BranchGLM: Fits GLMs

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

Fits GLMs

Description

Fits generalized linear models via RcppArmadillo. Also has the ability to fit the models with parallelization via OpenMP.

Usage

BranchGLM(
  formula,
  data,
  family,
  link,
  offset = NULL,
  method = "Fisher",
  grads = 10,
  parallel = FALSE,
  nthreads = 8,
  tol = 1e-06,
  maxit = NULL,
  init = NULL,
  fit = TRUE,
  contrasts = NULL,
  keepData = TRUE,
  keepY = TRUE
)

BranchGLM.fit(
  x,
  y,
  family,
  link,
  offset = NULL,
  method = "Fisher",
  grads = 10,
  parallel = FALSE,
  nthreads = 8,
  init = NULL,
  maxit = NULL,
  tol = 1e-06
)

Arguments

formula	a formula for the model.
data	a dataframe that contains the response and predictor variables.
family	distribution used to model the data, one of "gaussian", "gamma", "binomial", or "poisson".
link	link used to link mean structure to linear predictors. One of "identity", "logit", "probit", "cloglog", "sqrt", "inverse", or "log".
offset	offset vector, by default the zero vector is used.
method	one of "Fisher", "BFGS", or "LBFGS". BFGS and L-BFGS are quasi-newton methods which are typically faster than Fisher's scoring when there are many covariates (at least 50).
grads	number of gradients used to approximate inverse information with, only for method = "LBFGS".
parallel	whether or not to make use of parallelization via OpenMP.
nthreads	number of threads used with OpenMP, only used if parallel = TRUE.
tol	tolerance used to determine model convergence.
maxit	maximum number of iterations performed. The default for Fisher's scoring is 50 and for the other methods the default is 200.
init	initial values for the betas, if not specified then they are automatically selected.
fit	a logical value to indicate whether to fit the model or not. Setting this to false will make it so no coefficients matrix or variance-covariance matrix are returned.
contrasts	see contrasts.arg of model.matrix.default.
keepData	Whether or not to store a copy of data and design matrix, the default is TRUE. If this is FALSE, then the results from this cannot be used inside of VariableSelection.
keepY	Whether or not to store a copy of y, the default is TRUE. If this is FALSE, then the binomial GLM helper functions may not work and this cannot be used inside of VariableSelection.
x	design matrix used for the fit, must be numeric.
y	outcome vector, must be numeric.

Details

Can use BFGS, L-BFGS, or Fisher's scoring to fit the GLM. BFGS and L-BFGS are typically faster than Fisher's scoring when there are at least 50 covariates and Fisher's scoring is typically best when there are fewer than 50 covariates. This function does not currently support the use of weights. In the special case of gaussian regression with identity link the method argument is ignored and the normal equations are solved directly.

The models are fit in C++ by using Rcpp and RcppArmadillo. In order to help convergence, each of the methods makes use of a backtracking line-search using the strong Wolfe conditions to find an adequate step size. There are also two conditions used to control convergence, the first is whether there is a sufficient decrease in the negative log-likelihood, and the other is whether the norm of the score is sufficiently small. The tol argument controls both of these criteria. If the algorithm fails to converge, then iterations will be -1.

All observations with any missing values are removed before model fitting.

The dispersion parameter for gamma regression is estimated via maximum likelihood, very similar to the gamma.dispersion function from the MASS package.

BranchGLM.fit can be faster than calling BranchGLM if the x matrix and y vector are already available, but doesn't return as much information. The object returned by BranchGLM.fit is not of class BranchGLM, so all of the methods for BranchGLM objects such as predict or VariableSelection cannot be used.

Value

BranchGLM returns a BranchGLM object which is a list with the following components

coefficients	a matrix with the coefficients estimates, SEs, wald test statistics, and p-values
iterations	number of iterations it took the algorithm to converge, if the algorithm failed to converge then this is -1
dispersion	the value of the dispersion parameter
logLik	the log-likelihood of the fitted model
vcov	the variance-covariance matrix of the fitted model
resDev	the residual deviance of the fitted model
AIC	the AIC of the fitted model
preds	predictions from the fitted model
linpreds	linear predictors from the fitted model
tol	tolerance used to fit the model
maxit	maximum number of iterations used to fit the model
formula	formula used to fit the model
method	iterative method used to fit the model
grads	number of gradients used to approximate inverse information for L-BFGS
y	y vector used in the model, not included if keepY = FALSE
x	design matrix used to fit the model, not included if keepData = FALSE
offset	offset vector in the model, not included if keepData = FALSE
data	original dataframe supplied to the function, not included if keepData = FALSE
mf	the model frame, not included if keepData = FALSE
numobs	number of observations in the design matrix
names	names of the variables
yname	name of y variable
parallel	whether parallelization was employed to speed up model fitting process
missing	number of missing values removed from the original dataset
link	link function used to model the data
family	family used to model the data
ylevel	the levels of y, only included for binomial glms
xlev	the levels of the factors in the dataset
terms	the terms object used

BranchGLM.fit returns a list with the following components

coefficients	a matrix with the coefficients estimates, SEs, wald test statistics, and p-values
iterations	number of iterations it took the algorithm to converge, if the algorithm failed to converge then this is -1
dispersion	the value of the dispersion parameter
logLik	the log-likelihood of the fitted model
vcov	the variance-covariance matrix of the fitted model
resDev	the residual deviance of the fitted model
AIC	the AIC of the fitted model
preds	predictions from the fitted model
linpreds	linear predictors from the fitted model
tol	tolerance used to fit the model
maxit	maximum number of iterations used to fit the model

Examples

Data <- iris
### Using BranchGLM
BranchGLM(Sepal.Length ~ ., data = Data, family = "gaussian", link = "identity")

### Using BranchGLM.fit
x <- model.matrix(Sepal.Length ~ ., data = Data)
y <- Data$Sepal.Length
BranchGLM.fit(x, y, family = "gaussian", link = "identity")

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