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I am confused how to calculate r-squared for the glmnet fits (LASSO, elastic-net etc). One of the ways I have seen is through the cvm corresponding to one of lambdas:

cvfit2 <- glmnet::cv.glmnet(datam, fundm,alpha=1,nfolds=10)
cf<-coef(cvfit2, s = "lambda.1se")
i<-which(cvfit2$lambda == cvfit2$lambda.1se)
e<-cvfit2$cvm[i]
r2<-1-e/var(fundm)
r2
#[1]  0.4571688

The classic way via calculating the variance of the residuals:

datam2<-as.matrix(datam)
cc2<-as.matrix(cf[-1,]) #removing the intercept row
predict<-datam2 %*% cc2
err<-predict - fundm
View(err)
r2b<-1-var(err)/var(fundm)
r2b
#[1] 0.6100457

Quite a huge difference and I am not sure if the 1st way of calculating $R^2$ is correct.

My questions

  1. What is the correct way of calculating r-squared?

  2. A glmnet object has components dev.ratio and nulldev. From the glmnet docs:

    "The fraction of (null) deviance explained (for "elnet", this is the R-square)."

Should we rather use dev.ratio for the purpose of $R^2$ calculations? If yes, how to extract it for the given lambda index? The dev.ratio array has 100 values, but the cvfit2$lambda has only 88 values.

I am really confused and would appreciate your feedback.

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I'm using

r2 <- fit$glmnet.fit$dev.ratio[which(fitnet$glmnet.fit$lambda == fitnet$lambda.min)]

or if you have chosen the lambda.1se

r2 <- fit$glmnet.fit$dev.ratio[which(fitnet$glmnet.fit$lambda == fitnet$lambda.1se)] 

If you do a cross check with the traditional regression lm() and summary()$r.squared it will match the results if weights are close to the elastic net.

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I think I know why the two calculations produce different answers. The cvm variable from the cvm.glmnet object is a cross-validated error. It's calculated from the residuals in the validation folds. The predict() function on the other hand, is not cross-validated. It's calculated from the residuals of predictions on the whole data set.

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