A functional-based distribution diagnostic for a linear model with correlated outcomes
Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. ahousema{at}hsph.harvard.edu, bcoull{at}hsph.harvard.edu, lryan{at}hsph.harvard.edu
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Abstract |
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In this paper we present an easy-to-implement graphical distribution diagnostic for linear models with correlated errors. Houseman et al. (2004) constructed quantile–quantile plots for the marginal residuals of such models, suitably transformed. We extend the pointwise asymptotic theory to address the global stochastic behaviour of the corresponding empirical cumulative distribution function, and describe a simulation technique that serves as a computationally efficient parametric bootstrap for generating representatives of its stochastic limit. Thus, continuous functionals of the empirical cumulative distribution function may be used to form global tests of normality. Through the use of projection matrices, we generalised our methods to include tests that are directed at assessing the normality of particular components of the error. Thus, tests proposed by Lange & Ryan (1989) follow as a special case. Our method works well both for models having independent units of sampling and for those in which all observations are correlated.
Key Words: Conditional error; Empirical cumulative distribution function; Goodness-of-fit; Linear mixed model; Random effect; Residual diagnostic; Time series regression.
Received March 2004. Revised April 2006.
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