# Can R-squared be printed for Generalized Linear Models (GENLIN) results

## Problem

It appears that SPSS does not print the R^2 (R-squared) information for the output of Generalized Linear Models (GENLIN command), such as negative binomial regression. The Binary Logistic, Multinomial Logistic, and Ordinal Regression procedures will print R^2 statistics (Cox & Snell, Nagelkerke, and McFadden). Can these or similar statistics be printed for for generalized linear models? I have read that SAS and STATA report R^2 for negative binomial models.

## Resolving The Problem

You are correct that the Generalized Linear Models (GENLIN) procedure will not print the R-squared statistic (or pseudo R-squared, as it is called in the Binary (LOGISTIC REGRESSION) and Multinomial (NOMREG) Logistic Regression, and Ordinal Regression (PLUM) procedures).

In general, the pseudo R-squared is not discussed in generalized linear models texts (see McCullagh and Nelder, 1989), and SPSS follows that tradition. SAS's GENMOD and STATA's GLM for generalized linear models don't report R-squared either. In STATA, NBREG fits negative binomial (but with only the log link function) in addition to GLM, and reports the pseudo R-squared (it is the only software that we have found to report it). However, in SAS, NLMIXED and GLIMMIX fit negative binomial in addition to GENMOD, but none of them reports R-squared for these models.

GENLIN models which could be fit in one of the 3 procedures listed above, such as an ordinal regression model with a logit link, could be run in that procedure (PLUM, for this example) to obtain the pseudo R-squared. Negative binomial regression models cannot be fit by any of the procedures that currently print pseudo R-squared values.

McCullagh, P., & Nelder, J.A. (1989). Generalized Linear Models (2nd Ed.). London: Chapman and Hall.

## Related Information

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Modified date:
16 April 2020

swg21482027