Fit Generalized Linear Mixed Models via PQL

Fit a GLMM model with multivariate normal random effects, using Penalized Quasi-Likelihood.

glmmPQL(fixed, random, family, data, correlation, weights,
        control, niter = 10, verbose = TRUE, ...)

Arguments

fixed	a two-sided linear formula giving fixed-effects part of the model.
random	a formula or list of formulae describing the random effects.
family	a GLM family.
data	an optional data frame used as the first place to find variables in the formulae, `weights` and if present in `...`, `subset`.
correlation	an optional correlation structure.
weights	optional case weights as in `glm`.
control	an optional argument to be passed to `lme`.
niter	maximum number of iterations.
verbose	logical: print out record of iterations?
...	Further arguments for `lme`.

Value

A object of class "lme": see lmeObject.

Details

glmmPQL works by repeated calls to lme, so package nlme will be loaded at first use if necessary.

References

Schall, R. (1991) Estimation in generalized linear models with random effects. Biometrika 78, 719--727.

Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9--25.

Wolfinger, R. and O'Connell, M. (1993) Generalized linear mixed models: a pseudo-likelihood approach. Journal of Statistical Computation and Simulation 48, 233--243.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

library(nlme) # will be loaded automatically if omitted
summary(glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
                family = binomial, data = bacteria))
#> iteration 1
#> iteration 2
#> iteration 3
#> iteration 4
#> iteration 5
#> iteration 6
#> Linear mixed-effects model fit by maximum likelihood
#>  Data: bacteria 
#>   AIC BIC logLik
#>    NA  NA     NA
#> 
#> Random effects:
#>  Formula: ~1 | ID
#>         (Intercept)  Residual
#> StdDev:    1.410637 0.7800511
#> 
#> Variance function:
#>  Structure: fixed weights
#>  Formula: ~invwt 
#> Fixed effects: y ~ trt + I(week > 2) 
#>                     Value Std.Error  DF   t-value p-value
#> (Intercept)      3.412014 0.5185033 169  6.580506  0.0000
#> trtdrug         -1.247355 0.6440635  47 -1.936696  0.0588
#> trtdrug+        -0.754327 0.6453978  47 -1.168779  0.2484
#> I(week > 2)TRUE -1.607257 0.3583379 169 -4.485311  0.0000
#>  Correlation: 
#>                 (Intr) trtdrg trtdr+
#> trtdrug         -0.598              
#> trtdrug+        -0.571  0.460       
#> I(week > 2)TRUE -0.537  0.047 -0.001
#> 
#> Standardized Within-Group Residuals:
#>        Min         Q1        Med         Q3        Max 
#> -5.1985361  0.1572336  0.3513075  0.4949482  1.7448845 
#> 
#> Number of Observations: 220
#> Number of Groups: 50 
 # an example of offset
summary(glmmPQL(y ~ trt + week, random = ~ 1 | ID,
                family = binomial, data = bacteria))
#> iteration 1
#> iteration 2
#> iteration 3
#> iteration 4
#> iteration 5
#> iteration 6
#> Linear mixed-effects model fit by maximum likelihood
#>  Data: bacteria 
#>   AIC BIC logLik
#>    NA  NA     NA
#> 
#> Random effects:
#>  Formula: ~1 | ID
#>         (Intercept)  Residual
#> StdDev:    1.325243 0.7903088
#> 
#> Variance function:
#>  Structure: fixed weights
#>  Formula: ~invwt 
#> Fixed effects: y ~ trt + week 
#>                  Value Std.Error  DF   t-value p-value
#> (Intercept)  3.0302276 0.4791396 169  6.324310  0.0000
#> trtdrug     -1.2176812 0.6160113  47 -1.976719  0.0540
#> trtdrug+    -0.7886376 0.6193895  47 -1.273250  0.2092
#> week        -0.1446463 0.0392343 169 -3.686730  0.0003
#>  Correlation: 
#>          (Intr) trtdrg trtdr+
#> trtdrug  -0.622              
#> trtdrug+ -0.609  0.464       
#> week     -0.481  0.050  0.030
#> 
#> Standardized Within-Group Residuals:
#>        Min         Q1        Med         Q3        Max 
#> -4.2868074  0.2039043  0.3140333  0.5440835  1.9754065 
#> 
#> Number of Observations: 220
#> Number of Groups: 50 
summary(glmmPQL(y ~ trt + week + offset(week), random = ~ 1 | ID,
                family = binomial, data = bacteria))
#> iteration 1
#> iteration 2
#> iteration 3
#> iteration 4
#> iteration 5
#> iteration 6
#> Linear mixed-effects model fit by maximum likelihood
#>  Data: bacteria 
#>   AIC BIC logLik
#>    NA  NA     NA
#> 
#> Random effects:
#>  Formula: ~1 | ID
#>         (Intercept)  Residual
#> StdDev:    1.325243 0.7903088
#> 
#> Variance function:
#>  Structure: fixed weights
#>  Formula: ~invwt 
#> Fixed effects: y ~ trt + week + offset(week) 
#>                  Value Std.Error  DF    t-value p-value
#> (Intercept)  3.0302276 0.4791396 169   6.324310  0.0000
#> trtdrug     -1.2176812 0.6160113  47  -1.976719  0.0540
#> trtdrug+    -0.7886376 0.6193895  47  -1.273250  0.2092
#> week        -1.1446463 0.0392343 169 -29.174622  0.0000
#>  Correlation: 
#>          (Intr) trtdrg trtdr+
#> trtdrug  -0.622              
#> trtdrug+ -0.609  0.464       
#> week     -0.481  0.050  0.030
#> 
#> Standardized Within-Group Residuals:
#>        Min         Q1        Med         Q3        Max 
#> -4.2868074  0.2039043  0.3140333  0.5440835  1.9754065 
#> 
#> Number of Observations: 220
#> Number of Groups: 50