. Author manuscript; available in PMC: 2016 Jan 1.

Published in final edited form as: Int J Behav Dev. 2014 Oct 13;39(1):87–96. doi: 10.1177/0165025414552301

Table 3.

Simulation results, normally distributed and skewed data

		Multivariate Normal, No Interaction in Data		Multivariate Normal, Interaction in Data		Chi Square Distribution, No Interaction in Data		Chi Square Distribution, Interaction in Data

	Data generation	Mean Parameter (Mean Standard Error)
Path coefficients
Conduct Problems	1.074	1.083	(0.230)	1.083	(0.233)	1.089	(0.233)	1.019	(0.227)
Depressive Symptoms	0.109	0.112	(0.059)	0.112	(0.060)	0.104	(0.059)	0.088	(0.059)
Conduct Problems × Depressive Symptoms	0.000
Conduct Problems × Depressive Symptoms	0.620			0.619	(0.218)			1.736	(0.223)
Factor covariances
Conduct Problems with Depressive Symptoms	0.093	0.092	(0.020)	0.093	(0.020)	0.093	(0.021)	0.113	(0.020)
		Mean R² (Standard Deviation of R²)
R²
Alcohol		0.136	(0.036)	0.166	(0.041)	0.137	(0.042)	0.426	(0.324)
Δ R² of the interaction	0 or 0.03	0.004	(0.006)	0.034	(0.023)	0.014	(0.151)	0.193	(0.332)
		Mean Likelihood Ratio (Standard Deviation of Likelihood Ratio)
Likelihood Ratio		1.033	(1.476)	10.402	(6.65)	7.226	(22.329)	64.994	(56.603)
Proportion significant		0.061		0.841		0.349		0.987

Note. Path coefficients, factor covariances, and R2 represent mean values of parameter estimates from the correct model for each population and their corresponding standard error. For data populations not containing interactions, estimates are derived from Model 0, the model in which an interaction is not estimated. For data populations containing interactions, estimates are derived from Model 1, the model in which an interaction is estimated. Likelihood ratios and proportion of likelihood ratios significant are derived by estimating both Model 0 and Model 1 for each data population and comparing the likelihood ratio of the two models.