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 to which the less complex model (i.e. the model with more df) approximates the empirical genetic covariance matrix significantly worse than the more complex model (i.e. the model with fewer df). If the χ2 difference test is significant, the more complex model should be chosen. If the χ2 difference test is not significant, the less complex model should be chosen, as it is more parsimonious and approximates the empirical genetic covariance matrix no worse than the more complex model. Two models are nested when the set of possible model implied covariance matrices from one model is a subset of the set of possible model implied covariance matrices of the second model.55 Nesting can typically be confirmed if the less restrictive model can be derived from the more restrictive model by dropping or fixing parameters. Regardless of whether models are nested, they can be compared on CFI, SRMR, and AIC, so long as the same data are being modeled.
