Chapter 11 What should I do if DFI cutoffs don’t exist for my model type?

As of this writing, the DFI method supports CFA models with continuous indicators only and the simulation component of the software assumes multivariate normality. It takes some time to work out generalizations for other types of models because a general method for identifying relevant misspecifications must be done model by model. For instance, potential misspecification that are relevant to latent growth models would likely be very different than a confirmatory factor analysis because latent growth models are typically interested in aspects like the function form of growth being correct or whether the correlation between repeated measures is reasonable rather than things like omitted cross-loadings that are relevant to confirmatory factor analysis. Our current work is focused on extending the method to higher-order models, categorical indicators, non-normality, missing data, and measurement invariance; so we expect those or related extensions will be the next to be added to the DFI method.

In the meantime, researchers should rely on the chi-square test and investigate local areas of strain to look for obvious misfit (e.g., viewing the standardized residual covariance matrix). Researchers can also use the Exact Fit application in the Shiny App or the exactFit function in the R package to return the 95th or 99th percentile of the distribution of cutoff values for a correctly specified model (for researchers that used one of the currently available apps, this can also be found in the Level 0 tab). Because this is a distribution of cutoff values for the true model, the values that are returned are the strictest way to evaluate approximate model fit. If the researchers fit index values fall below these values, this indicates that the fit of their model is consistent with a model that is correctly specified. These cutoff values can be computed for any model with continuous outcomes (e.g., models estimated using ML or MLR).