Modeling the dynamics of language change: logistic regression, Piotrowski's law, and a handful of examples in Polish

The study discusses modeling diachronic processes by logistic regression. Such an approach was suggested by Raimund Piotrowski (hence labelled as Piotrowski's law), even if actual linguistic evidence usually speaks against using the notion of a "law" in this context. In our study, we apply logistic regression models to 9 changes which occurred between 15th and 18th century in the Polish language. The attested course of the majority of these changes closely follow the expected values, which proves that the language change might indeed resemble a nonlinear phase change scenario. We also extend the original Piotrowski's approach by proposing polynomial logistic regression for these cases which can hardly be described by its standard version. Also, we propose to consider individual language change cases jointly, in order to inspect their possible collinearity or, more likely, their different dynamics in the function of time. Last but not least, we evaluate our results by testing the influence of the subcorpus size on the model's goodness-of-fit.