Scottish Health Survey - topic report: The Glasgow Effect

Appendix 1: Pseudo R ²s

A variety of approaches exist for developing a pseudo R ², based on the different approaches for thinking about R ²s in ordinary least squares regression, which enable comparisons to be made between models ¹⁶. The two most appropriate approaches are considering R ² as the proportion of the total variability that is explained by the model, and the improvement in prediction from the null model to the fitted model.

McFadden's pseudo R ² mirrors both of these approaches, and is calculated as follows:

where is the estimated likelihood, M _Full is the model with predictors and M _Intercept is the model without predictors. The higher the R ², the better the fit of the full model compared to the intercept model. If two models were being compared on the same data, McFadden's pseudo R ² is higher for the model with the higher likelihood, indicating the model which fits the data better. This therefore enables models to be directly compared to find which of the discussed models best fits the data.