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Chunk #43 — Solution: extension of the univariate moderation model? — Simulation study 3

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A note on false positives and power in G × E modelling of twin data.
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We then fitted to these datasets a) the full bivariate moderation model including all 17 parameters, and b) the extended univariate moderation model in which both moderators M1 and M2 are modeled on the means with means parameters differing across zygosity (Eqs. 8 and 9). Within these models we constrained either β a, β c, or β e to zero to test for the significance of each parameter individually, i.e., a 1-df test. Since moderation parameters β a, β c, and β e were simulated as 0 in these data, we expect the distribution of the χdiff2 as calculated across all 2000 data sets to follow a central χ2(1) distribution. Given an nominal α of .05, we expected 5% of χdiff2 test to be significant, i.e., larger than the critical value of 3.84.