Properly addressing populatin heterogeneity in statistical modelling

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Failing to properly address population heterogeneity issue may result in serious problems in statistical modelling. For instance, an association between a pair of variables can be reversed in a population when the subpopulations are combined, which is called the Simpson's paradox in the statistics literature; the estimate of other regression coefficients may result in the opposite sign when a population characterizing variable is removed from the regression model. Marginal models had been very popular for longitudinal data analyses. Although there were some criticisms on this approach, it has not been pointed out that the marginal model and the mixed effects model are in effect mutually exclusive. The marginal setting for longitudinal data implies homogeneous population assumption, i.e. no population variability allowed except that explained by included regressors and error terms. I propose a class of random mean models for longitudinal data which not only naturally assumes population heterogeneity through setting the means of responses are random but also provides flexibility of specifying correlations among responses in the spirit of GEE. I will investigate its usefulness and properties for nonlinear regression analysis and for the non-normal responses.