Arbitrary Metrics in Multiple-Indicator Models of Latent Variables

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Abstract
It is well known that only ratios of lambda coefficients are identified from moments among measured variables in most covariance structure models with latent variables. Typically, researchers establish a metric for latent variables by fixing the lambda coefficient for an arbitrarily selected reference indicator. This paper demonstrates that this practice can produce arbitrary calibration of latent variables, undermine interpretation of metric parameters, and lead to invalid cross-population comparisons. The problem is illustrated with hypothetical examples. Analytical results are derived, and implications for sociological research are discussed.