A, C and E contribute to the covariance between M and T since the positive and negative semi-partial correlations as described in Table 1 can more or less cancel each other out.Table 2Results Simulation study 1: false positive rates under Purcell’s univariate moderation modelDrop β a Drop β c Drop β e Settings Simulation study 1 r(T,M) = .24 via A only% hits.07.07.05 r(T,M) = .24 via C only% hits.08.09.05 r(T,M) = .24 via E only% hits.53.55.08Additional simulations r(T,M) = .24 via A, C and E in equal proportionsa % hits.04.05.07 r(T,M) = .62 via A, C and E in equal proportionsb % hits.05.05.06 r(M1,M2) = 0c % hits.05.05.04 r(M1,M2) = 1d % hits.03.03.05 Note: The first three simulation settings are described under Simulation study 1. β a, β c, and β e denote the moderation parameters on the variance components unique to T (see Fig. 1). For all settings, 2000 datasets were simulated and analyzed. % hits denotes the percentage of likelihood-ratio tests smaller than the critical value 3.84 (i.e., significant given α = .05). A hit rate of .05 is expected given α = .05, and given that moderation effects were absent in the data. Hit rates outside
