To test for heterogeneity across samples for the various parameters of interest, we used a likelihood ratio test to compare the full model to the restricted model. Twice the difference between the log-likelihoods of the two models is, under certain regularity conditions, distributed as χ2 with degrees of freedom equal to the difference in the number of parameters in the two models. Thus, to test for heterogeneity in, e.g. the genetic parameter, we compared the model where all of the studies had unique genetic parameters to a model where all of the genetic parameters across the studies were equated. This is a multiple degrees-of-freedom test. To test for heterogeneity across sexes, assessment methods, or study design, we relied on a 1 df likelihood ratio test. For example, to test for genetic heterogeneity across sexes, we compared a model with one genetic parameter for males and one for females, to a restricted model where the genetic parameters were equated across sex. All modeling was performed in OpenMx (Boker et al. 2011, 2012).
