Generalized additive modeling for dialectology

• Introduction
  • Logistic regression
  • Standard Italian and Tuscan dialects
• Material: Standard Italian and Tuscan dialects
• Methods: R code
• Results
• Discussion

• Dependent variable is binary (1: success, 0: failure), not continuous
• Transform to continuous variable via log odds: \(\log(\frac{p}{1-p})\) = logit\((p)\)
  • Automatically in GAM by setting family="binomial"
  • Transformation of dependent variable: generalized additive model
• interpret coefficients w.r.t. success as logits: in R: plogis(x)

• Standard Italian originated in the 14th century as a written language
• It originated from the prestigious Florentine variety
• The spoken standard Italian language was adopted in the 20th century
  • People used to speak in their local dialect
• We investigate the relationahip between standard Italian and Tuscan dialects
  • We focus on lexical variation
  • We use social, geographical and lexical variables

• We use lexical data from the Atlante Lessicale Toscano (ALT)
• We focus on 2060 speakers from 213 locations and 170 concepts
• Total number of cases: 384,454
  • Binary dependent variable:
    • 1: lexical form was different from standard Italian
    • 0: lexical form was identical to standard Italian

• Speaker age
• Speaker gender
• Speaker education level
• Speaker employment history
• Number of inhabitants in each location
• Average income in each location
• Average age in each location
• Frequency of each concept

(R version 3.5.1 (2018-07-02), mgcv version 1.8.24, itsadug version 2.3)

library(mgcv)
library(itsadug)
geo <- bam(NotStd ~ s(Lon, Lat, k = 30), data = tuscan, family = "binomial", discrete = T)
summary(geo)  # slides only show the relevant part of the summary

# Parametric coefficients:
#             Estimate Std. Error z value Pr(>|z|)    
# (Intercept)   -0.247     0.0033   -75.1   <2e-16 ***
# 
# Approximate significance of smooth terms:
#             edf Ref.df Chi.sq p-value    
# s(Lon,Lat) 28.2     29   1591  <2e-16 ***

fvisgam(geo, view = c("Lon", "Lat"), too.far = 0.045, main = "")

geo2 <- bam(NotStd ~ s(km.e, Lat), data = tuscan, family = "binomial", discrete = T)
fvisgam(geo2, view = c("km.e", "Lat"), too.far = 0.045, main = "")

• Wieling, Nerbonne and Baayen (2011) showed that the effect of word frequency varied depending on geography
• Here we explicitly include this in the GAM with te(), which can model an \(N\)-way non-linear interaction:
  te(Lon, Lat, ConceptFreq, d=c(2,1))
• As this pattern may be presumed to differ depending on speaker age, we can integrate this in the model as well:
  te(Lon, Lat, ConceptFreq, YearBirth, d=c(2,1,1))

summary(m, re.test = FALSE)

# Parametric coefficients:
#                       Estimate Std. Error z value Pr(>|z|)    
# (Intercept)            -0.4282     0.1264   -3.39 0.000708 ***
# CommunitySize.log.z    -0.0629     0.0223   -2.82    0.005 ** 
# SpeakerJob_Farmer       0.0449     0.0169    2.66    0.008 ** 
# SpeakerEduLevel.log.z  -0.0678     0.0126   -5.38 7.29e-08 ***
# SpeakerIsMale           0.0378     0.0128    2.95    0.003 ** 
# 
# Approximate significance of smooth terms:
#                                                  edf Ref.df Chi.sq p-value    
# te(SpeakerBirthYear.z,ConceptFreq.log.z,Lon,Lat) 221    265   3270  <2e-16 ***

smry <- summary(m)  # takes 10 minutes to compute
tail(smry$s.table, 11)  # last 11 smooths are random effects

#                                                   edf Ref.df Chi.sq   p-value
# s(Speaker)                                       97.1   2005    106  9.40e-03
# s(Location)                                     175.0    209   5642  1.33e-96
# s(Concept)                                      167.0    168 436864  0.00e+00
# s(CommunityRecordingYear.z,Concept)             158.9    170 155893 4.88e-181
# s(CommunitySize.log.z,Concept)                  149.9    169  29991 2.41e-111
# s(CommunityAvgIncome.log.z,Concept)             158.0    170 143207 1.75e-160
# s(CommunityAvgAge.log.z,Concept)                154.4    170 110722 5.80e-195
# s(SpeakerJob_Farmer,Concept)                     86.1    169  26572  1.27e-07
# s(SpeakerJob_Executive_AuxiliaryWorker,Concept)  53.3    170   3319  8.07e-04
# s(SpeakerEduLevel.log.z,Concept)                139.1    169   9377  8.05e-49
# s(SpeakerIsMale,Concept)                         85.4    169 112400  6.55e-11

• Comparing Tuscan dialects to standard Italian revealed interesting patterns
• GAMs are very suitable to model the non-linear influence of geography
• The regression approach allowed for the simultaneous identification of important social, geographical and lexical predictors
• By including many concepts, results are less subjective than traditional analyses focusing on only a few pre-selected concepts
• The mixed-effects regression approach still allows a focus on individual concepts
• Analyses can be made reproducible via paper package with data and code

• We have applied GAMs to dialect data and learned how to:
  • use s() to model two-dimensional interactions on the same scale
  • model complex non-linear interactions using te()
  • use GAMs to conduct logistic regression (family="binomial")
• Associated lab session:
  • http://www.let.rug.nl/wieling/Statistics/GAM-Dialectology/lab