Estimation of Reliability and Stability in Single-Indicator Multiple-Wave Models

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Abstract
This article focuses on three main points: (1) Because a short-wave panel study such as the ALLBUS-Retest Study 1984 is suited optimally for reliability estimations, the quality of a larger number of items concerning attitudes about the welfare state and inequality and toward a minority group in West Germany (“guestworkers”) is investigated; (2) we show that most of the items are more reliable in the subgroup with high political interest than in the low-interest group; and (3) because we cannot rely on multiple indicators in most of the cases, methods and statistical models for the analysis of single indicators in multiple-wave panels are discussed. Because we can assume that the latent attitudes are continuous and the observed variables have ordered categories (at least), we confine our analyses to metric variable models. We show that (a) the assumptions underlying the classical models proposed by Heise (1969) and by Wiley and Wiley (1970, 1974) will often be violated if the times between the panel waves are very short; (b) frequently, models of parallel or tau-equivalent measurement, or some modifications of these models lead to parameter estimates that are more plausible from a theoretical point of view; (c) the ML- and ULS-estimators for these models can be easily calculated; (d) the use of polychoric correlation coefficients for these models is more appropriate if the observed variables have a badly skewed distribution and a small number of categories.