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The present research examined the distributional properties of construct reliability indices and model fit metrics, explored relationships between and among the indices and metrics, and investigated variables influencing the relative magnitudes of the indices and metrics in structural equation measurement models. A broad-based meta-analysis of reported construct reliability indices and selected model fit metrics revealed modest relationships among reliability indices, minimal relationships among model fit metrics, and a virtual absence of relationships between reliability indices and model fit metrics. Differences in magnitudes of selected reliability indices and model fit metrics were found to primarily be a function of the (total) number of items employed in a measurement model. The implications of the findings suggest that the current practice of indiscriminately computing and reporting of reliability indices and model fit metrics based only on arbitrary heuristics should be abolished and replaced by theoretically justified indices and metrics.

A meta-analysis of construct reliability indices and measurement model fit metrics