
## 396 harpagon 5
## 397 harpe 1
## 398 harpe 1
## 399 harpe 1
## 400 harpe 1
## 401 harpe 1
## 402 harpe 1
## 403 hart 2
## 404 hart 2
## 405 hasard 1
## 406 hasard 1
## 407 hasard 1
## 408 hasard 1
## 409 hasard 1
## 410 hasard 1
## 411 hasard 1
## 412 hasard 1
## 413 hasarde NA
## 414 hasarde NA
## 415 hasarde NA
## 416 hasarde NA
## 417 hasarde NA
## 418 hasarder 2
## 419 hasarder 2
## 420 hasarder 2
## 421 hasarder 2
## 422 hasarder 2
## 423 hasardeuse 2
## 424 hasardeuse 2
## 425 hasardeuse 2
## 426 hasardeuse 2
## 427 hasardeuse 2
## 428 hasardeux 2
## 429 hasardeux 2
## 430 hasardeux 2
## 431 hasardeux 2
## 432 hasardeux 2
## 433 hasardeux 2
## 434 hase 2
## 435 hase 2
## 436 hase 2
## 437 haste 2
## 438 haste 2
## 439 haste 2
## 440 hâte 1
## 441 hâte 1
## 442 hâte 1
## 443 hâte 1
## 444 hâte 1
## 445 hâte 1
## 446 hâte 1
## 447 hâte 1
## 448 hâte 1
## 449 hâte 1
## 450 hâter 2
## 451 hâter 2
## 452 hâter 2
## 453 hâter 2
## 454 hâter 2
## 455 Hathor 4
## 456 Hathor 4
## 457 haubert 2
## 458 haubert 2
## 459 haubert 2
## 460 haubert 2
## 461 haubert 2
## 462 hausse 2
## 463 hausse 2
## 464 hausse 2
## 465 hausse 2
## 466 hausse 2
## 467 hausse 2
## 468 hausse 2
## 469 hausse 2
## 470 hausse 2
## 471 hausse 2
## 472 haut 1
## 473 haut 1
## 474 haut 1
## 475 haut 1
## 476 haut 1
## 477 haut 1
## 478 haut 1
## 479 haut 1
## 480 haut 1
## 481 hautboïste 3
## 482 hautboïste 3
## 483 haute 1
## 484 haute 1
## 485 haute 1
## 486 haute 1
## 487 haute 1
## 488 haute 1
## 489 Hauterive 4
## 490 Hauterive 4
## 491 hauterivien 5
## 492 Hauterivien 5
## 493 Hauterivien 5
## 494 hauterivien 5
## 495 Hauterivien 5
## 496 Hauterivien 5
## 497 hauteur 1
## 498 hauteur 1
## 499 hauteur 1
## 500 hauteur 1
## 501 hauteur 1
## 502 hauteur 1
## 503 Hautmont 3
## 504 Hautmont 3
## 505 havre 1
## 506 havre 1
## 507 havre 1
## 508 havre 1
## 509 havre 1
## 510 havre 1
## 511 havre 1
## 512 havre 1
## 513 havre 1
## 514 hazard 2
## 515 hazard 2
## 516 hazard 2
## 517 hazard 2
## 518 hazard 2
## 519 heaume 2
## 520 heaume 2
## 521 heaume 2
## 522 heaume 2
## 523 heaume 2
## 524 hebdo 5
## 525 hebdo 5
## 526 hebdo 5
## 527 hebdo 5
## 528 hebdo 5
## 529 hebdo 5
## 530 hébergement 5
## 531 hébergement 5
## 532 hébergement 5
## 533 hébergement 5
## 534 hébergement 5
## 535 hébergement 5
## 536 Hécate 4
## 537 Hécate 4
## 538 hectare 5
## 539 hectare 5
## 540 hectare 5
## 541 hectare 5
## 542 hectare 5
## 543 hectare 5
## 544 hectolitre 5
## 545 hectolitre 5
## 546 hectolitre 5
## 547 hectolitre 5
## 548 hectolitre 5
## 549 Hector 5
## 550 Hector 5
## 551 Hector 5
## 552 Hector 5
## 553 Hector 5
## 554 Hector 5
## 555 Hector 5
## 556 hégélianisme 4
## 557 hégélianisme 4
## 558 hégélianisme 4
## 559 hégélianisme 4
## 560 hégélianisme 4
## 561 hégélianisme 4
## 562 hégélien 5
## 563 hégélien 5
## 564 hégélien 5
## 565 hégélien 5
## 566 hégélien 5
## 567 hégélien 5
## 568 hégélien 5
## 569 hégémonie 4
## 570 hégémonie 4
## 571 hégémonie 4
## 572 hégémonie 4
## 573 Hélène 4
## 574 Hélène 4
## 575 Hélène 4
## 576 Hélène 4
## 577 Hélène 4
## 578 hélice 4
## 579 hélice 4
## 580 hélice 4
## 581 hélice 4
## 582 hélio 5
## 583 hélio 5
## 584 hélion 5
## 585 hélion 5
## 586 hélium 5
## 587 hélium 5
## 588 hélium 5
## 589 hélium 5
## 590 hélium 5
## 591 hélix 5
## 592 hélix 5
## 593 hélix 5
## 594 hélix 5
## 595 Héloïse 4
## 596 Héloïse 4
## 597 Héloïse 4
## 598 Héloïse 4
## 599 hématite 4
## 600 hématite 4
## 601 hémoglobine 4
## 602 hémoglobine 4
## 603 hémoglobine 4
## 604 henné 2
## 605 henné 2
## 606 henné 2
## 607 henné 2
## 608 henné 2
## 609 hennin 2
## 610 hennin 2
## 611 hennin 2
## 612 hennin 2
## 613 hennuyer 3
## 614 Henri 3
## 615 Henri 3
## 616 Henri 3
## 617 Henri 3
## 618 Henri 3
## 619 Henri 3
## 620 Henri 3
## 621 Henri 3
## 622 Henriette 4
## 623 Henriette 4
## 624 Henriette 4
## 625 Henriette 4
## 626 Henriette 4
## 627 henry 3
## 628 Henry 3
## 629 Henry 3
## 630 Henry 3
## 631 Henry 3
## 632 henry 3
## 633 Henry 3
## 634 Henry 3
## 635 Henry 3
## 636 Henry 3
## 637 Héra 4
## 638 Héra 4
## 639 Héraclès 5
## 640 Héraclès 5
## 641 Héraclès 5
## 642 Héraclès 5
## 643 Héraclès 5
## 644 Héraclès 5
## 645 Héraclite 5
## 646 Héraclite 5
## 647 Héraclite 5
## 648 Héraclite 5
## 649 Héraclite 5
## 650 Hérault 4
## 651 Hérault 4
## 652 Hérault 4
## 653 Hérault 4
## 654 Hérault 4
## 655 Hérault 4
## 656 héraut 2
## 657 héraut 2
## 658 héraut 2
## 659 héraut 2
## 660 héraut 2
## 661 héraut 2
## 662 héraut 2
## 663 herbe 4
## 664 herbe 4
## 665 herbe 4
## 666 herbe 4
## 667 herbe 4
## 668 herbe 4
## 669 herbe 4
## 670 herbe 4
## 671 herbe 4
## 672 Herbert 3
## 673 Herbert 3
## 674 Herbert 3
## 675 Herbert 3
## 676 herbette 5
## 677 herbette 5
## 678 hercule 5
## 679 hercule 5
## 680 hercule 5
## 681 hercule 5
## 682 hercule 5
## 683 hérédité 4
## 684 hérédité 4
## 685 hérédité 4
## 686 hérédité 4
## 687 hérédité 4
## 688 hérédité 4
## 689 hérésie 4
## 690 hérésie 4
## 691 hérésie 4
## 692 hérésie 4
## 693 hérésie 4
## 694 hérésie 4
## 695 hérissant 3
## 696 hérissant 3
## 697 hérisse NA
## 698 hérisse NA
## 699 hérisse NA
## 700 hérisse NA
## 701 hérissent NA
## 702 hérissent NA
## 703 hérissent NA
## 704 hérissent NA
## 705 hérisser 3
## 706 hérisser 3
## 707 hérisser 3
## 708 hérisser 3
## 709 hérisson 2
## 710 hérisson 2
## 711 hérisson 2
## 712 hérisson 2
## 713 hérisson 2
## 714 hérisson 2
## 715 héritage 5
## 716 héritage 5
## 717 héritage 5
## 718 héritage 5
## 719 héritage 5
## 720 héritage 5
## 721 héritage 5
## 722 héritage 5
## 723 héritage 5
## 724 héritier 5
## 725 héritier 5
## 726 héritier 5
## 727 héritier 5
## 728 héritier 5
## 729 héritier 5
## 730 héritier 5
## 731 héritier 5
## 732 héritier 5
## 733 hermandad 2
## 734 hermandad 2
## 735 hermès 5
## 736 hermès 5
## 737 hermès 5
## 738 hermès 5
## 739 hermès 5
## 740 hermine 5
## 741 hermine 5
## 742 hermine 5
## 743 hermine 5
## 744 Hermite 5
## 745 Hermite 5
## 746 