Using a generalized additive model with autoregressive terms to study the effects of daily temperature on mortality

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
β ₀	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
β ₁	−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
β ₂	−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
β ₃	−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
β ₄	−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
β ₅	−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
c ₁	0.5										0.4982	−0.0018	0.0422	95.3
c ₂	0.25										0.2477	−0.0023	0.0947	93.4
c ₁	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= ${\overset{―}{\hat{β}}}_{i}$ or ${\overset{―}{\hat{c}}}_{i}$ .
Bias= ${\overset{―}{\hat{β}}}_{i} - β_{i}$ or ${\overset{―}{\hat{c}}}_{i} - c_{i}$ .
RelErr=Relative Error= $\overset{―}{|({\hat{β}}_{i} - β_{i}) / β_{i}|}$ or $\overset{―}{|({\hat{c}}_{i} - c_{i}) / c_{i}|}$ .
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.

ISSN: 1471-2288