Table S.1. Full List of Parameter Estimates of Covariate for Children Reported Asthma in the CHS in BMHMM.

	Mean	SD	2.5%	50%	97.5%	G-R^
Prevalence probability:
Intercept	-3.92	0.42	-4.81	-3.92	-3.13	1.00
Age	0.44	0.54	-0.63	0.45	1.47	1.00
Gender	-0.07	0.46	-0.97	-0.06	0.87	1.00
Ethnicity*: hispanic	-0.41	0.56	-1.56	-0.38	0.63	1.00
black	0.31	0.95	-1.74	0.34	1.98	1.00
asian	-0.87	1.06	-3.03	-0.82	1.00	1.00
others+mixed	-0.41	0.88	-2.23	-0.39	1.24	1.00
Medication Use	5.14	0.60	3.98	5.14	6.36	1.00
Allergy	0.90	0.47	-0.01	0.90	1.79	1.00
Severe Wheeze	1.65	0.56	0.52	1.67	2.71	1.00
FEV (log scale)	-0.61	1.06	-2.68	-0.59	1.45	1.00
Transition probability:
Intercept	-3.46	0.53	-4.50	-3.46	-2.36	1.00
Age	-0.76	0.38	-1.59	-0.71	-0.19	1.01
Gender	0.04	0.40	-0.71	0.02	0.86	1.00
Ethnicity: hispanic	0.15	0.45	-0.79	0.17	0.99	1.00
black	-0.23	1.00	-2.51	-0.09	1.46	1.00
asian	0.14	0.68	-1.33	0.18	1.32	1.00
others+mixed	-0.72	1.05	-3.03	-0.64	1.06	1.00
Allergy	0.98	0.39	0.18	0.98	1.69	1.00
Current wheeze	0.83	0.47	-0.15	0.82	1.73	1.01
Family History of Asthma	1.01	0.40	0.23	1.00	1.85	1.00
Ozone from 10 am to 6 pm	-0.03	0.02	-0.06	-0.03	0.00	1.00
Number of Sports	-0.54	0.73	-2.16	-0.48	0.72	1.00
Ozone*Number of Sports	0.97	1.08	-1.50	1.06	2.83	1.00
Misclassification probability:
Intercept	-4.31	0.42	-5.15	-4.31	-3.50	1.00
Latent True Asthma	5.34	0.71	4.01	5.32	6.77	1.00
Age	-0.16	0.25	-0.69	-0.14	0.28	1.00
Gender	0.11	0.42	-0.67	0.10	0.92	1.00
AboveHS†
When Latent True Asthma=0	-0.16	0.46	-1.08	-0.16	0.74	1.00
When Latent True Asthma=1	1.33	0.64	0.04	1.33	2.57	1.00
Current Wheeze	1.21	0.42	0.38	1.21	2.06	1.00
Age*Latent True Asthma	0.28	0.32	-0.33	0.27	0.93	1.00
Variance of Town Level Radom Effect	0.28	0.10	0.15	0.25	0.54	1.00

^{^}G-R: Gelman-Rubin Statistics.

^*The reference group is Non-Hispanic White group.

^†AboveHS: An indicator variable of whether children come from families with education above the high school level.