Variable selection for heterogeneous populations using the vennLasso penalty
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vennLasso

The vennLasso package provides methods for hierarchical variable selection for models with covariate effects stratified by multiple binary factors.

Installation and Help Files

The vennLasso package can be installed from CRAN using:

install.packages("vennLasso")

The development version can be installed using the devtools package:

devtools::install_github("jaredhuling/vennLasso")

or by cloning and building.

Load the vennLasso package:

library(vennLasso)

Access help file for the main fitting function vennLasso() by running:

?vennLasso

Help file for cross validation function cv.vennLasso() can be accessed by running:

?cv.vennLasso

A Quick Example

Simulate heterogeneous data:

set.seed(100)
dat.sim <- genHierSparseData(ncats = 3,  # number of stratifying factors
                             nvars = 25, # number of variables
                             nobs = 150, # number of observations per strata
                             nobs.test = 10000,
                             hier.sparsity.param = 0.5,
                             prop.zero.vars = 0.75, # proportion of variables
                                                   # zero for all strata
                             snr = 0.5,  # signal-to-noise ratio
                             family = "gaussian")

# design matrices
x        <- dat.sim$x
x.test   <- dat.sim$x.test

# response vectors
y        <- dat.sim$y
y.test   <- dat.sim$y.test

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

Inspect the populations for each strata:

plotVenn(grp)

Fit vennLasso model with tuning parameter selected with 5-fold cross validation:

fit.adapt <- cv.vennLasso(x, y,
                          grp,
                          adaptive.lasso = TRUE,
                          nlambda        = 50,
                          family         = "gaussian",
                          standardize    = FALSE,
                          intercept      = TRUE,
                          nfolds         = 5)

Plot selected variables for each strata (not run):

library(igraph)
## 
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union
plotSelections(fit.adapt)
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Num vars selected: 10<\/p>","

Num vars selected: 5<\/p>","

Num vars selected: 6<\/p>","

Num vars selected: 2<\/p>","

Num vars selected: 9<\/p>","

Num vars selected: 7<\/p>","

Num vars selected: 9<\/p>","

Num vars selected: 16<\/p>"],"x":[-0.444444444444444,-1,-0.333333333333333,0.333333333333333,-0.666666666666667,0.333333333333333,1,0.222222222222222],"y":[-1,1,1,1,0,0,0,-1]},"edges":{"from":[4,6,4,7,8,6,7,8,8],"to":[2,2,3,3,4,5,5,6,7],"value":[5,5,6,6,9,2,2,7,9]},"nodesToDataframe":true,"edgesToDataframe":true,"options":{"width":"100%","height":"100%","nodes":{"shape":"dot","mass":1,"physics":false,"font":{"size":35}},"manipulation":{"enabled":false},"edges":{"smooth":true},"physics":{"stabilization":false},"interaction":{"hover":true,"tooltipDelay":0}},"groups":null,"width":null,"height":null,"idselection":{"enabled":true,"style":"width: 150px; height: 26px","useLabels":true},"byselection":{"enabled":false,"style":"width: 150px; height: 26px","multiple":false,"hideColor":"rgba(200,200,200,0.5)"},"main":null,"submain":null,"footer":null,"igraphlayout":{"type":"full"},"highlight":{"enabled":true,"hoverNearest":true,"degree":1,"algorithm":"all","hideColor":"rgba(200,200,200,0.5)","labelOnly":true},"collapse":{"enabled":false,"fit":false,"resetHighlight":true,"clusterOptions":null},"tooltipStay":300,"tooltipStyle":"position: fixed;visibility:hidden;padding: 5px;white-space: nowrap;font-family: verdana;font-size:14px;font-color:#000000;background-color: #f5f4ed;-moz-border-radius: 3px;-webkit-border-radius: 3px;border-radius: 3px;border: 1px solid #808074;box-shadow: 3px 3px 10px rgba(0, 0, 0, 0.2);"},"evals":[],"jsHooks":[]}</script>

Predict response for test data:

preds.vl <- predict(fit.adapt, x.test, grp.test, s = "lambda.min",
                    type = 'response')

Evaluate mean squared error:

mean((y.test - preds.vl) ^ 2)
## [1] 0.6852124
mean((y.test - mean(y.test)) ^ 2)
## [1] 1.011026

Compare with naive model with all interactions between covariates and stratifying binary factors:

df.x <- data.frame(y = y, x = x, grp = grp)
df.x.test <- data.frame(x = x.test, grp = grp.test)

# create formula for interactions between factors and covariates
form <- paste("y ~ (", paste(paste0("x.", 1:ncol(x)), collapse = "+"), ")*(grp.1*grp.2*grp.3)" )

Fit linear model and generate predictions for test set:

lmf <- lm(as.formula(form), data = df.x)

preds.lm <- predict(lmf, df.x.test)

Evaluate mean squared error:

mean((y.test - preds.lm) ^ 2)
## [1] 0.8056107
mean((y.test - preds.vl) ^ 2)
## [1] 0.6852124