Table 3. Model selection results.

Differences in AIC values, ΔAIC = AIC—AIC_min, between the different models with 3 hidden states, where AIC_min is the value of the model with the lowest AIC. The best fit is given by the minimum AIC. For all the tested state distributions, covariate model 1 was preferred, and for all covariate models, the dependent log-normal state distribution was preferred. Because the runtimes for the correlated gamma model are high, only Model 1 was fitted. The best model is highlighted in bold. np: number of parameters.

	Independent Gamma distribution		Independent Log-normal distribution		Correlated Gamma distribution		Correlated Log-normal distribution
Model	np	ΔAIC	np	ΔAIC	np	ΔAIC	np	ΔAIC
1	60	5050.5	60	2309.1	63	1901.9	63	0
2	42	5386.9	42	2652.4	45	-	45	256.0
3	48	5096.5	48	2353.2	51	-	51	34.3
4	42	5194.4	42	2451.9	45	-	45	166.9