Table 1.

Results from GAM, GAMM, GAMAR(3) in simulation study 1

		GAM					GAMM (AR(3) correlation structure)				GAMAR(3)
	TruPar	MeaEst	Bias	RelErr	Coverage	Coverage2	MeaEst	Bias	RelErr	Coverage	MeaEst	Bias	RelErr	Coverage
β0	5.02	4.9991	−0.0209	0.0127	38	58.8	5.0065	−0.0135	0.0049	92	5.0182	−0.0018	0.0055	94.8
β1	−0.35	−0.3574	−0.0074	0.1922	33.5	52.4	−0.3576	−0.0076	0.0757	88	−0.3561	−0.0061	0.0686	93.9
β2	−0.36	−0.3672	−0.0072	0.229	35.3	56.4	−0.3662	−0.0062	0.0843	96	−0.362	−0.002	0.0885	94.6
β3	−0.38	−0.382	−0.002	0.1531	34.2	55.3	−0.3787	0.0013	0.0608	96	−0.3757	0.0043	0.0733	93.8
β4	−0.33	−0.3281	0.0019	0.428	38.6	62.6	−0.3418	−0.0118	0.1329	98	−0.3262	0.0038	0.1604	95.5
β5	−0.15	−0.1495	0.0005	0.4924	35.4	55.0	−0.1581	−0.0081	0.202	92	−0.1472	0.0028	0.2201	93.8
	Mea_co		0.0067	0.2512	35.8	56.8		–0.0077	0.0934	93.7		0.0035	0.1027	94.4
c1	0.5										0.4982	−0.0018	0.0422	95.3
c2	0.25										0.2477	−0.0023	0.0947	93.4
c1	0.12										0.1197	−0.0003	0.1737	94.7
	Mea_ar											0.0015	0.1035	94.5

TruPar=True Parameters= β_i or c_i.

MeaEst=Mean estimates= ${\bar{\widehat{\beta }}}_i$ or ${\bar{\widehat{c}}}_i$.

Bias= ${\bar{\widehat{\beta }}}_i-{\beta }_i$ or ${\bar{\widehat{c}}}_i-c_i$.

RelErr=Relative Error= $\overline{\left|\left({\widehat{\beta }}_i-{\beta }_i\right)/{\beta }_i\right|}$ or $\overline{\left|\left({\widehat{c}}_i-c_i\right)/c_i\right|}$.

Coverage: the percentage ofestimated 95%CI whichcovers true coefficient in all estimated 95%CI.

Coverage2: coverage from GAM which accounts for overdispersion.

Mea_co: Mean absolute Bias, RelErr, Coverage for parameters of covariates.

Mea_ar: Mean absolute Bias, RelErr, Coverage for parameters of AR terms.