Pseudo-R2 for Generalized Linear Models - A Study of Various Pseudo-R2s for the Logit Model and the Log-Linear Poisson Model

Abstract

No equivalent measure to R2 for ordinary least square regression exist for generalized linear models to assess model fit. Therefore, this master's project addresses various pseudo-R2s for generalized linear models. Six measures are presented for the logit model and five for the log-linear Poisson model. The pseudo-R2s are compared to the coefficient of determination with regards to interpretation and properties.

A simulation study is performed to investigate the properties of the pseudo-R2s. The response variable y is generated based on an underlying reference model containing five covariates. Seven different models are estimated, six of them misspecified and one correct. For each model are the pseudo-R2s calculated. Under varying conditions on the covariates and the underlying reference model, the behavior of the pseudo-R2s is examined. In addition, a case study is conducted where the pseudo-R2s for the logit model is applied on a real dataset on traumatic brain injury.

The measures are considered independently and compared to each other. In general they have higher values for models where a good fit might be expected, while lower values occur when a more poor fit is likely. They are generally able to distinguish between the correct model and incorrect models. The measures are also able to reflect the contribution of a covariate in a model. More specifically, the stronger the relation between a covariate and the response, the more will the pseudo-R2s increase in value when the covariate is included in the model. The study shows that most measures are suitable to assess model fit.