Fit Generalized Linear Mixed Model via PQL

Fit generalized linear mixed model (GLMM) with a single random effect using penalized quasi-likelihood (PQL)

Efficient Fit of Generalized Linear Mixed Model with a Single Random Effect

Usage

fastglmm(
  formula,
  data,
  family = gaussian(),
  weights = NULL,
  delta = NULL,
  delta.range = c(-10, 10),
  maxit = 100,
  tol = 0.001,
  tol.eta = 0.001,
  doCoxReid = nrow(data) < 1000,
  lambda = 0,
  nthreads = 6
)

Arguments

formula

a two-sided linear formula object describing both the fixed-effects and random-effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars (|) separating expressions for design matrices from grouping factors.

data

an optional data frame containing the variables named in

family

a description of the error distribution and link function to be used in the model.

weights

an optional vector of prior weights with a value for each sample.

delta

if NULL estimate delta, if value is given uses this fixed value

delta.range

min and max values (in log space), of the search space for delta to fit the random effect

maxit

max number of PQL iterations

tol

convergence criterion for the 1D search of the delta space

tol.eta

convergence criterion eta in the PQL iteration

doCoxReid

use Cox-Reid correction for estimating theta in negative binomial model

lambda

ridge shrinkage parameter

nthreads

number of threads

Value

model fit object

Examples

library(MASS)
library(lme4)
#> Loading required package: Matrix
#> 
#> Attaching package: ‘lme4’
#> The following object is masked from ‘package:nlme’:
#> 
#>     lmList

# GLMM via Laplace approximation
fit = glmer(y ~ trt + I(week > 2) + (1 | ID),
  family = binomial(), data = bacteria)
coef(summary(fit))
#>                   Estimate Std. Error   z value     Pr(>|z|)
#> (Intercept)      3.5479411  0.6957868  5.099178 3.411311e-07
#> trtdrug         -1.3666520  0.6769898 -2.018719 4.351647e-02
#> trtdrug+        -0.7826412  0.6831225 -1.145682 2.519267e-01
#> I(week > 2)TRUE -1.5984897  0.4759391 -3.358601 7.833796e-04

# GLMM via PQL
fit = glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
  family = binomial, data = bacteria, verbose = FALSE)
coef(summary(fit))
#>                      Value Std.Error  DF   t-value      p-value
#> (Intercept)      3.4120140 0.5185033 169  6.580506 5.646616e-10
#> trtdrug         -1.2473553 0.6440635  47 -1.936696 5.880736e-02
#> trtdrug+        -0.7543273 0.6453978  47 -1.168779 2.483867e-01
#> I(week > 2)TRUE -1.6072570 0.3583379 169 -4.485311 1.340324e-05

# GLMM via PQL
fit = fastglmm(y ~ trt + I(week > 2) + (1 | ID),
  family = binomial(), data = bacteria)
coef(summary(fit))
#>                   Estimate Std. Error    df    t value     Pr(>|t|)
#> (Intercept)      3.4127450  0.6552910 267.1  5.2079839 3.817213e-07
#> trtdrug         -1.2475583  0.8140663 123.8 -1.5325020 1.279496e-01
#> trtdrug+        -0.7545406  0.8157308 131.8 -0.9249872 3.566634e-01
#> I(week > 2)TRUE -1.6075955  0.4527311 485.7 -3.5508840 4.213332e-04