Model χ2 is an index of exact fit of a SEM. It indexes whether the model-implied genetic covariance matrix, Σ(θ), differs from the empirical genetic covariance matrix, S. Model χ2 can also be used as a relative fit index for comparing nested models. Conventional SEM approaches to indexing model χ2 are based on formulas that directly incorporate N. Because there is not an N that directly corresponds to the genetic covariance matrix that is modelled by Genomic SEM in the same way that N typically corresponds to an observed covariance matrix, we derived a formula for estimating model χ2 that does not require N, but instead incorporates the sampling covariance matrix of the model residuals. This is done in two steps. In Step 1, the proposed model (e.g., a common factor model) is estimated. In Step 2, all of the Step 1 estimates are fixed, and the residual covariances and residual variances of the indicators are freely estimated. Residual variances are estimated in Step 2 by estimating the variances of k residual factors defined by the indicators. This provides an
