Quick Usage Guide to the 'fastglm' Package
In fastglm: Fast and Stable Fitting of Generalized Linear Models using 'RcppEigen'

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  warning = FALSE,
  echo = TRUE,
  eval = TRUE
)

The fastglm package is intended to be a fast and stable alternative to the glm() and glm2::glm2() functions for fitting generalized linear models. fastglm is compatible with R's family objects (see ?family). The package can be installed via

pak::pak("fastglm")
# pak::pak("jaredhuling/fastglm") #development version

and loaded via:

library(fastglm)

Example

The main package function is fastglm(). Currently, fastglm() does not allow for formula-based data input and is restricted to matrices. We use the following example to demonstrate the usage of fastglm():

data(esoph)
x <- model.matrix(~ agegp + unclass(tobgp) + unclass(alcgp),
                  data = esoph)

y <- cbind(esoph$ncases, esoph$ncontrols)

gfit1 <- fastglm(x = x, y = y, family = binomial(link = "cloglog"))

summary(gfit1)

Alternatively, to use the built-in function of glm() for processing formulas and data frames, we can use glm() with method = fastglm_fit to call the fastglm fitting functionality:

gfit2 <- glm(cbind(ncases, ncontrols) ~ agegp + unclass(tobgp) +
                 unclass(alcgp), data = esoph,
             family = binomial(link = "cloglog"),
             method = fastglm_fit)

summary(gfit2, refit = FALSE)

Setting refit = FALSE in summary() uses the standard errors computed by the internal fitting functions of fastglm. The default, refit = TRUE, re-fits the model using glm() with method = "glm.fit" and one IRLS iteration with the coefficients computed previously as the starting values.

Computational stability

fastglm does not compromise computational stability for speed. In fact, for many situations where glm() and even glm2::glm2() do not converge, fastglm() does converge.

As an example, consider the following data scenario, where the response distribution is (mildly) misspecified, but the link function is quite badly misspecified. In such scenarios, the standard IRLS algorithm tends to have convergence issues. The glm2 package was designed to handle such cases, however, it still can have convergence issues. fastglm uses a similar step-halving technique as glm2::glm2(), but it starts at better initialized values and thus tends to have better convergence properties in practice.

set.seed(1)
x <- matrix(rnorm(10000 * 100), ncol = 100)
y <- exp(0.25 * x[,1] - 0.25 * x[,3] + 0.5 * x[,4] - 0.5 * x[,5] + rnorm(10000)) + 0.1


# fastglm
system.time(gfit1 <- glm(y ~ x, family = Gamma(link = "sqrt"),
                         method = fastglm_fit))

# glm
system.time(gfit2 <- glm(y ~ x, family = Gamma(link = "sqrt")))

# glm2
system.time(gfit3 <- glm(y ~ x, family = Gamma(link = "sqrt"),
                         method = glm2::glm.fit2))

## Note that fastglm() returns estimates with the
## largest likelihood
logLik(gfit1)
logLik(gfit2)
logLik(gfit3)

coef(gfit1)[1:5]
coef(gfit2)[1:5]
coef(gfit3)[1:5]

## check convergence of fastglm
gfit1$converged
## number of IRLS iterations
gfit1$iter

## now check convergence for glm()
gfit2$converged
gfit2$iter

## check convergence for glm2()
gfit3$converged
gfit3$iter


## increasing number of IRLS iterations for glm() does not help that much
system.time(gfit2 <- glm(y ~ x, family = Gamma(link = "sqrt"),
                         control = list(maxit = 100)))

gfit2$converged
gfit2$iter

logLik(gfit1)
logLik(gfit2)