Regresión escalonada utilizando valores p para eliminar variables con valores p no significativos

Muéstrale a tu jefe lo siguiente:

set.seed(100)
x1 <- runif(100,0,1)
x2 <- as.factor(sample(letters[1:3],100,replace=T))

y <- x1+x1*(x2=="a")+2*(x2=="b")+rnorm(100)
summary(lm(y~x1*x2))

Que da:

            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.1525     0.3066  -0.498  0.61995    
x1            1.8693     0.6045   3.092  0.00261 ** 
x2b           2.5149     0.4334   5.802 8.77e-08 ***
x2c           0.3089     0.4475   0.690  0.49180    
x1:x2b       -1.1239     0.8022  -1.401  0.16451    
x1:x2c       -1.0497     0.7873  -1.333  0.18566    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Ahora, basado en los valores p, ¿excluiría cuál? x2 es más significativo y más no significativo al mismo tiempo.

Edit : Para aclarar : Este exaxmple no es el mejor, como se indica en los comentarios. El procedimiento en Stata y SPSS es AFAIK tampoco basado en los valores de p de la prueba T en los coeficientes, sino en la prueba F después de la eliminación de una de las variables.

Tengo un función que hace exactamente eso. Esta es una selección en "el valor p", pero no de la prueba T en los coeficientes o en los resultados de anova. Bueno, siéntete libre de usarlo si te parece útil.

#####################################
# Automated model selection
# Author      : Joris Meys
# version     : 0.2
# date        : 12/01/09
#####################################
#CHANGE LOG
# 0.2   : check for empty scopevar vector
#####################################

# Function has.interaction checks whether x is part of a term in terms
# terms is a vector with names of terms from a model
has.interaction <- function(x,terms){
    out <- sapply(terms,function(i){
        sum(1-(strsplit(x,":")[[1]] %in% strsplit(i,":")[[1]]))==0
    })
    return(sum(out)>0)
}

# Function Model.select
# model is the lm object of the full model
# keep is a list of model terms to keep in the model at all times
# sig gives the significance for removal of a variable. Can be 0.1 too (see SPSS)
# verbose=T gives the F-tests, dropped var and resulting model after 
model.select <- function(model,keep,sig=0.05,verbose=F){
      counter=1
      # check input
      if(!is(model,"lm")) stop(paste(deparse(substitute(model)),"is not an lm object\n"))
      # calculate scope for drop1 function
      terms <- attr(model$terms,"term.labels")
      if(missing(keep)){ # set scopevars to all terms
          scopevars <- terms
      } else{            # select the scopevars if keep is used
          index <- match(keep,terms)
          # check if all is specified correctly
          if(sum(is.na(index))>0){
              novar <- keep[is.na(index)]
              warning(paste(
                  c(novar,"cannot be found in the model",
                  "\nThese terms are ignored in the model selection."),
                  collapse=" "))
              index <- as.vector(na.omit(index))
          }
          scopevars <- terms[-index]
      }

      # Backward model selection : 

      while(T){
          # extract the test statistics from drop.
          test <- drop1(model, scope=scopevars,test="F")

          if(verbose){
              cat("-------------STEP ",counter,"-------------\n",
              "The drop statistics : \n")
              print(test)
          }

          pval <- test[,dim(test)[2]]

          names(pval) <- rownames(test)
          pval <- sort(pval,decreasing=T)

          if(sum(is.na(pval))>0) stop(paste("Model",
              deparse(substitute(model)),"is invalid. Check if all coefficients are estimated."))

          # check if all significant
          if(pval[1]<sig) break # stops the loop if all remaining vars are sign.

          # select var to drop
          i=1
          while(T){
              dropvar <- names(pval)[i]
              check.terms <- terms[-match(dropvar,terms)]
              x <- has.interaction(dropvar,check.terms)
              if(x){i=i+1;next} else {break}              
          } # end while(T) drop var

          if(pval[i]<sig) break # stops the loop if var to remove is significant

          if(verbose){
             cat("\n--------\nTerm dropped in step",counter,":",dropvar,"\n--------\n\n")              
          }

          #update terms, scopevars and model
          scopevars <- scopevars[-match(dropvar,scopevars)]
          terms <- terms[-match(dropvar,terms)]

          formul <- as.formula(paste(".~.-",dropvar))
          model <- update(model,formul)

          if(length(scopevars)==0) {
              warning("All variables are thrown out of the model.\n",
              "No model could be specified.")
              return()
          }
          counter=counter+1
      } # end while(T) main loop
      return(model)
}