Abstract
Latent variable models are used extensively in the social and behavioral sciences for a variety of purposes, including measurement, description, and explanation. The latent variables may be continuous or discrete and the indicators of these may be continuous and/or discrete as well. Crossing the levels of measurement of the indicators with the assumptions on the level of measurement and distribution of the latent variables yields a variety of distinct latent variable models. A theme that unifies these different models is the assumption (or axiom) of conditional independence, which states that the indicators are independent, given the latent variable(s). The use of this axiom has been justified on various grounds, ranging from convenience to considerations of causality. This paper examines several of these justifications. First, the use of this axiom in the context of measurement and prediction is examined. Examples where the use of the axiom is scientifically plausible and implausible are considered, and the implications of the use of this assumption in both situations is discussed. I also show that the usual practice of viewing factor loadings as scaling factors that translate between units of measurement is incorrect. Second, the principle of the common cause is sometimes given as a justification for the use of the conditional independence assumption. The argument here is that the latent variables are the causes of the observed variables (indicators), and these indicators are not causes of one another. Hence (according to the argument), the association between the indicators is supposed to vanish when conditioning on the values of the latent variables. I show that this principle is not sound, and therefore cannot be used to justify the axiom of conditional independence. I also show that a modified version of this principle can be used to justify the conditional independence assumption in some instances.
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Sobel, M.E. (1997). Measurement, Causation and Local Independence in Latent Variable Models. In: Berkane, M. (eds) Latent Variable Modeling and Applications to Causality. Lecture Notes in Statistics, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1842-5_2
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DOI: https://doi.org/10.1007/978-1-4612-1842-5_2
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