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Abstract Background Browne et al. [Browne, MacCallum, Kim, Andersen, Glaser: When fit indices and residuals are incompatible. Psychol Methods 2002] employed a structural equation model of measurements of target cell lysing by natural killer cells as an example purportedly demonstrating that small but statistically significant ill model fit can be dismissed as "negligible from a practical point of view". Methods Reanalysis of the natural killer cell data reveals that the supposedly negligible ill fit obscured important, systematic, and substantial causal misspecifications. Results A clean-fitting structural equation model indicates that measurements employing higher natural-killer-cell to target-cell ratios are more strongly influenced by a progressively intrusive factor, whether or not the natural killer cell activity is activated by recombinant interferon γ (rIFN γ). The progressive influence may reflect independent rate limiting steps in cell recognition and attachment, spatial competition for cell attachment points, or the simultaneous lysings of single target cells by multiple natural killer cells. Conclusions If the progressively influential factor is ultimately identified as a mere procedural impediment, the substantive conclusion will be that measurements of natural killer cell activity made at lower effector to target ratios are more valid. Alternatively, if the individual variations in the progressively influential factor are modifiable, this may presage a new therapeutic route to enhancing natural killer cell activity. The methodological conclusion is that, when using structural equation models, researchers should attend to significant model ill fit even if the degree of covariance ill fit is small, because small covariance residuals do not imply that the underlying model misspecifications are correspondingly small or inconsequential.

Researchers using structural equation modeling (SEM) aspire to learn about the world by seeking models with causal specifications that match the causal forces extant in the world. This quest for a model matching existing worldly causal forces constitutes an ontology that orients, or perhaps reorients, thinking about measurement validity. This article illustrates several ways the seemingly innocuous quest for structural equation models that mirror "the world beyond" confronts entrenched notions of measurement validity. The article begins by considering simple measurement models and ends by "discovering" a new class of indicators called reactive indicators. Reactive indicators act as both the cause and effect of an underlying latent variable. The identifiability of a simple model containing a reactive indicator is proven and a research example illustrating the use of a reactive indicator is provided. However, the real challenge is to understand how an indicator can be both a cause and effect of the latent it measures. The understanding does not come from complying with the traditional rules for reliability and validity, but from focusing on the quest to make the structural equation model match the structuring of the worldly forces we seek to understand. Valid measurement in the context of a weirdly structured world requires an equally weird structural equation model. [ABSTRACT FROM AUTHOR]