hermite 5
## 747 Hermite 5
## 748 hermite 5
## 749 hermite 5
## 750 hermite 5
## 751 Hermite 5
## 752 hermite 5
## 753 hermite 5
## 754 hernie 1
## 755 hernie 1
## 756 hernie 1
## 757 hernie 1
## 758 hernie 1
## 759 hernie 1
## 760 Hérode 5
## 761 Hérode 5
## 762 Hérode 5
## 763 Hérode 5
## 764 Hérode 5
## 765 Hérode 5
## 766 Hérodote 5
## 767 Hérodote 5
## 768 Hérodote 5
## 769 Hérodote 5
## 770 Hérodote 5
## 771 Hérodote 5
## 772 Hérodote 5
## 773 héroïne 4
## 774 héroïne 4
## 775 héroïne 4
## 776 héroïne 4
## 777 héroïne 4
## 778 héroïne 4
## 779 héroïsme 5
## 780 héroïsme 5
## 781 héroïsme 5
## 782 héroïsme 5
## 783 héroïsme 5
## 784 héroïsme 5
## 785 héroïsme 5
## 786 héroïsme 5
## 787 héroïsme 5
## 788 héroïsme 5
## 789 héron 2
## 790 héron 2
## 791 héron 2
## 792 héron 2
## 793 héron 2
## 794 héron 2
## 795 héros 1
## 796 héros 1
## 797 héros 1
## 798 héros 1
## 799 héros 1
## 800 héros 1
## 801 héros 1
## 802 héros 1
## 803 héros 1
## 804 herpès 5
## 805 herpès 5
## 806 herpès 5
## 807 herpès 5
## 808 herpès 5
## 809 hertz 2
## 810 hertz 2
## 811 hertz 2
## 812 Hervé 3
## 813 Hervé 3
## 814 Hervé 3
## 815 Hervé 3
## 816 Herzégovine 4
## 817 Herzégovine 4
## 818 hésite NA
## 819 hésite NA
## 820 hésite NA
## 821 hésiter 4
## 822 hésiter 4
## 823 hésiter 4
## 824 hesse 3
## 825 Hesse 1
## 826 Hesse 1
## 827 Hesse 1
## 828 hetman 4
## 829 hetman 4
## 830 hetman 4
## 831 hetman 4
## 832 hetman 4
## 833 hetman 4
## 834 hetman 4
## 835 hêtre 1
## 836 hêtre 1
## 837 hêtre 1
## 838 hêtre 1
## 839 hêtre 1
## 840 hêtre 1
## 841 hêtre 1
## 842 hêtre 1
## 843 heur 5
## 844 heur 5
## 845 heur 5
## 846 heur 5
## 847 heur 5
## 848 heur 5
## 849 heure 4
## 850 heure 4
## 851 heure 4
## 852 heure 4
## 853 heure 4
## 854 heure 4
## 855 heureuse 4
## 856 heureuse 4
## 857 heureuse 4
## 858 heureuse 4
## 859 heureuse 4
## 860 heureuse 4
## 861 heureux 5
## 862 heureux 5
## 863 heureux 5
## 864 heureux 5
## 865 heureux 5
## 866 heureux 5
## 867 heureux 5
## 868 heureux 5
## 869 heureux 5
## 870 heurt 2
## 871 heurt 2
## 872 heurt 2
## 873 heurt 2
## 874 heurt 2
## 875 heurt 2
## 876 heurter 2
## 877 heurter 2
## 878 heurter 2
## 879 heurter 2
## 880 heurter 2
## 881 heurter 2
## 882 hiatus 3
## 883 hiatus 3
## 884 hiatus 3
## 885 hiatus 3
## 886 hiatus 3
## 887 hiatus 3
## 888 hibiscus 5
## 889 hibiscus 5
## 890 hibiscus 5
## 891 hibiscus 5
## 892 hibiscus 5
## 893 hibou 2
## 894 hibou 2
## 895 hibou 2
## 896 hibou 2
## 897 hibou 2
## 898 hibou 2
## 899 hickory 4
## 900 hickory 4
## 901 hideuse 2
## 902 hideuse 2
## 903 hideuse 2
## 904 hideuse 2
## 905 hideuse 2
## 906 hideux 2
## 907 hideux 2
## 908 hideux 2
## 909 hideux 2
## 910 hideux 2
## 911 hideux 2
## 912 hiérarchie 1
## 913 hiérarchie 1
## 914 hiérarchie 1
## 915 hiérarchie 1
## 916 hiérarchie 1
## 917 hiérarchie 1
## 918 hiérarchisation 2
## 919 hiérarchisation 2
## 920 hiérarchisation 2
## 921 hiérarchiser 2
## 922 hiérarchiser 2
## 923 hiérarchiser 2
## 924 hiérarque 2
## 925 hiérarque 2
## 926 hiérarque 2
## 927 hiérarque 2
## 928 hiérarque 2
## 929 hiératisme 3
## 930 hiératisme 3
## 931 hiératisme 3
## 932 hiératisme 3
## 933 hiératisme 3
## 934 hiérogamie 3
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## 1219 hosanna 5
## 1220 hosanna 5
## 1221 hosanna 5
## 1222 hospice 5
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## 1224 hospice 5
## 1225 hospice 5
## 1226 hospice 5
## 1227 hospice 5
## 1228 hospice 5
## 1229 hospice 5
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## 1249 hôtel 4
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## 1253 hôtel 4
## 1254 hôtel 4
## 1255 hôtel 4
## 1256 hôtel 4
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## 1401 humiliât NA
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## 1474 hyaloplasme 3
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## 1501 hydrologie 4
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## 1503 hydrolyse 4
## 1504 hydrolyse 4
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## 1506 hydrolyse 4
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## 1508 hyène 3
## 1509 hyène 3
## 1510 Hygie 4
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## 1513 hygiène 4
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## 1515 hygiène 4
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## 1518 hyper 5
## 1519 hyper 5
## 1520 hyper 5
## 1521 hyper 5
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## 1523 Hypérion 5
## 1524 Hypérion 5
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## 1529 hypothèque 4
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## 1531 hypothèque 4
## 1532 hypothèque 4
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## 1534 hypothèque 4
## 1535 hypothèque 4
## 1536 hypothèque 4
## 1537 hypothèque 4
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## 1545 iambe 5
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## 1552 Iénisséi 5
## 1553 Iénisséi 5
## 1554 Iénisséi 5
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## 1556 iodate 5
## 1557 iodate 5
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## 1562 iode 5
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## 1573 iodure 5
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## 1575 iodure 5
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## 1577 Ionie 4
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## 1580 ionisation 4
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## 1584 iota 4
## 1585 iota 4
## 1586 iota 4
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## 1588 Iowa 5
## 1589 Iowa 5
## 1590 Iowa 5
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## 1592 iule 4
## 1593 iule 4
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## 1611 oing 5
## 1612 oing 5
## 1613 oing 5
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## 1615 oint 4
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## 1617 oint 4
