## first install all necessary packages

install.packages(c("Rcpp", "RcppEigen", "RcppNumerical", "VennDiagram", "visNetwork"))


## simulate data where covariate effects are different based on two stratifying factors

set.seed(123)

dat.sim <- genHierSparseData(ncats = 2, nvars = 100, nobs = 200, nobs.test = 1000)

## covariates 
x        <- dat.sim$x
x.test   <- dat.sim$x.test

## responses 
y        <- dat.sim$y
y.test   <- dat.sim$y.test

## stratifying factors
grp      <- dat.sim$group.ind
grp.test <- dat.sim$group.ind.test


## fit adaptive vennLasso model
## and select tuning parameter
## using 5-fold cross validation
fit <- cv.vennLasso(x = x, 
                    y = y,
                    groups = grp,
                    adaptive.lasso = TRUE,
                    family         = "gaussian",
                    gamma          = 1,          ## adaptive lasso tuning parameter
                    one.intercept  = FALSE,      ## allow separate intercept for each subpopulation
                    nfolds         = 5)

## plot CV MSEs and the tuning parameter
## which minimizes CV MSE
plot(x = log(fit$lambda), 
     y = fit$cvm, 
     ylab = "CV MSE",
     xlab = expression(log(lambda)))
abline(v = log(fit$lambda)[which.min(fit$cvm)])

## plot the number of variables selected for 
## each subpopulation using the tuning parameter
## selected by cross validation
plotSelections(fit)

#create predictions for a test set
test.preds <- predict(fit, x.test, grp.test, s = "lambda.min")

## evaluate performance of predictions

mean((y.test - test.preds) ^ 2)

mean((y.test - mean(y.test)) ^ 2)

min(fit$cvm)


## inspect the estimated coefficients.
## each column corresponds to a variable, each row is a subpopulaton
round(fit$vennLasso.fit$beta[,, which.min(fit$cvm)], 3)

## look at the true coefficients from the data-generating model:
round(dat.sim$beta.mat, 3)

## compare the first few variables
round(fit$vennLasso.fit$beta[, 2:9, which.min(fit$cvm)], 3)
round(dat.sim$beta.mat[, 1:8], 3)