Fit Generalized Linear Mixed Models via PQL — glmmPQL • MASS

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, list or environment 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 c("glmmPQL", "lme"): see lmeObject.

Details

glmmPQL works by repeated calls to lme, so namespace nlme will be loaded at first use. (Before 2015 it used to attach nlme but nowadays only loads the namespace.)

Unlike lme, offset terms are allowed in fixed – this is done by pre- and post-processing the calls to lme.

Note that the returned object inherits from class "lme" and that most generics will use the method for that class. As from version 3.1-158, the fitted values have any offset included, as do the results of calling predict.

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.

See also

Examples

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 an offset: the coefficient of 'week' changes by one.
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