## 1618 oint 4
## 1619 oint 4
## 1620 oint 4
## 1621 oint 4
## 1622 oint 4
## 1623 oint 4
## 1624 Oise 4
## 1625 Oise 4
## 1626 oiseau 5
## 1627 oiseau 5
## 1628 oiseau 5
## 1629 oiseau 5
## 1630 oiseau 5
## 1631 oiseau 5
## 1632 oiseau 5
## 1633 oiseau 5
## 1634 oiseau 5
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## 1636 oison 5
## 1637 oison 5
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## 1648 Ouadi 3
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## 1651 Ouadi 3
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## 1653 Ouadi 3
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## 1703 yard 2
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## 1710 Yémen 2
## 1711 Yémen 2
## 1712 Yémen 2
## 1713 Yémen 2
## 1714 yen 1
## 1715 yen 1
## 1716 yen 1
## 1717 yen 1
## 1718 yen 1
## 1719 yen 1
## 1720 yen 1
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## 1722 yeuse 5
## 1723 yoga 1
## 1724 yoga 1
## 1725 yoga 1
## 1726 yoga 1
## 1727 yoga 1
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## 1729 Yokohama 2
## 1730 Yokohama 2
## 1731 yole 2
## 1732 yole 2
## 1733 yole 2
## 1734 yole 2
## 1735 Yonne 4
## 1736 Yonne 4
## 1737 Yunnan 1
## 1738 Yunnan 1
## 1739 Yunnan 1
## 1740 Yunnan 1
## 1741 Yunnan 1Preliminaries to fitting grammar models
For the 8 word1s examined above, and the 5 word2 categories, make a table of V and C token-weighted type counts, by summing (not averaging) voculences, and also summing (1-voculence)s:
#Get the target subset
mySubset <-subset(french,french$word1 == "au_àl" | french$word1 == "beau_bel" | french$word1 == "de_d" | french$word1 == "du_del" | french$word1 == "la_l" | french$word1 == "le_l" | french$word1 == "ma_mon" | french$word1 == "vieux_vieil" )
#Get rid of unused levels
mySubset$word1 <- factor(mySubset$word1)
#Make table for this subset
v_counts_subset <- tapply(mySubset$voculence, list(mySubset$word1, mySubset$aspire_rank_word), FUN=sum, na.rm=TRUE)
c_counts_subset <- tapply((1-mySubset$voculence), list(mySubset$word1, mySubset$aspire_rank_word), FUN=sum, na.rm=TRUE)
v_and_c_table_subset <- cbind(as.data.frame.table(v_counts_subset),as.data.frame.table(c_counts_subset))
colnames(v_and_c_table_subset) <- c("word1", "word2_group", "v_count", "word1_dup", "word2_group_dup", "c_count")Multiplicative model
One of the models to fit to the data is a multiplicative model: give each Word1 a probability of creating a configuration compatible with resyllabification/unaspiratedness, and give each Word2 a probability of behaving as unaspirated, if it’s in the right configuration. The probability of Word1+Word2 combination behaving as unaspirated is then the product of those two probabilities (hence, ‘multiplicative’). The problem is that a model like this can create a pinch only at one end, resulting in a “claw” shape rather than a “wug” shape (Dustin Bowers’s term).
Fit the optimal probabilities:
myMultiplicative <- function(x) { #define the error function that is to be minimized
#log likelihood
log_likelihood <- 0
for (i in 1:8) { #loop over word1s
for(j in 1:5) { #loop over word2 groups
#increment log likelihood by (token-weighted) number of V items times the log of their probability, plus (token-weighted) number of C items items log of their probability
log_likelihood <- log_likelihood + v_and_c_table_subset[i+8*(j-1),3]*log(x[i]*x[8+j]) + v_and_c_table_subset[i+8*(j-1),6]*log(1-(x[i]*x[8+j])) #This is rather fiddly. The idea is that x[1:8] are the probabilities for the Word1s, and x[9:13] are the probabilities for the Word2 groups. We're using the loops to step through the rows of v_and_c_table_subset
}
}
return(-1*log_likelihood) #by default optim() minimizes, so we minimize the negative log likelihood (that is, get log likelihood as close to zero as possible)
}
#run the optimizer
myOptimization <- optim(par=c(0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5, 0.5,0.5,0.5,0.5,0.5), fn=myMultiplicative, lower=0.000001, upper=1-0.000001, method="L-BFGS-B") #we have to keep the parameters away from actual 0 and 1 or else undefined log()s will result and an error is thrown
#view the parameters
myOptimization$par## [1] 0.995604 0.999999 0.982975 0.967096 0.995730 0.960713 0.999999
## [8] 0.955863 0.005954 0.027870 0.340271 0.937182 0.999999#get the log likelihood
-1*myOptimization$value## [1] -207.9Take a look at the resulting model:
#make a matrix of predicted probabilities
multVector <- c()
for (i in 1:8) {
for (j in 9:13) {
multVector <- c(multVector,myOptimization$par[i]*myOptimization$par[j])
}
}
multMatrix <- matrix(multVector, nrow=8, ncol=5, byrow=TRUE)
#put it in a matrix, and fix the column names and levels of word1 and word2Group
multDataFrame <- as.data.frame.table(multMatrix)
colnames(multDataFrame) <- c("word1","word2Group", "multiplicativePrediction")
levels(multDataFrame$word1) <- c("au_àl", "beau_bel", "de_d", "du_del", "la_l","le_l","ma_mon", "vieux_vieil")
levels(multDataFrame$word2Group) <- c(1,2,3,4,5)
#make an interaction plot
interaction.plot(x.factor=multDataFrame$word2Group, trace.factor=multDataFrame$word1, response=multDataFrame$multiplicativePrediction, main="Fitted multiplicative model", xlab="Word2 unaspiratedness group",ylab="rate of non-alignment", trace.label="Word1 group", fixed=TRUE, xaxt="n")
axis(1, at=1:5, labels=1:5)
Make an interaction plot that groups the Word1s into three groups (one can’t just take the average, because each Word1 occurs with a different number of Word2s in each group). To do this, add a new column to the french dataframe that contains the multiplicative model’s prediction, then make an interaction plot on that new variable:
#initialize new column
french$multiplicativePrediction <- NA
#look up values
for (i in 1:length(french$word1)) {
#get the value; we need to use as.character() because "word1" has more levels in the full "french" data frame than in the "maxEntPredictions" data frame.
