VariableSelection Vignette"

In BranchGLM: Efficient Branch and Bound Variable Selection for GLMs using 'RcppArmadillo'

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
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Performing variable selection

• Forward selection, backward elimination, and branch and bound selection can be done using VariableSelection().
• VariableSelection() can accept either a BranchGLM object or a formula along with the data and the desired family and link to perform the variable selection.
• Available metrics are AIC, BIC and HQIC, which are used to compare models and to select the best models.
• VariableSelection() returns some information about the search, more detailed information about the best models can be seen by using the summary() function.
• Note that VariableSelection() will properly handle interaction terms and categorical variables.
• keep can also be specified if any set of variables are desired to be kept in every model.

Metrics

• The 3 different metrics available for comparing models are the following
• Akaike information criterion (AIC), which typically results in models that are useful for prediction
  • $AIC = -2logLik + 2 \times p$
• Bayesian information criterion (BIC), which results in models that are more parsimonious than those selected by AIC
  • $BIC = -2logLik + \log{(n)} \times p$
• Hannan-Quinn information criterion (HQIC), which is in the middle of AIC and BIC
  • $HQIC = -2logLik + 2 * \log({\log{(n)})} \times p$

Stepwise methods

• Forward selection and backward elimination are both stepwise variable selection methods.
• They are not guaranteed to find the best model or even a good model, but they are very fast.
• Forward selection is recommended if the number of variables is greater than the number of observations or if many of the larger models don't converge.
• These methods will only return 1 best model.
• Parallel computation can be used for the methods, but is generally only necessary for large datasets.

Forward selection example

# Loading BranchGLM package
library(BranchGLM)

# Fitting gamma regression model
cars <- mtcars

# Fitting gamma regression with inverse link
GammaFit <- BranchGLM(mpg ~ ., data = cars, family = "gamma", link = "inverse")

# Forward selection with mtcars
forwardVS <- VariableSelection(GammaFit, type = "forward")
forwardVS

## Getting final model
fit(forwardVS, which = 1)

Backward elimination example

# Backward elimination with mtcars
backwardVS <- VariableSelection(GammaFit, type = "backward")
backwardVS

## Getting final model
fit(backwardVS, which = 1)

Branch and bound

• The branch and bound methods can be much slower than the stepwise methods, but they are guaranteed to find the best models.
• The branch and bound methods are typically much faster than an exhaustive search and can also be made even faster if parallel computation is used.

Branch and bound example

• If showprogress is true, then progress of the branch and bound algorithm will be reported occasionally.
• Parallel computation can be used with these methods and can lead to very large speedups.

# Branch and bound with mtcars
VS <- VariableSelection(GammaFit, type = "branch and bound", showprogress = FALSE)
VS

## Getting final model
fit(VS, which = 1)

• A formula with the data and the necessary BranchGLM fitting information can also be used instead of supplying a BranchGLM object.

# Can also use a formula and data
formulaVS <- VariableSelection(mpg ~ . ,data = cars, family = "gamma", 
                               link = "inverse", type = "branch and bound",
                               showprogress = FALSE, metric = "AIC")
formulaVS

## Getting final model
fit(formulaVS, which = 1)

Using bestmodels

• The bestmodels argument can be used to find the top k models according to the metric.

# Finding top 10 models
formulaVS <- VariableSelection(mpg ~ . ,data = cars, family = "gamma", 
                               link = "inverse", type = "branch and bound",
                               showprogress = FALSE, metric = "AIC", 
                               bestmodels = 10)
formulaVS

## Plotting results
plot(formulaVS, type = "b")

## Getting best model
fit(formulaVS, which = 1)

Using cutoff

• The cutoff argument can be used to find all models that have a metric value that is within cutoff of the minimum metric value found.

# Finding all models with an AIC within 2 of the best model
formulaVS <- VariableSelection(mpg ~ . ,data = cars, family = "gamma", 
                               link = "inverse", type = "branch and bound",
                               showprogress = FALSE, metric = "AIC", 
                               cutoff = 2)
formulaVS

## Plotting results
plot(formulaVS, type = "b")

Using keep

• Specifying variables via keep will ensure that those variables are kept through the selection process.

# Example of using keep
keepVS <- VariableSelection(mpg ~ . ,data = cars, family = "gamma", 
                               link = "inverse", type = "branch and bound",
                               keep = c("hp", "cyl"), metric = "AIC",
                               showprogress = FALSE, bestmodels = 10)
keepVS

## Getting summary and plotting results
plot(keepVS, type = "b")

## Getting final model
fit(keepVS, which = 1)

Convergence issues

• It is not recommended to use branch and bound if the upper models do not converge since it can make the algorithm very slow.
• Sometimes when using backwards selection and all the upper models that are tested do not converge, no final model can be selected.
• For these reasons, if there are convergence issues it is recommended to use forward selection.

BranchGLM documentation built on Aug. 31, 2023, 5:17 p.m.