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 gamma (rIFN gamma). 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.