multiplicativeValue <- multDataFrame$multiplicativePrediction[as.character(multDataFrame$word1)==as.character(french$word1[i]) & multDataFrame$word2Group==french$aspire_rank_word[i]]
#use it if it's not NA
if(is.na(multiplicativeValue[1])==FALSE) { #use just first element of maxEntValue, to avoid throwing warning when maxEntValue is vector of NAs, e.g. c(NA,NA,NA); when it's not NA, it will be a single number
french$multiplicativePrediction[i] <- multiplicativeValue
}
}
#Make interaction plot as before:
par(mar=c(5,5,3,6))
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=multiplicativePrediction,
xlab="Word2 alignancy group",ylab="Decision tree predicted rate of non-alignment"
, trace.label="Word1 group", fixed=TRUE)
})
#Since this will appear in the paper, also do a PNG file:
png(file="multiplicative_predictions_plot.png",width=myResMultiplier*460,height=myResMultiplier*300, res=myResMultiplier*72, family=myFontFamily)
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=multiplicativePrediction,
xlab="Word2 alignancy group",ylab="Decision tree predicted rate of non-alignment"
, trace.label="Word1 group", fixed=TRUE)
})
dev.off()## pdf
## 2Making OTSoft input file
To aid reproducibility and record-keeping, we generate an OTSoft input file automatically from this script.
Print first two rows (constraint names):
write(c("\t\t\tAlign_1\tAlign_2\tAlign_3\tAlign_4\tAlign_5\tNoHiatus\tUseAu\tUseBeau\tUseDe\tUseDu\tUseLa\tUseLe\tUseMa\tUseVieux","\t\t\tAlign_1\tAlign_2\tAlign_3\tAlign_4\tAlign_5\tNoHiatus\tUseAu\tUseBeau\tUseDe\tUseDu\tUseLa\tUseLe\tUseMa\tUseVieux"), file="French_for_OTSoft_targetWord1sOnly.txt",append=FALSE) #overwrite anything there alreadyA function to turn each word1 into a number (will be usedful in following code chunk). This works because the order of Use constraints is alphabetical, as is the order of word1 levels in the data frame v_and_c_table.
#Yes, I know I could make this more general by making the table another input argument to the function, but I didn't bother. It's a little different for each output-file format, so it's probably best to do this afresh for each model below.
word1_to_num_subset <- function(myString) {
for(i in 1:length(levels(v_and_c_table_subset$word1))) {
if(myString==levels(v_and_c_table_subset$word1)[i]) {
return(i)
}
}
}Print each row of v_and_c_table_subset as two tableau rows
for(i in 1:dim(v_and_c_table_subset)[1]) {
#don't use this row if it has NAs
if(is.na(v_and_c_table_subset$v_count[i])==FALSE) {
#put together the input string
myInput <- paste(v_and_c_table_subset$word1[i],"+","group_",v_and_c_table_subset$word2_group[i],sep="")
#get the violation vector for the "voculent" (unaspirated) candidate
#one violation of Align and one of UseX
voc_violations <- rep(0,14) #initialize to all zeros--note that there are only 14 now
voc_violations[as.numeric(v_and_c_table_subset$word2_group[i])] <- 1 # add 1 for the Align constraint
voc_violations[word1_to_num_subset(v_and_c_table_subset$word1[i])+6] <- 1 #add 6: 5 for the Align constraints and 1 for NoHiatus; substitute 1 violation for the relevant UseX constraint
voc_violations <- paste(as.character(voc_violations),collapse="\t")
#get the violation vector for the "consulent" (aspirated) candidate
#just a violation of NoHiatus (#6 constraint)
cons_violations <- rep(0,14) #initialize to all zeros
cons_violations[6] <- 1
cons_violations <- paste(as.character(cons_violations),collapse="\t")
write(c(paste(myInput,"voculent",v_and_c_table_subset$v_count[i],voc_violations,sep="\t"),paste("","consulent",v_and_c_table_subset$c_count[i],cons_violations,sep="\t")),file="French_for_OTSoft_targetWord1sOnly.txt",append=TRUE)
}
}
#While the above produces an output file that *looks* fine, and that the MaxEnt Grammar Tool has no problem with, OTSoft ignores its last line for some reason. This seems to fix the problem:
write(c("\t\t\t\t\t\t\t\t\t"),file="French_for_OTSoft_targetWord1sOnly.txt",append=TRUE)
##BUT! The line with the tabs has to be removed in order to run Bruce's multifold GLA program, or else it acts as an additional candidate (with no constraint violations, so always wins)Constraint models
Outside of this script, the resulting file French_for_OTSoft_targetWord1sOnly.txt (moved to folder \\French\OTModels_new is then used as input for a few constraint models. (With some easy modifications, we could also use French_for_OTSoft.txt if we wanted, but I decided it makes more sense to fit the model just to the data that we’re talking about in the empirical section.)
MaxEnt
The MaxEnt Grammar Tool (http://www.linguistics.ucla.edu/people/hayes/MaxentGrammarTool/), is used, with default settings. In particular, we use the default values of mu and sigma for every constrain(mu=0, sigma=10000). The large sigma means that, in effect, there no regularization/smoothing/prior–just as close a fit as possible. The output file is named French_for_OTSoft_targetWord1sOnly_MaxEnt_output.txt.
Read in the MaxEnt output file:
conn <- file("French_for_OTSoft_targetWord1sOnly_MaxEnt_output.txt",open="r")
maxEntLines <- readLines(conn)
close(conn)Find and parse the lines at end that give probabilities for candidates:
#Initialize data frame
maxEntPredictions <- data.frame(word1=character(0), word2Group=character(0), unaspProb = numeric(0))
#Define function to find the header row for this part
getHeaderRowIndex <- function() {
for(i in 1:length(maxEntLines)) {
if(maxEntLines[i]=="Input:\tCandidate:\tObserved:\tPredicted:") {
return(i)
}
}
}
#Use the function to see where to start for loop
headerRowIndex <- getHeaderRowIndex()
for(i in headerRowIndex:length(maxEntLines)){
#split into columns
lineParts <- strsplit(maxEntLines[i],split="\t")
#Don't bother proceeding futher if it's a "consulent" candidate line
if(lineParts[[1]][2]=="voculent") {
#extract word1, word2 group, and probability of unaspirated ("voculent") candidate
myWord1 <- strsplit(lineParts[[1]][1],split="+",fixed=TRUE)[[1]][1]
myGroup <- str_sub(lineParts[[1]][1],-1)
myVoculenceProbability <- as.numeric(lineParts[[1]][4])
#add to data frame
maxEntPredictions <- rbind(maxEntPredictions,data.frame(word1=myWord1,word2Group=myGroup,unaspProb=myVoculenceProbability))
}
}Make an interaction plot:
par(mar=c(5,5,2,6))
with(maxEntPredictions, {
interaction.plot(x.factor=as.factor(maxEntPredictions$word2Group),
trace.factor=factor(word1),
response=unaspProb,
xlab="Word2 unaspiratedness group",ylab="rate of behaving as if Word2 is unaspirated"
, trace.label="Word1 group", fixed=TRUE, main="MaxEnt model")
})
To match the presentation of the observed data, we want to group these word1s into groups A, B, and C as before for the observed data. But, we can’t just take averages over all the word1s in a group, because in the original interaction plot of the observed data, average rate is weighted by number of items in that cell. In other words, if there are a lot more beau than vieux that occur with Group2 word2s, then beau contributes more heavily to the Group A+Group 2 average unaspiratedness rate. So instead we add MaxEnt prediction as a column to the main data frame, and plot it in the same way as the observed probabilities.
