Three models for combining information from causal indicators

Sometimes we have multiple measures of the same concept. Combining the information of these multiple measures would allow us to improve the measurement. When combining the information from different indicators one needs to distinguish between two types of relationships between the observed indicators and the underlying latent variable: either the latent variable influences the indicators or the indicators influence the latent variable. To distinguish between these two situations some authors, following Bollen (Quality and Quantity, 1984) and Bollen and Lennox (Psychological Bulletin, 1991), call the observed variables "effect indicators" when they are influenced by the latent variable, while they call the observed variables "causal indicators" when they influence the latent variable. Distinguishing between these two is important as they require very different strategies for recovering the latent variable. In a basic (exploratory) factor analysis, which is a model for effect indicators, one assumes that the only thing that the observed variables have in common is the latent variable, so any correlation between the observed variables must be due to the latent variable, and it is this correlation that is used to recover the latent variable. In the models for causal indicators that will discussed in this talk, we assume that the latent variable is a weighted sum of the observed variables (and optionally an error term), and the weights are estimated such that they are optimal for predicting the dependent variable. The three models for dealing with causal indicators that will be discussed are: A model with "sheaf coefficients" (Heise, Sociological Methods & Research, 1972), a model with "parametricaly weighted covariates" (Yamaguchi, Sociological Methodology, 2002), and a Multiple Indicators and Multiple Causes (MIMIC) model (Hauser Goldberger, Sociological Methodoloy, 1971). The latter two can be estimated using -propcnsreg-, while the former can be estimated using -sheafcoef-. Both are available from SSC.