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Adjusted $$R^2$$-type measures for tweedie models. (English) Zbl 05564594
Summary: $$R^{2}$$-type measures are commonly used tools for assessing the predictive power of linear regression models; for generalized linear models this measure is based on deviances. For small samples, it is necessary to adjust $$R^{2}$$ for the number of covariates. This article shows that some of the adjustments that have been proposed for logistic, Poisson, gamma and inverse Gaussian models, can be expressed in a general form that covers all exponential dispersion models with power variance function (also called Tweedie models). The adjusted measure is asymptotically unbiased. Numerical results of a simulation study are presented to explore the estimator behavior under different sample sizes, different number of covariates and different population values of the adjusted deviance based measure. The performances of the adjusted measures are also investigated on a data set used by Box and Cox.

##### MSC:
 62-XX Statistics
##### Keywords:
tweedie models; $$R^{2}$$-type measures; shrinkage
##### Software:
R; Statmod; Tweedie
Full Text:
##### References:
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