Add a column to french that is MaxEnt predicted prob:
#initialize new column
french$MaxEntPrediction <- NA
#look up values
for (i in 1:length(french$word1)) {
#get the value; we need to use as.character() because "word1" has more levels in the full "french" data frame than in the "maxEntPredictions" data frame.
maxEntValue <- maxEntPredictions$unaspProb[as.character(maxEntPredictions$word1)==as.character(french$word1[i]) & maxEntPredictions$word2Group==french$aspire_rank_word[i]]
#use it if it's not NA
if(is.na(maxEntValue[1])==FALSE) { #use just first element of maxEntValue, to avoid throwing warning when maxEntValue is vector of NAs, e.g. c(NA,NA,NA); when it's not NA, it will be a single number
french$MaxEntPrediction[i] <- maxEntValue
}
}Make interaction plot as before:
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=MaxEntPrediction,
xlab="Word2 alignancy group",ylab="MaxEnt predicted rate of non-alignment"
, trace.label="Word1 alignancy group", fixed=TRUE)
})
#Since this will appear in the paper, also do a PNG file:
png(file="MaxEnt_predictions_plot.png",width=myResMultiplier*460,height=myResMultiplier*300, res=myResMultiplier*72, family=myFontFamily)
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=MaxEntPrediction,
xlab="Word2 alignancy group",ylab="MaxEnt predicted rate of non-alignment"
, trace.label="Word1 alignancy group", fixed=TRUE)
})
dev.off()## pdf
## 2Get a table of constraint names and weights:
#Initialize data frame
maxEntGrammar <- data.frame(constraintName=character(0), constraintWeight = numeric(0))
#Define function to find the header row for this part
getConstraintHeaderRowIndex <- function() {
for(i in 1:length(maxEntLines)) {
if(maxEntLines[i]=="|weights| after optimization:") {
return(i)
}
}
}
#Use the function to see where to start for loop
constraintHeaderRowIndex <- getConstraintHeaderRowIndex()
#Extract names and weights and add to data frame
for(i in (constraintHeaderRowIndex+1):(headerRowIndex-1)){
lineParts <- strsplit(maxEntLines[i],split="\t")
myConstraintName <- strsplit(lineParts[[1]][1],split=" ")[[1]][1]
myConstraintWeight <- lineParts[[1]][2]
maxEntGrammar <- rbind(maxEntGrammar,data.frame(constraintName=myConstraintName, constraintWeight=myConstraintWeight))
}
#Print to console, for pasting into Word document
maxEntGrammar## constraintName constraintWeight
## 1 Align_1 10.131961658471631
## 2 Align_2 8.008200752338379
## 3 Align_3 4.950545256495552
## 4 Align_4 2.0633383837085844
## 5 Align_5 0.0
## 6 NoHiatus 6.198762474587922
## 7 UseAu 2.260387406596071
## 8 UseBeau 0.2826195950363789
## 9 UseDe 1.5600878659640336
## 10 UseDu 2.7769451224452797
## 11 UseLa 1.3403914301234388
## 12 UseLe 2.5436458101675825
## 13 UseMa 0.0
## 14 UseVieux 0.8793520626192605Noisy Harmonic Grammar
We use OTSoft (http://www.linguistics.ucla.edu/people/hayes/otsoft/) to fit a Noisy Harmonic Grammar model using the Gradual Learning Algorithm. Default options were used everywhere:
- number of times to run learning: 10,000,000
- apply noise by tableau cell not constraint? NO
- apply noise after multiplication of weights by violation? NO
- Allow constraint weights to go negative? NO
- initial plasticity: 0.01 (used to be 2, but we reduced it to get smaller weights)
- final plasticity: 0.001
- number of times to test grammar: 1,000,000
- default initial rankings (all same)
The only non-default option is that in the main screen, Options > Sort candiates in tableaux by harmony is turned off, to make dealing with the OTSoft output, below, easier.
Read in the Noisy HG output file:
conn <- file("French_for_OTSoft_targetWord1sOnlyTabbedOutput_NHG.txt",open="r")
NHGLines <- readLines(conn)
close(conn)Find and parse the lines at end that give probabilities for candidates–we need to find the third line that starts with " 1 " :
#Initialize data frame
NHGPredictions <- data.frame(word1=character(0), word2Group=character(0), unaspProb = numeric(0))
#Define function to find the header row for this part
howManyTimes1Seen <- 0 #initialize counter
getNHGStartingRowIndex <- function() {
for(i in 1:length(NHGLines)) {
if(str_sub(NHGLines[i],1,4)==" 1 \t") {
howManyTimes1Seen <- howManyTimes1Seen + 1
if(howManyTimes1Seen==3) {
return(i) #once we hit the third one, return the index
}
}
}
}
#Use the function to see where to start for loop
startingRowIndex <- getNHGStartingRowIndex()
for(i in startingRowIndex:length(NHGLines)){
#split into columns
lineParts <- strsplit(NHGLines[i],split="\t")
#extract word1, word2 group, and probability of unaspirated ("voculent") candidate
myWord1 <- strsplit(lineParts[[1]][2],split="+",fixed=TRUE)[[1]][1]
myGroup <- str_sub(lineParts[[1]][2],-1)
#different lines have candidates in different orders
if(lineParts[[1]][4]=="consulent") {
myVoculenceProbability <- 1 - as.numeric(lineParts[[1]][7])/1000000
}
else if(lineParts[[1]][4]=="voculent") {
myVoculenceProbability <- as.numeric(lineParts[[1]][7])/1000000
}
#add to data frame
NHGPredictions <- rbind(NHGPredictions,data.frame(word1=myWord1,word2Group=myGroup,unaspProb=myVoculenceProbability))
}Make an interaction plot:
par(mar=c(5,5,2,6))
with(NHGPredictions, {
interaction.plot(x.factor=as.factor(NHGPredictions$word2Group),
trace.factor=factor(word1),
response=unaspProb,
xlab="Word2 unaspiratedness group",ylab="rate of behaving as if Word2 is unaspirated"
, trace.label="Word1 group", fixed=TRUE, main="Noisy Harmonic Grammar model")
})
Just as we did for Maxent, we now group the Word1s into groups A, B, C.
Add a column to french that is NGH predicted prob:
#initialize new column
french$NHGPrediction <- NA
#look up values
for (i in 1:length(french$word1)) {
#get the value; we need to use as.character() because "word1" has more levels in the full "french" data frame than in the "NHGPredictions" data frame.
NHGValue <- NHGPredictions$unaspProb[as.character(NHGPredictions$word1)==as.character(french$word1[i]) & NHGPredictions$word2Group==french$aspire_rank_word[i]]
#use it if it's not NA
if(is.na(NHGValue[1])==FALSE) { #use just first element of NHGValue, to avoid throwing warning when maxEntValue is vector of NAs, e.g. c(NA,NA,NA); when it's not NA, it will be a single number
french$NHGPrediction[i] <- NHGValue
}
}Make interaction plot:
par(mar=c(5,5,3,6))
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=NHGPrediction,
xlab="Word2 unaspiratedness group",ylab="NHG predicted rate of behaving as if Word2 is unasp."
