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

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

   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
  1. TruPar=True Parameters= β i or c i .
  2. MeaEst=Mean estimates= β ^ i or c ^ i .
  3. Bias= β ^ i β i or c ^ i c i .
  4. RelErr=Relative Error= β ^ i β i / β i or c ^ i c i / c i .
  5. Coverage: the percentage ofestimated 95%CI whichcovers true coefficient in all estimated 95%CI.
  6. Coverage2: coverage from GAM which accounts for overdispersion.
  7. Mea_co: Mean absolute Bias, RelErr, Coverage for parameters of covariates.
  8. Mea_ar: Mean absolute Bias, RelErr, Coverage for parameters of AR terms.