Designing a Pseudo R-Squared Goodness-of-Fit Measure in Generalized Linear Models

H. I. Mbachu, E. C. Nduka, M. E. Nja


The coefficient of determination is a function of residuals in the General Linear Models. The deviance, logit, standardized and the studentized residuals were examined in generalized linear models in order to determine the behaviour of residuals in this class of models and thereby design a new pseudo R-squared goodness-of-fit measure. The Newton-Raphson estimation procedure was adopted. It was observed that these residuals exhibit patterns that are unique to the subpopulations defined by levels of categorical predictors. Residuals block on the basis of signs, where positive signs indicate success responses and negative signs failure responses. It was also observed that the deviance is a close approximation of the studentized residual. The logit residual is two times the size of the standardized residuals. Borrowing from the Nagelkerke's improvement of Cox and Snell's goodness-of-fit measure in generalized linear models and the coefficient of determination counterpart of the general linear model, a new pseudo R squared goodness-of-fit test which uses predicted probabilities and a monotonic link function is here proposed to serve both the linear and Generalized Linear Models.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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