, trace.label="Word1 group", fixed=TRUE)
})
#Since this will appear in the paper, also do a PNG file:
png(file="NHG_predictions_plot.png",width=myResMultiplier*460,height=myResMultiplier*300, res=myResMultiplier*72, family=myFontFamily)
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=NHGPrediction,
xlab="Word2 alignancy group",ylab="NHG predicted rate of non-alignment"
, trace.label="Word1 alignancy group", fixed=TRUE)
})
dev.off()## pdf
## 2Get a table of constraint names and weights:
#Initialize data frame
NHGGrammar <- data.frame(constraintName=character(0), constraintWeight = numeric(0))
#Define function to find the header row for this part
getNHGConstraintEndingRowIndex <- function() {
for(i in 1:length(NHGLines)) {
if(str_sub(NHGLines[i],1,4)==" 1 \t") { #find first instance of row that starts with "1" (rather than constraint rame)
return(i)
}
}
}
#Use the function to see where to start for loop
constraintEndingRowIndex <- getNHGConstraintEndingRowIndex()
#Extract names and weights and add to data frame
for(i in 1:(constraintEndingRowIndex-1)){
lineParts <- strsplit(NHGLines[i],split="\t")
myConstraintName <- lineParts[[1]][1]
myConstraintWeight <- as.numeric(lineParts[[1]][2])
NHGGrammar <- rbind(NHGGrammar,data.frame(constraintName=myConstraintName, constraintWeight=myConstraintWeight))
}
#Print to console, for pasting into Word document
NHGGrammar## constraintName constraintWeight
## 1 Align_1 17.5130
## 2 Align_2 14.9080
## 3 Align_3 9.5782
## 4 Align_4 3.7487
## 5 Align_5 0.1941
## 6 NoHiatus 12.1251
## 7 UseAu 4.6129
## 8 UseBeau 0.2151
## 9 UseDe 3.3023
## 10 UseDu 5.5242
## 11 UseLa 2.9153
## 12 UseLe 5.0722
## 13 UseMa 0.0130
## 14 UseVieux 1.9459Stochastic OT and Stratal OT with multiple runs
The GLA is not deterministic, and results can vary substantially from one run to the next. We used a (non-distributed) version of OTSoft that can run the GLA 10, 100, or 1000 times on the same input file, collating the results in a single file. We can then choose the best-fit model from this set.
We did this three times, twice in an attempt to find the best StOT model, and once to find the best stratal Anttilan model–in each case, the learner was run 1000 times:
- NoMagri:
- number of times to go through data: 1000000
- starting plasticity: 2
- ending plasticity: 0.001
- number of times to test grammar: 100000
use Magri update rule: no
- WithMagri:
- number of times to go through data: 1000000
- starting plasticity: 2
- ending plasticity: 0.001
- number of times to test grammar: 100000
use Magri update rule: yes
- Stratal:
- number of times to go through data: 1000000
- starting plasticity: 20
- ending plasticity: 20
- number of times to test grammar: 100000
use Magri update rule: no
To examine the results, we read in the collated files:
conn <- file("CollateRuns_NoMagri.txt",open="r")
collated_NoMagri <- readLines(conn)
close(conn)
conn <- file("CollateRuns_WithMagri.txt",open="r")
collated_WithMagri <- readLines(conn)
close(conn)
conn <- file("CollateRuns_Stratal.txt",open="r")
collated_Stratal <- readLines(conn)
close(conn)A function to read in all 1000 runs from a collated file, and find the one with the best log likelihood: (I wrote this function in a lazy way so that if the very last grammar gets ignored, even if it’s the best one; this is equivalent to doing 999 runs rather than 1000)
find_best_grammar <- function(collatedFile, backoff=1/100000) {
#initialize
best_log_like <- -Inf #the log likelihood to beat; starts out infinitely bad
current_log_like <- 0
best_grammar <- data.frame(constraintName=character(0), rankingValue=numeric(0))
current_grammar <- data.frame(constraintName=character(0), rankingValue=numeric(0))
best_probabilities <- data.frame(input=character(0), output=character(0), observedFreq=numeric(0), predictedProb=numeric(0))
current_probabilities <- data.frame(input_word1=character(0), input_word2_group=character(0), output=character(0), observedFreq=numeric(0), predictedProb=numeric(0))
current_index <- 1
#step through lines of collated file
for(i in 1:length(collatedFile)) {
#parse the line
myLine <- strsplit(collatedFile[i], split="\t")
#if index has gone up, then before going on to the next grammar, it's time to assess the one just finished
if(as.numeric(myLine[[1]][2]) > current_index) {
if(current_log_like > best_log_like) { #this grammar is the new winner
best_log_like <- current_log_like
best_grammar <- current_grammar
best_probabilities <- current_probabilities
}
#either way [i.e., whether latest grammar was new winner or not], start the grammar, probabilities, and log likelihood fresh and update the index
current_grammar <- data.frame(constraintName=character(0), rankingValue=numeric(0))
current_probabilities <- data.frame(input_word1=character(0), input_word2_group=character(0), output=character(0), observedFreq=numeric(0), predictedProb=numeric(0))
current_log_like <- 0
current_index <- as.numeric(myLine[[1]][2])
}
#process current line
if(myLine[[1]][1] == "G") { #if starts with G, add to grammar
current_grammar <- rbind(current_grammar, data.frame(constraintName=myLine[[1]][3], rankingValue=myLine[[1]][4]))
} else if(myLine[[1]][1] == "O" & (myLine[[1]][6]=="consulent" | myLine[[1]][6]=="voculent")) { #if starts with O [that's a capital letter, not a number], add to probabilities, and update log likelihood; don't both if it's one of those weird lines at the end of each group with a nonexistent output
#split out the word1 and the word2-group
myWord1 <- strsplit(myLine[[1]][4],split="+",fixed=TRUE)[[1]][1]
myGroup <- str_sub(myLine[[1]][4],-1)
#add line to data frame
current_probabilities <- rbind(current_probabilities, data.frame(input_word1=myWord1, input_word2_group=myGroup, output=myLine[[1]][6], observedFreq=myLine[[1]][7], predictedProb=myLine[[1]][8]))
myProb <- as.numeric(myLine[[1]][8])
if(myProb == 0) {
myProb <- backoff
} else if (myProb==1) {
myProb <- 1 - backoff
}
current_log_like <- current_log_like + as.numeric(myLine[[1]][7])*log(myProb)
}
}
#return best grammar, probabilities, and log likelihood
return(c(best_grammar,best_probabilities,best_log_like))
}Find the best grammar from each group:
best_NoMagri <- find_best_grammar(collated_NoMagri) #-233.6096
