a score test for homogeneity in the generalised linear mixed model. In this paper we propose an improvement to Lin's test that exploits the fact that covariance parameters associated with random effects in the model are constrained so as to form a positive semidefinite covariance matrix. Therefore, an omnibus score test will have power against alternatives that are known never to occur. Our improvement works by concentrating the score test into directions given by the positive semidefiniteness constraint. We apply the same sort of modification to the bias-corrected version of her score test in the generalised linear mixed model context and, in a nonlinear mixed model context, to a score test analogous to hers. We show how to obtain the limiting distribution of our proposed test statistic. We also argue, via simulations and local alternative power calculations, that the restricted test has better power than the unrestricted one. Some key words: Lagrange multiplier test; Nonlinear regression; Random effect; Order-restricted inference; Tangent cone; Variance component. Both generalised linear models and normal error nonlinear regression models have been extended by incorporating random effects into the expectation function of the model. Although these generalised linear mixed models and nonlinear mixed models have been enthusiastically received by both practitioners and researchers, substantial theoretical and practical challenges remain. A natural question is whether or not the inclusion of random effects and the accompanying, often-cumbersome mixed model methodology is necessary for any particular dataset. Lin (1997) has addressed this issue by proposing a score test for homogeneity in the generalised linear mixed model. One of the nice features of her test is that it does not require the fitting of the mixed model, because its approximations to the score function and information matrix are derived under the null hypothesis of homogeneity. As a consequence, the analyst can directly check the significance of the hypothesised covariance structure against an ordinary fixed-effect null model. If no significant improvement is obtained by incorporating random effects, for example to model the
REF provides Order-Restricted Score Tests for generalized linear and nonlinear mixed models.
Order-restricted score tests for homogeneity in generalised linear and nonlinear mixed models
Biometrika
Mathematics