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Table 2 Fitting the smoking status time-varying coefficient model

From: Application of the varying coefficient model to the behaviour risk factor surveillance data in Italy: a study of changing smoking prevalence among sub-populations

Model Description Time (min) p-value H0 used AIC df
    of test for test   
Selection of variables that have varying coefficients
LM logistic model <1 - - 206590.4 21.00
Model age LM + s(t):age 4.7 <0.001 LM 206554.4 28.88
Model alcohol LM + s(t):alcohol use 2.1 <0.001 LM 206566.0 27.39
Model physical LM + s(t):physical activity 2.1 <0.001 LM 206570.1 26.19
Model income LM + s(t):income 2.2 <0.001 LM 206574.8 26.33
Model mstatus LM + s(t):martital status 2.1 <0.001 LM 206573.8 26.50
Model edu LM + s(t):education 3.1 <0.001 LM 206573.2 26.26
Model sex LM + s(t):sex 1.4 <0.001 LM 206572.4 25.37
Model work LM + s(t):work status 1.4 <0.001 LM 206575.2 25.08
Model region LM + s(t):region 2.2 <0.001 LM 206573.2 26.81
Model depress LM + s(t):depression status 1.4 <0.001 LM 206574.2 24.49
Model time LM + s(t) 1.6 <0.001 LM 206572.7 23.72
Finding the full varying coefficient model
Model I Model age + s(t):alcohol use 8.9 0.008 Model age 206548.7 33.21
Model II Model I + s(t):physical activity 16.8 0.070 Model I 206547.6 36.40
Model III Model II + s(t):income 25.7 0.261 Model II 206549.0 38.45
Model IV Model II + s(t):marital status 24.4 0.539 Model II 206550.8 38.72
Model V Model II + s(t):education 36.5 0.227 Model II 206549.4 39.48
Model VI Model II + s(t):sex 24.4 0.125 Model II 206547.3 37.34
Model VII Model II + s(t):work status 21.4 0.550 Model II 206549.3 27.38
Model VIII Model II + s(t):region 26.5 0.470 Model II 206550.0 38.32
Model IX Model II + s(t):depression status 22.0 0.369 Model II 206548.9 37.42
Model X Model I + s(t) 10.4 0.006 Model I 206548.7 33.21
Notes: s(t) - spline of time
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