best_WithMagri <- find_best_grammar(collated_WithMagri) #-238.9304
best_Stratal <- find_best_grammar(collated_Stratal) #-410.639Print the grammars and their log likelihoods:
best_NoMagri_grammar <- data.frame(matrix(unlist(best_NoMagri[1:2]), nrow=14, byrow=F))
colnames(best_NoMagri_grammar) <- names(best_NoMagri)[1:2]
best_NoMagri_grammar## constraintName rankingValue
## 1 Align_1 193.52133194562
## 2 Align_2 192.393226945096
## 3 Align_3 188.270604312033
## 4 Align_4 182.861897681478
## 5 Align_5 -344.226598038655
## 6 NoHiatus 187.17953715443
## 7 UseAu 181.113234466165
## 8 UseBeau 11.7665862139545
## 9 UseDe 90.6703754255064
## 10 UseDu 183.058838889673
## 11 UseLa 76.7507514227784
## 12 UseLe 182.891195260894
## 13 UseMa -34.5212974679407
## 14 UseVieux 21.0907786345409best_NoMagri[[8]][1] #log likelihood## [1] -233.6best_WithMagri_grammar <- data.frame(matrix(unlist(best_WithMagri[1:2]), nrow=14, byrow=F))
colnames(best_WithMagri_grammar) <- names(best_WithMagri)[1:2]
best_WithMagri_grammar## constraintName rankingValue
## 1 Align_1 64.183428237863
## 2 Align_2 -145.500889005994
## 3 Align_3 -151.031979970691
## 4 Align_4 -222.331583684614
## 5 Align_5 -1087.46722000522
## 6 NoHiatus -151.105564779652
## 7 UseAu -155.137618634362
## 8 UseBeau -154.041881165981
## 9 UseDe -157.627182669382
## 10 UseDu -154.967224313928
## 11 UseLa -155.116729593185
## 12 UseLe -155.193752930466
## 13 UseMa -154.76460367086
## 14 UseVieux -155.299251450449best_WithMagri[[8]][1] #log likelihood## [1] -238.9best_Stratal_grammar <- data.frame(matrix(unlist(best_Stratal[1:2]), nrow=14, byrow=F))
colnames(best_Stratal_grammar) <- names(best_Stratal)[1:2]
best_Stratal_grammar## constraintName rankingValue
## 1 Align_1 3460
## 2 Align_2 3460
## 3 Align_3 3420
## 4 Align_4 3420
## 5 Align_5 -16580
## 6 NoHiatus 3420
## 7 UseAu 3400
## 8 UseBeau -3100
## 9 UseDe -1820
## 10 UseDu 3380
## 11 UseLa -1260
## 12 UseLe 3400
## 13 UseMa -4640
## 14 UseVieux -1880best_Stratal[[8]][1] #log likelihood## [1] -410.6Plot the wugs for the NoMagri StOT model:
#Get the items and probabilities into a data frame
best_NoMagri_probs <- data.frame(matrix(unlist(best_NoMagri[3:7]), nrow=80, byrow=F))
colnames(best_NoMagri_probs) <- names(best_NoMagri)[3:7]
#Make an interaction plot:
par(mar=c(5,5,2,6))
with(best_NoMagri_probs[best_NoMagri_probs$output=="voculent",], {
interaction.plot(x.factor=as.factor(best_NoMagri_probs[best_NoMagri_probs$output=="voculent",]$input_word2_group),
trace.factor=factor(input_word1),
response=as.numeric(as.character(predictedProb)),
xlab="Word2 unaspiratedness group",ylab="rate of Word2 unasp., best-fit StOT model"
, trace.label="Word1 group", fixed=TRUE)
})
And for the Stratal model:
#Get the items and probabilities into a data frame
best_Stratal_probs <- data.frame(matrix(unlist(best_Stratal[3:7]), nrow=80, byrow=F))
colnames(best_Stratal_probs) <- names(best_Stratal)[3:7]
#Make an interaction plot:
par(mar=c(5,5,2,6))
with(best_Stratal_probs[best_Stratal_probs$output=="voculent",], {
interaction.plot(x.factor=as.factor(best_Stratal_probs[best_Stratal_probs$output=="voculent",]$input_word2_group),
trace.factor=factor(input_word1),
response=as.numeric(as.character(predictedProb)),
xlab="Word2 unaspiratedness group",ylab="rate of Word2 unasp., best-fit Stratal model"
, trace.label="Word1 group", fixed=TRUE)
})
As with Maxent, we now group the Word1s into groups A, B, C.
#Add columns to `french` that is StOT predicted prob (no Magri):
#initialize new column
french$StOTPrediction_best_NoMagri <- NA
french$StOTPrediction_best_Stratal <- NA
#look up values
for (i in 1:length(french$word1)) {
#get the value; we need to use as.character() because "word1" has more levels in the full "french" data frame than in the "StOTPredictions" data frame.
StOTPrediction_best_NoMagri <- best_NoMagri_probs$predictedProb[as.character(best_NoMagri_probs$input_word1)==as.character(french$word1[i]) & best_NoMagri_probs$input_word2_group==french$aspire_rank_word[i] & best_NoMagri_probs$output=="voculent"]
StOTPrediction_best_Stratal <- best_Stratal_probs$predictedProb[as.character(best_Stratal_probs$input_word1)==as.character(french$word1[i]) & best_Stratal_probs$input_word2_group==french$aspire_rank_word[i] & best_Stratal_probs$output=="voculent"]
#use it if it's not NA
if(is.na(StOTPrediction_best_NoMagri[1])==FALSE) { #use just first element of NHGValue, to avoid throwing warning when maxEntValue is vector of NAs, e.g. c(NA,NA,NA); when it's not NA, it will be a single number
french$StOTPrediction_best_NoMagri[i] <- as.numeric(as.character(StOTPrediction_best_NoMagri))
}
if(is.na(StOTPrediction_best_Stratal[1])==FALSE) {
french$StOTPrediction_best_Stratal[i] <- as.numeric(as.character(StOTPrediction_best_Stratal))
}
}
#Make interaction plots as before:
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=StOTPrediction_best_NoMagri,
xlab="Word2 unaspiratedness group",ylab="best StOT model's predicted unasp. rate"
, trace.label="Word1 group", fixed=TRUE)
})
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=StOTPrediction_best_Stratal,
xlab="Word2 unaspiratedness group",ylab="best Stratal model's predicted unasp. rate"
, trace.label="Word1 group", fixed=TRUE)
})
#Since this will appear in the paper, also do a PNG file:
png(file="best_StOT_plot.png",width=myResMultiplier*460,height=myResMultiplier*300, res=myResMultiplier*72, family=myFontFamily)
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=StOTPrediction_best_NoMagri,
xlab="Word2 alignancy group",ylab="best StOT model's predicted non-alignment rate"
, trace.label="Word1 alignancy group", fixed=TRUE)
})
dev.off()## pdf
## 2png(file="best_Stratal_plot.png",width=myResMultiplier*460,height=myResMultiplier*300, res=myResMultiplier*72, family=myFontFamily)
par(mar=c(5,4,2,0)+0.1)
with(french, {
interaction.plot(x.factor=as.factor(french$aspire_rank_word),
trace.factor=factor(word1_group),
response=StOTPrediction_best_Stratal,
xlab="Word2 alignancy group",ylab="best Stratified model's predicted non-alignment rate"
, trace.label="Word1 alignancy group", fixed=TRUE)
})
dev.off()## pdf
## 2Pseudo-Hasse diagram for StOT model
Vertical axis represents ranking value, with all the bottom constraints clumped together.
