'How to use Wald Ch-Sq test Statistic in a GAM to determine which smooth term has the largest impact on the response?
I am tasked with determining, from a summary function of a generalized linear model, which smooth term is most impactful to the response. Intuitively I understand that to be the smooth term with the largest Chi-Sq test stat listed in the summary, so it would be s(tests) in this case below:
Family: poisson
Link function: log
Formula:
daily_confirmed_cases ~ s(tests, k = 18) + s(vaccines, k = 18) +
s(people_fully_vaccinated, k = 18) + s(hosp) + s(icu) + s(ndate,
k = 18)
Parametric coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 7.405421 0.001489 4973 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df Chi.sq p-value
s(tests) 16.793 16.98 14076 <2e-16 ***
s(vaccines) 16.982 17.00 9744 <2e-16 ***
s(people_fully_vaccinated) 16.923 17.00 7337 <2e-16 ***
s(hosp) 8.988 9.00 6893 <2e-16 ***
s(icu) 8.985 9.00 7246 <2e-16 ***
s(ndate) 16.674 16.96 11156 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) = 0.965 Deviance explained = 97.7%
fREML = 19764 Scale est. = 1 n = 460
Is this approach true, and if so can you explain some rational as to why a high Chi-Sq stat indicates the greater impact on the GAM?
Thanks
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