causalreg (version 0.1.2)

cgam: Causal generalized additive model

Description

This function does a search for a causal submodel within the generalized additive model provided.

Usage

cgam(
  formula,
  family,
  data,
  alpha = 0.05,
  pval = c("bootstrap", "chi-squared"),
  B = 100,
  search = c("all", "stepwise"),
  ...
)

Value

A gam object of the selected causal submodel.

Arguments

formula

A formula object.

family

A distributional family object. Currently supported options are: binomial and poisson.

data

A data frame containing the variables in the model.

alpha

Significance level for statistical test.

pval

If pval="bootstrap", a bootstrap test is conducted to test whether Pearson risk is 1. When family="poisson" a chi-squared test can be conducted by setting pval="chi-square".

B

Number of bootstrap samples when pval="bootstrap". Default is 100.

search

If search="stepwise", a greedy forward stepwise search is conducted. Default is search="all", in which case all possible submodels are considered.

...

Further arguments to be passed to the gam function.

References

Polinelli, A., V. Vinciotti and E.C. Wit. (2026). "Causal generalized linear models via Pearson risk invariance" Journal of Causal Inference.

Examples

##############################
#causal Poisson gam##########
n<-1000
set.seed(123)
X1<-rnorm(n,0,1)
Y<-rpois(n,exp(sin(X1)))
X2<-log(Y+1)+rnorm(n,0,0.5)
data<-data.frame(X1, X2, Y)
cm_all<-cgam(Y ~ s(X1)+s(X2),"poisson",data,pval="chi-square",search="all")
cm_all$model.opt
cm_step<-cgam(Y ~ s(X1)+s(X2),"poisson",data,pval="chi-square",search="stepwise")
cm_step$model.opt
# \donttest{
#bigger simulation with 7 covariates
set.seed(123)
n<-1000
X1<-rnorm(n=n,sd=sqrt(0.04))
X2<-X1+rnorm(n=n,sd=sqrt(0.04))
X3<-X1+X2+rnorm(n=n,sd=sqrt(0.04))
m<-sin(X2*5)+X3^3
Z<-m+rnorm(n=n,sd=sqrt(0.04))
X4<-X2+rnorm(n=n,sd=sqrt(0.04))
X5<-Z+rnorm(n=n,sd=sqrt(0.04))
X6<-Z+rnorm(n=n,sd=sqrt(0.04))
X7<-X6+rnorm(n=n,sd=sqrt(0.04))
Y<-qpois(pnorm(Z, mean = m, sd = sqrt(0.04)), lambda=exp(m))
dat<-data.frame(X1, X2, X3, X4, X5, X6, X7,Y)
fml<- Y~s(X1)+s(X2)+s(X3)+s(X4)+s(X5)+s(X6)+s(X7)
mod.all <-cgam(fml,"poisson",dat,pval="chi-square",search="all")
mod.all$model.opt
mod.step <-cgam(fml,"poisson",dat,pval="chi-square",search="stepwise")
mod.step$model.opt
####################################
#causal logistic gam################
n<-1000
set.seed(123)
X1<-rnorm(n,0,1)
Y<-rbinom(n,1,exp(X1)/(1+exp(X1)))
flip<-rbinom(n,1,0.1)
X2<-(1-flip)*Y+rnorm(n,0,0.3)
data<-data.frame(X1, X2, Y)
set.seed(1)
cm_all<-cgam(Y ~ s(X1)+s(X2),"binomial",data,pval="bootstrap",search="all")
cm_all$model.opt
set.seed(1)
cm_step<-cgam(Y ~ s(X1)+s(X2),"binomial",data,pval="bootstrap",search="stepwise")
cm_step$model.opt
# }