Table 2.

Comparison of the Bayesian and Maximum Likelihood Estimation (MLE) of Group Probabilities

	True Parameter	Estimate from MLE	SE from MLE	Estimated Median of the Posterior Distribution	Estimated SD of the Posterior Distribution	95% Credible Interval
Panel A: Marginal Probabilities for Series A Latent Group
Group 1	30%	30.5%	1.5	30.5%	1.5	[27.7%, 33.5%]
Group 2	50%	48.0%	1.6	47.9%	1.6	[44.8%, 51.1%]
Group 3	20%	21.5%	1.3	21.5%	1.3	[19.1%, 24.1%]
Panel B: Marginal Probabilities for Series B Latent Group
Group 1	23.20%	20.8%	--	20.9%	1.3	[18.5%, 23.5%]
Group 2	31%	33.2%	--	33.2%	1.5	[30.3%, 36.0%]
Group 3	45.80%	46.0%	--	45.9%	1.6	[42.8%, 49.0%]
Panel C: Transition Probabilities from Series A to Series B
1|1	10%	9.2%	1.7	9.3%	1.7	[6.4%, 12.9%]
2|1	20%	20.7%	2.3	20.7%	2.3	[16.5%, 25.5%]
3|1	70%	70.2%	2.6	69.8%	2.6	[64.6%, 74.7%]
1|2	40%	37.5%	2.2	37.4%	2.2	[33.2%, 41.9%]
2|2	30%	32.3%	2.1	32.2%	2.1	[28.2%, 36.5%]
3|2	30%	30.2%	2.1	30.2%	2.1	[26.2%, 34.5%]
1|3	1%	0.0%	0.0	0.3%	0.5	[0.01%, 1.7%]
2|3	50%	53.0%	3.4	52.7%	3.4	[46.3%, 59.4%]
3|3	49%	47.0%	3.4	46.9%	3.4	[40.2%, 53.4%]
Panel D: Transition Probabilities from Series B to Series A
1|1	12.9%	13.5%	--	13.6%	2.4	[9.5%, 18.7%]
2|1	86.2%	86.5%	--	85.9%	2.4	[80.7%, 90.2%]
3|1	0.8%	0.0%	--	0.3%	0.5	[0.0%, 1.7%]
1|2	19.4%	19.0%	--	19.1%	2.2	[15.1%, 23.5%]
2|2	48.4%	46.7%	--	46.6%	2.7	[41.4%, 52.0%]
3|2	32.3%	34.3%	--	34.2%	2.6	[29.3%, 39.4%]
1|3	45.9%	46.5%	--	46.4%	2.4	[41.7%, 51.0%]
2|3	32.8%	31.5%	--	31.6%	2.2	[27.4%, 36.0%]
3|3	21.4%	22.0%	--	21.9%	1.9	[18.3%, 26.0%]

Note: Maximum likelihood estimates are obtained from the package “traj” in Stata 16. i|j refers to the conditional probability of being in Group j in the Series B (A) conditional on being in Group i in the Series A (B). -- indicates that Traj does not compute standard errors for this paramater.