We recommend that model fit indices be considered concurrently, as individual indices each have their own strengths and limitations. Model χ2 is an index of exact fit, with lower values indicating better fit. Model χ2 may oftentimes be statistically significant, indicating that the model-implied genetic covariance matrix significantly differs from the empirical (unrestricted) genetic covariance matrix, even when the model-implied covariance matrix very closely approximates the empirical genetic covariance matrix. Oftentimes, models that closely, albeit imperfectly approximate the empirical genetic covariance matrix may be scientifically and inferentially useful. We thus recommend considering CFI and SRMR indices of absolute fit, even when model χ2 is significant. We also recommend using indices of relative fit to compare competing models of the same data (i.e. different models fit to genetic covariance matrices derived from the exact same summary data for the exact same phenotypes). When models are nested, their respective χ2 values can be subtracted from one another to calculate a χ2 difference test, with df equal to the difference in df between the two models. This χ2 difference test, indexes the extent
