Simulating Topic–Audience Interactions in Sociolinguistic Style-Shifting: Speaker Heterogeneity, Missing Data and Inferential Performance

Abstract

Topic and audience can be examined jointly in repeated observations of linguistic variation, but evaluating an analysis requires a clearly defined interaction and an appropriate account of dependence and missingness. This computer experiment compares three estimators of a population-averaged log-odds interaction: a naive binomial analysis, an analysis with speaker-level sandwich uncertainty, and stratified inverse probability weighting. The factorial design crosses four speaker sample sizes, two token densities, three latent heterogeneity regimes, three interaction magnitudes and four observation regimes. It comprises 288 conditions with 2000 replications each. All observations are synthetic and computer-generated; no participants or empirical data were involved. Every numerical parameter is an illustrative assumption, not an estimate extracted from previous research. Conditional generating coefficients are calibrated to the same marginal target before bias, coverage, false-positive rates and positive detection are evaluated. With 60 hypothetical speakers, 100 tokens per cell and complete observations, the naive false-positive rate rises from 2.85% with a random intercept to 21.35% with additional random slopes; the corresponding speaker-level rate in the latter condition is 6.10%. With random slopes, 240 speakers and a target interaction odds ratio of 1.26, weighted positive detection is 99.95% with complete observations and 63.30% under covariate-dependent missingness. Weighting does not remove bias caused by latent selection. The contribution is a transparent benchmark linking the interaction target, repeated-observation structure and missingness assumptions to inferential performance; it provides no empirical evidence about actual speakers or stylistic preferences.