How to predict and extract R Squared with .lm.fit? - r

Question

As the title suggest, I have seen some user mentioned that .lm.fit() functions has an advantage of more speed than a regular lm(), but when i look deeper at .lm.fit() in help, it is supposed to be a fitter functions, it returns a set of list instead of a model, which makes me to think is it still possible to extract components like R squared, Adj R Squared, and lastly do a predict() out of it?
Below is sample data and executions:
test_dat <- data.frame(y = rnorm(780, 20, 10))
for(b in 1:300){
name_var <- paste0("x",b)
test_dat[[name_var]] <- rnorm(780, 0.01 * b, 5)
}
tic()
obj_lm <- lm(y ~ ., data = test_dat)
print(class(obj_lm))
print(summary(obj_lm)$r.squared)
print(summary(obj_lm)$adj.r.squared)
predict(obj_lm)
toc() #approximately 0.4 seconds
tic()
datm <- as.matrix(test_dat)
obj_lm_fit <- .lm.fit(cbind(1,datm[,-1]), datm[,1])
print(class(obj_lm_fit))
toc() #approximately 0.2 seconds

Answer 1

Functions predict and resid are generic and since .lm.fit returns an object of class "list", all you have to do is to write methods implementing the definitions of what you want. Below are methods to compute fitted values, residuals and R^2.
set.seed(2023) # make the results reproducible
test_dat <- data.frame(y = rnorm(780, 20, 10))
for(b in 1:300){
name_var <- paste0("x",b)
test_dat[[name_var]] <- rnorm(780, 0.01 * b, 5)
}
obj_lm <- lm(y ~ ., data = test_dat)
datm <- as.matrix(test_dat)
obj_lm_fit <- .lm.fit(cbind(1,datm[,-1]), datm[,1])
#------------------------------------------------------------------------
# the methods for objects of class "list"
#
fitted.list <- function(object, X) {
X %*% coef(object)
}
resid.list <- residuals.list <- function(object, X, y) {
y_fitted <- fitted(object, X)
y - y_fitted
}
rsquared <- function(x, ...) UseMethod("rsquared")
rsquared.default <- function(x, ...) {
summary(x)$r.squared
}
rsquared.list <- function(object, X, y) {
e <- resid.list(object, X, y)
1 - sum(e^2)/sum( (y - mean(y))^2 )
}
rsquared(obj_lm_fit, cbind(1,datm[,-1]), datm[,1])
#> [1] 0.3948863
rsquared(obj_lm)
#> [1] 0.3948863
Created on 2023-01-03 with reprex v2.0.2
Edit 1
Added method to also calculate adj.R2
adj_rsquared_list <- function(object, X, y){
r2 <- rsquared.list(object, X, y)
k <- ncol(X) - 1
n <- nrow(X)
rate_of_error <- (1 - r2) * (n - 1) / (n - k - 1)
adj_r2 <- 1 - rate_of_error
return(adj_r2)
}
adj_rsquared_list(obj_lm_fit, cbind(1,datm[,-1]), datm[,1])
#> [1] 0.01590061
Edit 2
After the edit by Jovan, I have changed fitted.list above to use coef(), a function that extracts the first arguments list member "coefficients", if it exists, and rewrote the default and list methods of rsquared to accept a adj argument. The code to compute the adjusted R^2 is a copy&paste of Jovan's code.
rsquared <- function(x, ...) UseMethod("rsquared")
rsquared.default <- function(x, adj = FALSE, ...) {
if(adj) {
summary(x)$adj.r.squared
} else summary(x)$r.squared
}
rsquared.list <- function(object, X, y, adj = FALSE) {
e <- resid.list(object, X, y)
r2 <- 1 - sum(e^2)/sum( (y - mean(y))^2 )
if(adj) {
k <- ncol(X) - 1
n <- nrow(X)
rate_of_error <- (1 - r2) * (n - 1) / (n - k - 1)
adj_r2 <- 1 - rate_of_error
adj_r2
} else r2
}
# same as above
rsquared(obj_lm_fit, cbind(1,datm[,-1]), datm[,1])
#> [1] 0.3948863
rsquared(obj_lm)
#> [1] 0.3948863
# new, `adj = TRUE`
rsquared(obj_lm_fit, cbind(1,datm[,-1]), datm[,1], adj = TRUE)
#> [1] 0.01590061
rsquared(obj_lm, adj = TRUE)
#> [1] 0.01590061
Created on 2023-01-03 with reprex v2.0.2