Central to the current exercise, when the full model is estimated for the true latent parameters, with all the parameters for the main effects and interaction of genes and environment, the precise pattern of simulated values for all five cases is recovered. In each case, parameter estimates are very close to their simulated values and the values of non-zero parameters typically yield highly significant t-values with these very large samples. Thus, for data simulated under the digenic additive model with no non-additive genetic effects or G × E (Table 5), estimates of da and db are 0.989 and 0.959 respectively, the regression on phenotype on environment is 0.501 and the residual variance is 1.006 as expected. All other estimates are close to their zero expected values. The results for the other data sets (Tables 6, 7, 8, 9) also correspond to their expected values as long as the true latent phenotypes are measured directly.