The Effects of Unequal Covariances and Reliabilities on Contemporaneous Inference: The Case of Hostility and Marital Happiness

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Abstract
In family research, changes in attitudes and behaviors, and processes of interaction in close relationships, are inherently reciprocal. Yet models with reciprocal effects are rightfully viewed with suspicion. This article removes some of the mystery surrounding these models by carefully examining the simple two-wave, two-variable contemporaneous model. Three distinct pairs of factors -cross-lagged covariances, stability covariances, and reliabilities-are shown to affect inference. The implications of these factors are illustrated with artificial data and with models of husbands' hostility and wives' marital happiness. The results demonstrate that stability and reliability are two distinct and sometimes conflicting statistical mechanisms linking theoretical arguments to empirical results. Failure to distinguish between these mechanisms may lead one to inadvertently draw conclusions inconsistent with the characteristics of the data. Distinguishing between these mechanisms is particularly important when researchers are developing new indicators of concepts or when indicators are obtained from multiple sources.