TABLE 5.

Mean Estimate and Relative Bias of the Latent Interaction Effect (Statistical Power = 0.7)
Sample Size	Distribution	γ3	CPI		GAPI		UPI		LMS
			E (γ̂3)	RB(γ̂3)	E (γ̂3)	RB(γ̂3)	E (γ̂3)	RB(γ̂3)	E (γ̂3)	RB(γ̂3)
100	Normal	3.233	3.337	3.2% *	3.909	20.9%	3.874	19.8%	3.220	−0.4% *
	Uniform	3.233	3.074	−4.9% *	4.106	27.0%	4.006	23.9%	2.987	−7.6% *
	K1	3.233	3.837	18.7%	3.845	18.9%	3.713	14.9%	3.981	23.2%
	K2	3.233	4.130	27.7%	3.816	18.1%	3.907	20.9%	4.237	31.1%
	${\chi }_1^2$	3.233	5.759	78.1%	3.974	22.9%	3.556	10.0%	6.147	90.1%
200	Normal	2.309	2.392	3.6% *	2.637	14.2%	2.533	9.7% *	2.426	5.1% *
	Uniform	2.309	2.121	−8.1% *	2.651	14.8%	2.714	17.6%	2.070	−10.3%
	K1	2.309	2.793	20.9%	2.492	7.9% *	2.420	4.8% *	2.833	22.7%
	K2	2.309	2.830	22.6%	2.440	5.7% *	2.469	6.9% *	3.069	32.9%
	${\chi }_1^2$	2.309	4.352	88.5%	2.532	9.7% *	2.586	12.0%	4.918	113.0%
500	Normal	1.469	1.511	2.8% *	1.554	5.8% *	1.554	5.7% *	1.510	2.7% *
	Uniform	1.469	1.315	−10.5%	1.548	5.3% *	1.545	5.1% *	1.298	−11.6%
	K1	1.469	1.790	21.8%	1.509	2.7% *	1.498	2.0% *	1.921	30.7%
	K2	1.469	1.849	25.9%	1.549	5.4% *	1.529	4.1% *	2.063	40.4%
	${\chi }_1^2$	1.469	3.244	120.8%	1.566	6.6% *	1.556	5.9% *	3.969	170.1%
1000	Normal	1.041	1.035	−0.6% *	1.048	0.7% *	1.044	0.3% *	1.051	0.9% *
	Uniform	1.041	0.929	−10.8%	1.071	2.8% *	1.067	2.5% *	0.920	−11.6%
	K1	1.041	1.267	21.7%	1.052	1.0% *	1.048	0.7% *	1.363	30.9%
	K2	1.041	1.283	23.2%	1.057	1.6% *	1.054	1.2% *	1.465	40.7%
	${\chi }_1^2$	1.041	2.577	147.5%	1.116	7.2% *	1.113	6.9% *	3.311	218.0%
5000	Normal	0.466	0.487	4.4% *	0.490	5.0% *	0.489	4.8% *	0.489	4.7% *
	Uniform	0.466	0.426	−8.7% *	0.480	2.9% *	0.480	3.0% *	0.423	−9.4% *
	K1	0.466	0.567	21.5%	0.465	−0.2% *	0.465	−0.3% *	0.634	35.8%
	K2	0.466	0.552	18.3%	0.463	−0.8% *	0.463	−0.6% *	0.668	43.3%
	${\chi }_1^2$	0.466	1.770	279.6%	0.483	3.5% *	0.483	3.5% *	2.410	416.6%

Mean Estimate and Relative Bias of the Latent Interaction Effect (Statistical Power = 0.9)
Sample Size	Distribution	γ3	CPI		GAPI		UPI		LMS
			E (γ̂3)	RB(γ̂3)	E (γ̂3)	RB(γ̂3)	E (γ̂3)	RB(γ̂3)	E (γ̂3)	RB(γ̂3)
100	Normal	4.133	4.277	3.5% *	5.220	26.3%	4.824	16.7%	4.175	1.0% *
	Uniform	4.133	3.730	−9.8% *	5.005	21.1%	4.924	19.1%	3.794	−8.2% *
	K1	4.133	5.084	23.0%	4.923	19.1%	4.784	15.7%	5.141	24.4%
	K2	4.133	5.241	26.8%	4.831	16.9%	4.720	14.2%	5.540	34.0%
	${\chi }_1^2$	4.133	6.549	58.5%	5.018	21.4%	4.588	11.0%	7.164	73.3%
200	Normal	2.981	3.063	2.7% *	3.393	13.8%	3.362	12.8%	2.991	0.3% *
	Uniform	2.981	2.772	−7.0% *	3.502	17.5%	3.561	19.4%	2.762	−7.4% *
	K1	2.981	3.740	25.5%	3.297	10.6%	3.257	9.2% *	3.831	28.5%
	K2	2.981	3.837	28.7%	3.364	12.8%	3.291	10.4%	4.087	37.1%
	${\chi }_1^2$	2.981	5.260	76.4%	3.403	14.2%	3.402	14.1%	5.821	95.3%
500	Normal	1.909	1.995	4.5% *	2.058	7.8% *	2.051	7.4% *	1.934	1.3% *
	Uniform	1.909	1.652	−13.5%	1.914	0.2% *	1.908	−0.1% *	1.670	−12.5%
	K1	1.909	2.362	23.7%	1.990	4.2% *	1.964	2.9% *	2.536	32.8%
	K2	1.909	2.395	25.5%	1.990	4.2% *	1.985	4.0% *	2.643	38.4%
	${\chi }_1^2$	1.909	3.684	93.0%	2.044	7.1% *	2.027	6.2% *	4.529	137.3%
1000	Normal	1.356	1.362	0.4% *	1.384	2.1% *	1.383	2.0% *	1.371	1.2% *
	Uniform	1.356	1.232	−9.1% *	1.414	4.3% *	1.409	3.9% *	1.247	−8.0% *
	K1	1.356	1.693	24.9%	1.405	3.7% *	1.402	3.4% *	1.836	35.5%
	K2	1.356	1.681	24.0%	1.405	3.6% *	1.391	2.6% *	2.198	62.2%
	${\chi }_1^2$	1.356	2.883	112.7%	1.385	2.2% *	1.388	2.4% *	3.709	173.6%
5000	Normal	0.608	0.613	0.7% *	0.616	1.2% *	0.616	1.2% *	0.625	2.7% *
	Uniform	0.608	0.546	−10.2%	0.622	2.3% *	0.623	2.4% *	0.552	−9.2% *
	K1	0.608	0.739	21.4%	0.610	0.3% *	0.609	0.1% *	0.820	34.7%
	K2	0.608	0.730	19.9%	0.614	0.9% *	0.613	0.8% *	0.876	44.1%
	${\chi }_1^2$	0.608	1.909	213.8%	0.612	0.5% *	0.613	0.7% *	2.597	326.9%

Note. RB means relative bias.

^*means relative bias ≤ |10%| criterion met.

Note. RB means relative bias.

^*means relative bias ≤ |10%| criterion met.