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 relationship 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 4.1.0 (2021-05-18), mgcv version 1.8.36, itsadug version 2.4)

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 ***