Get all models from leaps regsubsets

Question

I used regsubsets to search for models. Is it possible to automatically create all lm from the list of parameter selections?

library(leaps)
leaps<-regsubsets(y ~ x1 + x2 + x3, data, nbest=1, method="exhaustive")
summary(leaps)$which
  (Intercept)      x1        x2    x3                                                                                   
1        TRUE   FALSE     FALSE  TRUE                                                                                   
2        TRUE   FALSE      TRUE  TRUE                                                                                   
3        TRUE    TRUE      TRUE  TRUE                                                                                   

Now i would manually do model_1 <- lm(y ~ x3) and so on. How can this be automated to have them in a list?

Answer 1

I don't know why you want a list of all models. summary and coef methods should serve you well. But I will first answer your question from a pure programming aspect, then come back to this point.

---

A simple way to do this is via reformulate:

reformulate(termlabels, response = NULL, intercept = TRUE)

Here is how:

## you are masking `leaps` and `data` function!!
leaps <- regsubsets(y ~ x1 + x2 + x3, data, nbest = 1, method = "exhaustive")
X <- summary(leaps)$which

xvars <- dimnames(X)[[2]][-1]  ## column names (all covariates except intercept)
responsevar <- "y"  ## name of response

lst <- vector("list", dim(X)[1])  ## set up an empty model list

## loop through all rows / model specifications
for (i in 1:dim(X)[1]) {
  id <- X[i, ]
  form <- reformulate(xvars[which(id[-1])], responsevar, id[1])
  lst[[i]] <- lm(form, data)
  }

There is no need for a *apply solution. lm is costly, so for loop has no overhead at all.

---

A faster way is to set up a model matrix containing all covariates, and select its columns dynamically (use assign attributes of the model matrix; especially true when you have factor variables). Model fitting is then via .lm.fit. However, you will have difficulty in producing model summary / prediction with raw output of .lm.fit unless you are a linear model guru, but I think summary(leaps) should return you various useful statistic already.

leaps:::coef.regsubsets function is an equivalence of this .lm.fit route. Simply do:

coef(leaps, 1:dim(X)[1], TRUE)

and you will get coefficients and variance-covariance matrix for all models.