BranchGLM Vignette"

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

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Fitting GLMs

• BranchGLM() allows fitting of gaussian, binomial, gamma, and poisson GLMs with a variety of links available.
• Parallel computation can also be done to speed up the fitting process, but it is only useful for larger datasets.

Optimization methods

• The optimization method can be specified, the default method is fisher scoring, but BFGS and L-BFGS are also available.
• BFGS and L-BFGS typically perform better when there are many predictors in the model (at least 50 predictors), otherwise fisher scoring is typically faster.
• The grads argument is for L-BFGS only and it is the number of gradients that are stored at a time and are used to approximate the inverse information. The default value for this is 10, but another common choice is 5.
• The tol argument controls how strict the convergence criteria are, lower values of this will lead to more accurate results, but may also be slower.
• The method argument is ignored for linear regression and the OLS solution is used.

Initial values

• Initial values for the coefficient estimates may be specified via the init argument.
• If no initial values are specified, then the initial values are estimated via linear regression with the response variable transformed by the link function.

Parallel computation

• Parallel computation can be employed via openMP by setting the parallel argument to TRUE and setting the nthreads argument to the desired number of threads used.
• For smaller datasets this can actually slow down the model fitting process, so parallel computation should only be used for larger datasets.

Families

Gaussian

• Permissible links for the gaussian family are
• identity, which results in linear regression
• inverse
• log
• square root (sqrt)
• The most commonly used link function for the gaussian family is the identity link.
• The dispersion parameter for this family is estimated by using the mean square error.

# Loading in BranchGLM
library(BranchGLM)

# Fitting gaussian regression models for mtcars dataset
cars <- mtcars

## Identity link
BranchGLM(mpg ~ ., data = cars, family = "gaussian", link = "identity")

Gamma

• Permissible links for the gamma family are
• identity
• inverse, this is the canonical link for the gamma family
• log
• square root (sqrt)
• The most commonly used link functions for the gamma family are inverse and log.
• The dispersion parameter for this family is estimated via maximum likelihood,
  similar to the MASS::gamma.dispersion() function.

# Fitting gamma regression models for mtcars dataset
## Inverse link
GammaFit <- BranchGLM(mpg ~ ., data = cars, family = "gamma", link = "inverse")
GammaFit

## Log link
GammaFit <- BranchGLM(mpg ~ ., data = cars, family = "gamma", link = "log")
GammaFit

Poisson

• Permissible links for the poisson family are
• identity
• log, this is the canonical link for the poisson family
• square root (sqrt)
• The most commonly used link function for the poisson family is the log link.
• The dispersion parameter for this family is always 1.

# Fitting poisson regression models for warpbreaks dataset
warp <- warpbreaks

## Log link
BranchGLM(breaks ~ ., data = warp, family = "poisson", link = "log")

Binomial

• Permissible links for the binomial family are
• cloglog
• log
• logit, this is the canonical link for the binomial family
• probit
• The most commonly used link functions for the binomial family are logit and probit.
• The dispersion parameter for this family is always 1.

# Fitting binomial regression models for toothgrowth dataset
Data <- ToothGrowth

## Logit link
BranchGLM(supp ~ ., data = Data, family = "binomial", link = "logit")

## Probit link
BranchGLM(supp ~ ., data = Data, family = "binomial", link = "probit")

Functions for binomial GLMs

• BranchGLM has some utility functions for binomial GLMs
• Table() creates a confusion matrix based on the predicted classes and observed classes
• ROC() creates an ROC curve which can be plotted with plot()
• AUC() and Cindex() calculate the area under the ROC curve
• MultipleROCCurves() allows for the plotting of multiple ROC curves on the same plot

Table

# Fitting logistic regression model for toothgrowth dataset
catFit <- BranchGLM(supp ~ ., data = Data, family = "binomial", link = "logit")

Table(catFit)

ROC

# Creating ROC curve
catROC <- ROC(catFit)

plot(catROC, main = "ROC Curve", col = "indianred")

Cindex/AUC

# Getting Cindex/AUC
Cindex(catFit)

AUC(catFit)

MultipleROCPlots

# Showing ROC plots for logit, probit, and cloglog
probitFit <- BranchGLM(supp ~ . ,data = Data, family = "binomial", 
                       link = "probit")

cloglogFit <- BranchGLM(supp ~ . ,data = Data, family = "binomial", 
                       link = "cloglog")

MultipleROCCurves(catROC, ROC(probitFit), ROC(cloglogFit), 
                  names = c("Logistic ROC", "Probit ROC", "Cloglog ROC"))

Using predictions

• For each of the methods used in this section predicted probabilities and observed classes can also be supplied instead of the BranchGLM object.

preds <- predict(catFit)

Table(preds, Data$supp)

AUC(preds, Data$supp)

ROC(preds, Data$supp) |> plot(main = "ROC Curve", col = "deepskyblue")

Useful functions

• BranchGLM has many utility functions for GLMs such as
• coef() to extract the coefficients
• logLik() to extract the log likelihood
• AIC() to extract the AIC
• BIC() to extract the BIC
• predict() to obtain predictions from the fitted model
• The coefficients, standard errors, wald test statistics, and p-values are stored in the coefficients slot of the fitted model

# Predict method
predict(GammaFit)

# Accessing coefficients matrix
GammaFit$coefficients

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