Hi all,

I am not sure how to handle interactions with categorical predictors in the
GAM models. For example what is the different between these bellow two
models. Tests are indicating that they are different but their predictions
are essentially the same.

Thanks a bunch,

> gam.1 <- gam(mortality.under.2~ maternal_age_c+ I(maternal_age_c^2)+
+                s(birth_year,by=wealth) +
+                + wealth + sex +
+                residence+ maternal_educ + birth_order,
+              ,data=rwanda2,family="binomial")
>
> gam.2 <- gam(mortality.under.2~ maternal_age_c+ I(maternal_age_c^2)+
+                s(birth_year,by=wealth) +
+                 + sex +
+                residence+ maternal_educ + birth_order,
+              ,data=rwanda2,family="binomial")
>
> anova(gam.1,gam.2,test="Chi")
Analysis of Deviance Table

Model 1: mortality.under.2 ~ maternal_age_c + I(maternal_age_c^2) +
s(birth_year,
    by = wealth) + +wealth + sex + residence + maternal_educ +
    birth_order
Model 2: mortality.under.2 ~ maternal_age_c + I(maternal_age_c^2) +
s(birth_year,
    by = wealth) + +sex + residence + maternal_educ + birth_order
  Resid. Df Resid. Dev      Df Deviance  Pr(>Chi)
1     28986      24175
2     28989      24196 -3.6952  -21.378 0.0001938 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> str(rwanda2)
'data.frame': 29027 obs. of  18 variables:
 $ CASEID            : Factor w/ 10718 levels "        1  5  2",..: 289
2243 7475 9982 6689 10137 7426 428 8415 10426 ...
 $ mortality.under.2 : int  0 1 0 0 0 0 0 0 1 0 ...
 $ maternal_age_disct: Factor w/ 3 levels "-25","+35","25-35": 1 1 1 1 1 1
3 1 3 1 ...
 $ maternal_age      : int  18 21 21 23 21 22 26 18 27 21 ...
 $ time              : int  3 3 3 3 3 3 3 3 3 3 ...
 $ child_mortality   : num  0.232 0.232 0.232 0.232 0.232 ...
 $ democracy         : Factor w/ 1 level "dictatorship": 1 1 1 1 1 1 1 1 1
1 ...
 $ wealth            : Factor w/ 5 levels "Lowest quintile",..: 2 4 1 4 5 1
4 1 4 5 ...
 $ birth_year        : int  1970 1970 1970 1970 1970 1970 1970 1970 1970
1970 ...
 $ residence         : Factor w/ 2 levels "Rural","Urban": 1 1 1 1 2 1 1 1
1 2 ...
 $ birth_order       : int  1 2 2 5 1 1 3 1 2 2 ...
 $ maternal_educ     : Factor w/ 4 levels "Higher","No education",..: 3 2 2
3 4 2 3 2 2 2 ...
 $ sex               : Factor w/ 2 levels "Female","Male": 1 1 2 2 1 1 2 2
2 2 ...
 $ quinquennium      : Factor w/ 7 levels "00-5's","70-4",..: 2 2 2 2 2 2 2
2 2 2 ...
 $ time.1            : int  3 3 3 3 3 3 3 3 3 3 ...
 $ new_time          : int  0 0 0 0 0 0 0 0 0 0 ...
 $ maternal_age_c    : num  -6.12 -3.12 -3.12 -1.12 -3.12 ...
 $ birth_year_c      : num  -14.8 -14.8 -14.8 -14.8 -14.8 ...

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