Author: Jared Huling
Date: 2025-12-16

# Quick Usage Guide to the ‘fastglm’ Package

#### Jared Huling

#### 2025-12-16

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

    devtools::install_github("jaredhuling/fastglm")

and loaded via:

    library(fastglm)
    #> Loading required package: bigmemory

## Example

Currently, the `fastglm` package 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(cbind(ncases, ncontrols) ~ 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)
    #>
    #> Call:
    #> fastglm.default(x = x, y = y, family = binomial(link = "cloglog"))
    #>
    #> Coefficients:
    #>                Estimate Std. Error z value Pr(>|z|)
    #> (Intercept)    -4.29199    0.29777 -14.414  < 2e-16 ***
    #> agegp.L         3.30677    0.63454   5.211 1.88e-07 ***
    #> agegp.Q        -1.35525    0.57310  -2.365    0.018 *
    #> agegp.C         0.20296    0.43333   0.468    0.640
    #> agegp^4         0.15056    0.29318   0.514    0.608
    #> agegp^5        -0.23425    0.17855  -1.312    0.190
    #> unclass(tobgp)  0.33276    0.07285   4.568 4.93e-06 ***
    #> unclass(alcgp)  0.80384    0.07538  10.664  < 2e-16 ***
    #> ---
    #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    #>
    #> (Dispersion parameter for binomial family taken to be 1)
    #>
    #>     Null deviance: 61.609  on 87  degrees of freedom
    #> Residual deviance: 96.950  on 80  degrees of freedom
    #> AIC: 228
    #>
    #> Number of Fisher Scoring iterations: 6

## Computational stability

The `fastglm` package does not compromise computational stability for speed. In fact, for many situations where `glm()` and even `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. The `fastglm()` package uses a similar step-halving technique as `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

    system.time(gfit1 <- fastglm(cbind(1, x), y, family = Gamma(link = "sqrt")))
    #>    user  system elapsed
    #>   0.257   0.004   0.262

    system.time(gfit2 <- glm(y~x, family = Gamma(link = "sqrt")) )
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: glm.fit: algorithm did not converge
    #>    user  system elapsed
    #>   1.343   0.025   1.369

    system.time(gfit3 <- glm2::glm2(y~x, family = Gamma(link = "sqrt")) )
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #> Warning: step size truncated due to increasing deviance
    #>    user  system elapsed
    #>   1.024   0.021   1.048

    ## Note that fastglm() returns estimates with the
    ## largest likelihood
    logLik(gfit1)
    #> 'log Lik.' -16030.81 (df=102)
    logLik(gfit2)
    #> 'log Lik.' -16704.05 (df=102)
    logLik(gfit3)
    #> 'log Lik.' -16046.66 (df=102)

    coef(gfit1)[1:5]
    #>  (Intercept)           X1           X2           X3           X4
    #>  1.429256009  0.125873599  0.005321164 -0.129389740  0.238937255
    coef(gfit2)[1:5]
    #>   (Intercept)            x1            x2            x3            x4
    #>  1.431168e+00  1.251936e-01 -6.896739e-05 -1.281857e-01  2.366473e-01
    coef(gfit3)[1:5]
    #>   (Intercept)            x1            x2            x3            x4
    #>  1.426864e+00  1.242616e-01 -9.860241e-05 -1.254873e-01  2.361301e-01

    ## check convergence of fastglm
    gfit1$converged
    #> [1] TRUE
    ## number of IRLS iterations
    gfit1$iter
    #> [1] 17

    ## now check convergence for glm()
    gfit2$converged
    #> [1] FALSE
    gfit2$iter
    #> [1] 25

    ## check convergence for glm2()
    gfit3$converged
    #> [1] TRUE
    gfit3$iter
    #> [1] 19

    ## 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)) )
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: step size truncated: out of bounds
    #> Warning: glm.fit: algorithm did not converge
    #> Warning: glm.fit: algorithm stopped at boundary value
    #>    user  system elapsed
    #>   5.225   0.105   5.330

    gfit2$converged
    #> [1] FALSE
    gfit2$iter
    #> [1] 100

    logLik(gfit1)
    #> 'log Lik.' -16030.81 (df=102)
    logLik(gfit2)
    #> 'log Lik.' -16068.27 (df=102)