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Joint modelling of location and scale parameters of the t distribution

BiometricsSA, The University of Adelaide and South Australian Research and Development Institute, Australia, julian.taylor{at}adelaide.edu.au

Arnas Verbyla

BiometricsSA, The University of Adelaide and South Australian Research and Development Institute, Australia

Joint modelling of location and scale parameters has generally been confined to exponential families. In this paper the location and scale parameters of the t distribution are allowed to depend on covariates. The closed form of the likelihood allows inference to proceed in a similar fashion to the Gaussian location and scale model and provides a framework for a simple scoring algorithm to estimate the parameters. The algorithm includes a procedure to estimate the degrees of freedom parameter of the t distribution. Homogeneity and asymptotic tests are discussed and a methodology is derived to detect heteroscedasticity when the response is t distributed. Simulations reveal considerable bias in the estimates of the degrees of freedom parameter and only minor bias in the estimated fixed effects associated with the scale parameter. In comparison, the estimated location effects are well behaved. To illustrate the joint modelling of location and scale parameters of the t distribution the methodology is applied to two data sets.

Key Words: heteroscedastic regression • location and scale models • maximum likelihood • random effects • t distribution

Statistical Modelling, Vol. 4, No. 2, 91-112 (2004)
DOI: 10.1191/1471082X04st068oa


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