Fitting Misspecified Linear Mixed Models
报告人： Alan Welsh,The Australian National University
时间：2016-05-03 14:00 ~ 15:00
Linear mixed models are widely used in a range of application areas, including ecology and environmental science. We study in detail the effects of fitting the two-level linear mixed model with a single explanatory variable that is misspecified because it incorrectly ignores contextual effects. In particular, we make explicit the effect of (the usually ignored) within-cluster correlation in the explanatory variable. This approach produces a number of unexpected findings. (i) Incorrectly omitting contextual effects affects estimators of both the regression and variance parameters not just, as is currently thought, estimators of the regression parameters and the effects are different for different estimators. (ii) Increasing the within cluster correlation of the explanatory variable can introduce a second local maximum into the log-likelihood and REML criterion functions which eventually becomes the global maximum, producing a jump discontinuity (at different values) in the maximum likelihood and REML estimators of the parameters. (iii) Standard statistical software such as SAS, SPSS, STATA, lmer (from lme4 in R) and GenStat do not always return global maximum likelihood and REML estimates in this very simple problem. (iv) Local maximum likelihood and REML estimators may fit the data better than their global counterparts but, in these situations, ordinary least squares may perform even better than the local estimators, albeit not as well as if we fit the correct model.
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