Control of Type I Errors with Multiple Tests of Constraints in Structural Equation Modeling

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Abstract
Two contrasting views toward the evaluation of multiple tests of constraints and control of Type 1 errors in structural equation modeling are presented. (a) Exploring; data helps researchers make decisions about inclusion of relevant model parameters and control of Type 1 errors hinders this process. (b) Exploring data is not likely to yield meaningful models unless we can limit the process on the basis of methods and theory, and controlling Type I errors is a useful device: to force us to limit our searches. Also, in evaluating multiple tests of constraints for applications other than exploratory analyses, we should control for Type I errors as we do in testing multiple comparisons in analysis of variance. We argue for the second perspective and present examples to illustrate methods for controlling Type 1 errors when making model comparisons.