Table 2.

Model fit statistics and likelihood ratio rests in models examining causal influences between smoking status and alcohol use.

Base model	Comparison model	# Estimated parameters	−2lnL	df	AIC	LRT
						NCP	△df	p
I. CLPM
Full CLPM		18	31,699.08	12,828	31,735.08
Full CLPM	No bidirectional lagged effects	16	31,707.37	12,830	31,739.37	8.29	2	0.0159
Full CLPM	No Smoking → Alcohol lagged effect	17	31,704.29	12,829	31,738.29	5.21	1	0.0225
Full CLPM	No Alcohol → Smoking lagged effect	17	31,701.83	12,829	31,735.83	2.75	1	0.0971
II. IV-CLPM
Global tests
Full IV-CLPM		31	59,109.02	22,605	59,171.02
Full IV-CLPM	No bidirectional causal effects	25	59,123.10	22,611	59,173.10	14.08	6	0.0288
Full IV-CLPM	No Smoking → Alcohol causal effects	28	59,115.69	22,608	59,171.69	6.67	3	0.0833
Full IV-CLPM	No Alcohol → Smoking causal effects	28	59,115.97	22,608	59,171.97	6.94	3	0.0738
Smoking → Alcohol
Full IV-CLPM	No proximal effects at waves 1 and 2	29	59,110.24	22,607	59,168.24	1.21	2	0.5451
Full IV-CLPM	No distal + wave-2 proximal effects	29	59,114.39	22,607	59,172.39	5.37	2	0.0683
Alcohol → Smoking
Full IV-CLPM	No proximal effects at waves 1 and 2	29	59,113.10	22,607	59,171.10	4.07	2	0.1305
Full IV-CLPM	No distal + wave-2 proximal effects	29	59,111.70	22,607	59,169.70	2.67	2	0.2626
Best-fitting IV-CLPM (Smoking → Alcohol distal effect, plus Alcohol → Smoking proximal effect at wave 1)
Full IV-CLPM	Best-fit IV-CLPM	27	59,112.89	22,609	59,166.89	3.86	4	0.4247
Best-fit IV-CLPM	No Smoking → Alcohol distal effect	26	59,118.65	22,610	59,170.65	5.77	1	0.0163
Best-fit IV-CLPM	No Alcohol → Smoking proximal effect	26	59,117.28	22,610	59,169.28	4.39	1	0.0362

−2lnL: −2 × log-likelihood of the model; df: degrees of freedom; AIC: Akaike information criterion; LRT: likelihood ratio test; NCP: non-centrality parameter = △−2lnL.