Causal indicator models: identification, estimation, and testing
In 1993 we presented "Causal Indicator Models: Identification, Estimation, and Testing" in a methodology session at the American Sociological Association Convention in Miami. Less than 2 years earlier, Bollen and Lennox (1991) was published in Psychological Bulletin and the interest in indicators that determined latent variables seemed to intensify in response. The Bollen and Lennox article was directed toward calling attention to causal indicators and their implications for psychological and other social science research. However, this article provided little guidance on how to analyze causal indicators. The aforementioned conference paper was an attempt to provide such guidance. As its title suggests, we had separate sections on issues of identification, methods of estimation, and ways to assess model fit in causal indicator models. We created two rules of identification that were particularly helpful in models with causal indicators and drafted a separate paper to prove these rules. For a variety of reasons, we never published these works. Yet somehow word got out and we have had numerous requests for copies of the conference paper throughout the years, but particularly over the last few years. Part of the reason for the interest in this conference paper is that awareness of causal (or formative) indicators continues to grow. The recent debate in Psychological Methods is just the latest evidence of this interest and uncertainty about how to handle such indicators (see Bagozzi, 2007; Bollen, 2007; Howell, Breivik, & Wilcox, 2007). Another part of the reason is that researchers have sparse practical advice on methods to incorporate causal indicators into models. Our paper attempted to provide such advice where we systematically laid out the options of treating models under different scenarios. The researchers requesting our paper did not know of other papers that did the same. George A. Marcoulides, the editor of Structural Equation Modeling, was aware of this situation and suggested that we could publish the paper and an accompanying paper that proves the identification rules in the journal to make this work more accessible. We are extremely grateful for his offer and hope that our work will be useful to some researchers and stimulate debate and further work among others.We have left the work largely intact to reflect its original form in a slightly revised 1994 version. The identification paper was in a rough draft form and was revised more recently for this publication.