Abstract
As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we assess a range of candidate distributions, including the Sichel, Delaporte, Box-Cox Green and Cole, and Box-Cox t distributions. We find that the Box-Cox t distribution, with appropriate modeling of its parameters, best fits the conditional distribution of phonemic inventory size. We finally discuss the specificities of phoneme counts, weak effects, and how GAMLSS should be considered for other linguistic variables.
Highlights
Comparing the two models with penalization, one sees that cubic splines lead to high degrees of non-linearity for Distance from Africa and Local linguistic density, which is reflected by the larger values of the effective degrees of freedom of these two smooth terms (8.90 and 8.72, respectively, to be compared to 5.82 and 4.47 for P-splines), while discarding an influence of Number of speakers
Generalized additive models for location, scale and shapes are an extension of GAM(M) which allows one to consider a wide range of options for the conditional distribution of the dependent variable, while Generalized linear models (GLM)(M) and GAM(M) are restricted to the exponential family of distributions (Rigby and Stasinopoulos, 2005)
One can observe here that strictly referring to AIC values, the Box-Cox Cole and Green distribution (BCCG) and Box-Cox t distribution (BCT) distributions provide better fits that the SICHEL and DEL distributions. Do these results suggest that the BCCG should be the distribution to use in a GAMLSS with our various predictors? One must be cautious here, since the marginal distribution is not the same as the conditional distribution of the dependent variable, i.e., its distribution when factoring in the various predictors
Summary
What drives linguistic diversity? What phenomena, and in particular what external factors, explain the distribution of linguistic structures across the globe? These questions are at the heart of linguistics, and can be considered at various levels of linguistic analysis, either with qualitative or more quantitative approaches. Comparing the two models with penalization, one sees that cubic splines lead to high degrees of non-linearity for Distance from Africa and Local linguistic density, which is reflected by the larger values of the effective degrees of freedom of these two smooth terms (8.90 and 8.72, respectively, to be compared to 5.82 and 4.47 for P-splines), while discarding an influence of Number of speakers (owing to the modified penalty introduced above) It looks as if canceling the influence of this predictor resulted in increased non-linearity in the two other continuous predictors. Generalized additive models for location, scale and shapes are an extension of GAM(M) which allows one to consider a wide range of options for the conditional distribution of the dependent variable, while GLM(M) and GAM(M) are FIGURE 4 | Smooth terms for Distance from Africa, Number of Speakers, and Local linguistic density, for three smoothing approaches in an inverse-Gaussian GAMM: cubic splines (top), P-splines (middle), and cubic splines with a fixed smoothing parameter equal to 3. This could be due to less satisfying statistical approaches, but should serve as a warning of the limited trust one should put in this result
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