Random Forests in Count Data Modelling: An Analysis of the Influence of Data Features and Overdispersion on Regression Performance

Abstract

Machine learning algorithms, especially random forests (RFs), have become an integrated part of the modern scientific methodology and represent an efficient alternative to conventional parametric algorithms. This study aimed to assess the influence of data features and overdispersion on RF regression performance. We assessed the effect of types of predictors (100, 75, 50, and 20% continuous, and 100% categorical), the number of predictors (p = 816 and 24), and the sample size (N = 50, 250, and 1250) on RF parameter settings. We also compared RF performance to that of classical generalized linear models (Poisson, negative binomial, and zero-inflated Poisson) and the linear model applied to log-transformed data. Two real datasets were analysed to demonstrate the usefulness of RF for overdispersed data modelling. Goodness-of-fit statistics such as root mean square error (RMSE) and biases were used to determine RF accuracy and validity. Results revealed that the number of variables to be randomly selected for each split, the proportion of samples to train the model, the minimal number of samples within each terminal node, and RF regression performance are not influenced by the sample size, number, and type of predictors. However, the ratio of observations to the number of predictors affects the stability of the best RF parameters. RF performs well for all types of covariates and different levels of dispersion. The magnitude of dispersion does not significantly influence RF predictive validity. In contrast, its predictive accuracy is significantly influenced by the magnitude of dispersion in the response variable, conditional on the explanatory variables. RF has performed almost as well as the models of the classical Poisson family in the presence of overdispersion. Given RF’s advantages, it is an appropriate statistical alternative for counting data.