constraint_names <- c("A\U029F\U026A\U0262\U02741 (193.52)","A\U029F\U026A\U0262\U02742 (192.39)","A\U029F\U026A\U0262\U02743 (188.27)","A\U029F\U026A\U0262\U02744 (182.66)","N\U1D0FH\U026A\U1D00\U1D1B\U1D1Cs (187.18)","Us\U1D07 A\U1D1C (181.11)","Us\U1D07 L\U1D07\n(182.89)","Us\U1D07 D\U1D1C\n(183.06)", "Us\U1D07 D\U1D07 (90.67)\nUs\U1D07 L\U1D00 (76.75)\nUs\U1D07 V\U026A\U1D07\U1D1Cx (21.09)\nUs\U1D07 B\U1D07\U1D00\U1D1C (11.77)\nUs\U1D07 M\U1D00 (-34.52)","A\U029F\U026A\U0262\U02745 (-344.23)")
dummyValueForBottom <- 180
#x <- c(20,20,20,5,20,20,20,35,20) #horizontal positions
x <- c(30,30,30,30, 20, 10,8,12,10, 30) #horizontal positions
y <- c(193.52,192.39,188.27,182.66,187.18,181.11,182.89,183.06,dummyValueForBottom-6,dummyValueForBottom-8) #ranking values
vert_increment <- 0.4
plot(x,y, xlab="",ylab="ranking value",type="n",xaxt="n",yaxt="n",xlim=c(5,35),ylim=c(dummyValueForBottom-8,194))
suppressWarnings(text(x,y,labels=constraint_names, cex=1))
yat <- pretty(y)
yat <- yat[yat>dummyValueForBottom]
axis(2,at=yat)
axis.break(2,dummyValueForBottom-2,style="slash")
#Add in line segments
segments(x[1],y[1]-vert_increment,x[2],y[2]+vert_increment) #add line segment from Align1 to Align2
segments(x[2],y[2]-vert_increment,x[3],y[3]+vert_increment) #from Align2 to Align3
segments(x[3],y[3]-vert_increment,x[4],y[4]+vert_increment) #from Align3 to Align4
segments(x[4],y[4]-vert_increment,x[10],y[10]+vert_increment) #from Align4 to Align5
segments((x[7]+x[8])/2,(y[7]+y[8])/2-vert_increment-0.5,x[6],y[6]+vert_increment) #from UseLe/UseDu to UseAu
segments(x[6],y[6]-vert_increment,x[9],y[9]+2+vert_increment-0.5) #from UseAu to big clump
#write it to a file
png(file="French_PseudoHasse2.png",width=myResMultiplier*460,height=myResMultiplier*460, res=myResMultiplier*72,family=myFontFamily)
par(mar=c(0,4,0,0)+0.1)
plot(x,y, xlab="",ylab="ranking value",type="n",xaxt="n",yaxt="n",xlim=c(5,35),ylim=c(dummyValueForBottom-8,194))
#text(x,y,labels=constraint_names, cex=c(1,1,1,1,1.3,1,1,1,1,1,1,1,1,1))
text(x,y,labels=constraint_names, cex=1)
yat <- pretty(y)
yat <- yat[yat>dummyValueForBottom]
axis(2,at=yat)
axis.break(2,dummyValueForBottom-2,style="slash")
#Add in line segments
segments(x[1],y[1]-vert_increment,x[2],y[2]+vert_increment) #add line segment from Align1 to Align2
segments(x[2],y[2]-vert_increment,x[3],y[3]+vert_increment) #from Align2 to Align3
segments(x[3],y[3]-vert_increment,x[4],y[4]+vert_increment) #from Align3 to Align4
segments(x[4],y[4]-vert_increment,x[10],y[10]+vert_increment) #from Align4 to Align5
segments((x[7]+x[8])/2,(y[7]+y[8])/2-vert_increment-0.5,x[6],y[6]+vert_increment) #from UseLe/UseDu to UseAu
segments(x[6],y[6]-vert_increment,x[9],y[9]+2+vert_increment-0.5) #from UseAu to big clump
dev.off()## pdf
## 2Log likelihood of each constraint model
Note that we already retrieved the log likelihood of the multiplicative model above. For reference, it is -1 * myOptimization\(value, or `{r} -1*myOptimization\)value`. We also already got them for the best StOT and Stratal models.
Make a function for getting log Likelihood using v_and_c_table_subset and french:
#for StOT and NHG models, where we use similation to get predicted probabilities, we'll get some zeroes. Since we run 1,000,000 trials, we back of zeros to 1/1000000 by default.
getLogLike <- function(colName, backoff = 1/1000000) {
log_likelihood <- 0 #initialize
for(i in levels(v_and_c_table_subset$word1)) {
for(j in levels(v_and_c_table_subset$word2_group)) {
v_value <- french[,colName][french$word1==i & french$aspire_rank_word==j][1]
if(v_value==0) { #avoid log of 0
v_value <- v_value + backoff
}
else if(v_value == 1) { #avoid log of 1-1=0
v_value <- v_value - backoff
} #multiply log prob (according to model) by (token-weighted type) frequency
log_likelihood <- log_likelihood + v_and_c_table_subset$v_count[v_and_c_table_subset$word1==i & v_and_c_table_subset$word2_group==j] * log(v_value) + v_and_c_table_subset$c_count[v_and_c_table_subset$word1==i & v_and_c_table_subset$word2_group==j] * log(1-v_value)
}
}
return(log_likelihood)
}Now get them all, including multiplicative model, as a check that the function is correct. I’m doing it with the default backoff (1/1000000), appropriate for NHG, where grammar was checked 1,000,000 times, and also the backoff used for picking best StOT and Stratal grammars (100,000, since those grammars were checked 100,000 times)
#multiplicative:
getLogLike("multiplicativePrediction") #-207.9451## [1] -207.9# MaxEnt:
getLogLike("MaxEntPrediction") #-197.7132## [1] -197.7#NHG:
getLogLike("NHGPrediction") #-198.7964## [1] -198.8getLogLike("NHGPrediction", backoff=1/100000) #-198.7964: no 0s or 1s, so backoff doesn't matter## [1] -198.8#best StOT (no Magri):
getLogLike("StOTPrediction_best_NoMagri") #-241.1755## [1] -241.2getLogLike("StOTPrediction_best_NoMagri", backoff=1/100000) #-233.6096## [1] -233.6#best Stratal (no Magri):
getLogLike("StOTPrediction_best_Stratal") #-443.9495## [1] -443.9getLogLike("StOTPrediction_best_Stratal", backoff=1/100000) #-410.639## [1] -410.6Baseline (“perfect”) model
For comparison, we also include a baseline model, with perfect frequency matching for each combination of word2-group and word1. It will still not fit the data perfectly, because it it predicts voculence 60% of the time, for a category that has 60% voculence, it will still sometimes predict voculence when the datum is non-voculent (0.6 * 0.4), and vice-versa (0.4 * 0.6), for a total error rate of 48%. This provides a ceiling on how well any model (that makes the same distinctions ours do) could do.
To do this, we add another column to the french data frame that has the overall rate for that word1-word2group combination.
french$voculence_for_this_bin <- NA #initialize the new column
for(i in 1:length(french$voculence)) {
#look up the value in v_and_c_table
myValue <- v_and_c_table_subset$v_count[as.character(v_and_c_table_subset$word1)==as.character(french$word1[i]) & v_and_c_table_subset$word2_group==french$aspire_rank_word[i]] / (v_and_c_table_subset$v_count[as.character(v_and_c_table_subset$word1)==as.character(french$word1[i]) & v_and_c_table_subset$word2_group==french$aspire_rank_word[i]] + v_and_c_table_subset$c_count[as.character(v_and_c_table_subset$word1)==as.character(french$word1[i]) & v_and_c_table_subset$word2_group==french$aspire_rank_word[i]])
#use it only if match achieved; otherwise leave it NA
if(length(myValue) > 0) {
french$voculence_for_this_bin[i] <- myValue
}
}Now we can use the function above to get the log likelihood::
getLogLike("voculence_for_this_bin") #-189.3649## [1] -189.4