title: Rationale, Detection, and Implications of Interactions Between Independent Variables and Unmeasured Variables in Linear Models.
abstract: Conceptual rationales from five research contexts are presented which share the similarity that all posit unmeasured variables which interact with observed independent variables to produce a complete model of the dependent variable. For the class of linear underspecified models involving only observed effects, it is shown that estimated effects of the observed independent variables are overestimated, that squared error of the misspecified model overestimates true error, and that this misspecified squared error is a function of at least the square of the measured independent variable(s). A statistical test for this last relationship is presented (Cook & Weisberg, 1983). The effect of this phenomenon on statistical power is discussed. Possible analytic and design strategies to overcome the effect of such unmeasured interactions include use of the rank transform (Conover & Iman, 1981), use of several longitudinal assessments, and oversampling of levels of independent variables where variance heterogeneity is large relative to other levels. Limitations of these strategies are discussed.
authors.forename: P K
authors.initials: PK
authors.lastname: Wood
authors.forename: P
authors.initials: P
authors.lastname: Games