pseudoR2

PseudoR2, or pseudo R-squared, refers to a family of statistics used to assess goodness-of-fit for generalized linear models, especially logistic regression, where the traditional R-squared from ordinary least squares is not defined. These measures provide a rough indication of model fit and enable model comparison, but they do not have the same interpretation as the proportion of variance explained in linear models.

The most widely used variant is McFadden's R-squared. It is defined as 1 minus the ratio of the fitted model’s log-likelihood to the intercept-only model’s log-likelihood. Values are typically between 0 and 1, with higher values indicating better fit; however, they do not map directly to the OLS notion of explained variance. In practice, values around 0.2 to 0.4 are often considered indicative of decent fit, depending on the context.

Other common measures include Cox and Snell’s R-squared and Nagelkerke’s R-squared. Cox and Snell’s measure is based on a likelihood-ratio principle but has a maximum that can be less than 1, making direct interpretation difficult. Nagelkerke’s R-squared rescales this statistic to span the full [0,1] interval, facilitating comparison across models and datasets.

Additional variants include Cragg–Uhler (also known as Cox–Snell with a different scaling) and Efron’s R-squared, each with its own interpretation and scaling. Tjur’s R-squared, tailored for binary outcomes, gauges fit as the difference between the mean predicted probability for events and non-events.

Interpretation of pseudo R-squared values should be cautious. They are primarily comparative rather than absolute measures of explained variance. Different definitions can yield different magnitudes, and values depend on model specification, outcome distribution, and sample size. In practice, researchers report one or several pseudo R-squared indicators alongside likelihood-based statistics for a fuller assessment of model fit.