Testing for omitted variables and non-linearity in regression models for longitudinal data

Abstract

When fitting regression models to investigate the relationship between an outcome variable and independent variables of primary interest, there is often concern whether omitted variables or assuming a different functional relationship could have changed the conclusion or interpretation of the results. In longitudinal studies of ageing, the concern with omitted variables is well known in the context of cohort and period effects, which refer to unmeasured variables systematically related to the individual's year of birth and secular trends in outcome, respectively. We present and compare three approaches to detecting omitted confounders and non‐linearity in the random effects model for longitudinal data (Laird and Ware, 1982) with random slope and intercept across individuals. The first approach compares simple unweighted within and between regression coefficients, the second is the Hausman specification test for regression models, and the third approach involves testing directly the significance of functions of individual specific covariate means x̄i, in the random effects regression model. This last approach is motivated by the models that arise when cohort or period effects are ignored. We compare the three approaches, and illustrate their application.