# Bootstrap for Generalized Linear Model Parametric bootstrap for generalized linear model. ```r bootglm(model, data, func, B, ...) ``` ## Arguments - `model`: An object of class `lm` or `glm`. - `data`: The dataframe used to fit the model. - `func`: The function to apply to each sample. - `B`: A positive integer; the number of bootstrap replications - `...`: Optional additional arguments for the `func` function. ## Returns `bootglm` returns an object of class `boodd` (see class.boodd ). ## Details The parametric bootstrap simply consists in resampling data in the model with estimated parameters. `bootglm` uses this principle for Generalized Linear Models (GLM) conditionally to the explanatory variables (see Beran (1997)) for the conditions of validity of this method. ## Examples ```r B <- 999 x <- runif(100) e <- rnorm(100) y <- x + e>0 data <- data.frame(x,y) glm_probit <- glm(y ~ x, family=binomial(link="probit"),data=data) # Define the function to bootstrap: the mle in the probit model coeff <- function(data){gg=glm(y ~ x, family=binomial(link="probit"),data=data)$coeff} boo1 <- bootglm(glm_probit,data,coeff,B) # parametric bootstrap of the coeffitients of a probit model plot(boo1,main=c("Boostrap of GLM : probit model","Coefficient")) # coeffv : a function to return coeff and variance of coefficients coeffv <- function(data){ gg <- glm(y~ x, family=binomial(link="probit"),data=data) var <- diag(summary(gg)$cov.u) c(gg$coeff,var) } # Parametric bootstrap of all coeff and variances boo2 <- bootglm(glm_probit,data,coeffv,B) # Construct all type of confidence intervals including bootstrap-t # and symmetric bootstrap-t confint(boo2,method="all") # Family Poisson (Poisson regression) counts <- c(18,17,15,20,10,20,25,13,12) outcome <- gl(3,1,9) treatment <- gl(3,3) data <- data.frame(treatment,outcome,counts) gl <- glm(counts ~ outcome + treatment,family=poisson()) meancounts <- function(data) {mean(data$counts)} boo3 <- bootglm(gl,data,meancounts,B) confint(boo3,method="all") plot(boo3) ``` ## References Bertail, P. and Dudek, A. (2025). **Bootstrap for Dependent Data, with an R package** (by Bernard Desgraupes and Karolina Marek)- submitted. Beran, R. (1997). Diagnosing Bootstrap Success, **Annals of the Institute of Statistical Mathematics**, 49 , 1-24. ## See Also `bootsemi`.

bootglm function