. Author manuscript; available in PMC: 2016 Apr 8.

Published in final edited form as: Psychol Methods. 2014 Mar;19(1):39–55. doi: 10.1037/a0035314

Table 6.

Standardized Bias: MAR Mechanism and N = 200

		Small interaction effect					Large interaction effect
Distribution	Parameter	CCA	FMLV	CMLV	FMC	CMC	CCA	FMLV	CMLV	FMC	CMC
Normal	α	1.72	0.16	0.04	0.16	0.04	1.82	0.29	0.05	0.29	0.04
	γ ₁	0.40	–0.06	–0.06	–0.08	–0.08	0.94	–0.12	–0.12	–0.14	–0.14
	γ ₂	0.15	–0.20	–0.20	–0.19	–0.19	0.30	–0.44	–0.44	–0.43	–0.43
	γ ₃	–0.05	–0.07	–0.07	–0.08	–0.08	0.02	–0.06	–0.06	–0.07	–0.07

Skewed (lower tail missing)	α	1.19	0.11	0.03	0.11	0.03	1.14	0.25	0.08	0.25	0.08
	γ ₁	0.29	–0.02	–0.02	–0.05	–0.05	0.52	–0.10	–0.10	–0.12	–0.12
	γ ₂	0.10	0.06	0.06	0.07	0.07	0.17	0.00	0.00	0.01	0.01
	γ ₃	–0.03	–0.06	–0.06	–0.06	–0.06	–0.02	–0.11	–0.11	–0.12	–0.12

Skewed (upper tail missing)	α	–1.70	0.03	–0.07	0.04	–0.07	–1.54	0.05	–0.23	0.05	–0.23
	γ ₁	–0.31	0.26	0.26	0.23	0.23	–0.81	0.42	0.42	0.38	0.38
	γ ₂	–0.13	–0.02	–0.02	0.00	0.00	–0.26	0.21	0.21	0.22	0.22
	γ ₃	0.01	0.07	0.07	0.06	0.06	–0.03	0.30	0.30	0.27	0.27

Kurtotic	α	1.66	0.18	0.03	0.18	0.03	1.69	0.36	0.10	0.36	0.10
	γ ₁	0.39	–0.07	–0.07	–0.09	–0.09	0.87	–0.07	–0.07	–0.09	–0.09
	γ ₂	0.10	–0.34	–0.34	–0.33	–0.33	0.25	–0.59	– 0.59	–0.57	–0.57
	γ ₃	0.01	–0.01	–0.01	–0.02	–0.02	–0.04	–0.10	–0.10	–0.11	–0.11

Note. Bold typeface denotes bias that exceeds .40 of a complete-data standard error unit. The x and xz variables (γ₁ and γ₃, respectively) have 20% missing data. MAR = missing at random; CCA = complete-case analysis; FMLV = free mean latent variable model; CMLV = constrained mean latent variable model; FMC = free mean centering; CMC = constrained mean centering.