glmmPQL {MASS} | R Documentation |

## Fit Generalized Linear Mixed Models via PQL

### Description

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

### Usage

```
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, |

`correlation` |
an optional correlation structure. |

`weights` |
optional case weights as in |

`control` |
an optional argument to be passed to |

`niter` |
maximum number of iterations. |

`verbose` |
logical: print out record of iterations? |

`...` |
Further arguments for |

### 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`

.

### Value

A object of class `c("glmmPQL", "lme")`

: see `lmeObject`

.

### 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))
## an example of an offset: the coefficient of 'week' changes by one.
summary(glmmPQL(y ~ trt + week, random = ~ 1 | ID,
family = binomial, data = bacteria))
summary(glmmPQL(y ~ trt + week + offset(week), random = ~ 1 | ID,
family = binomial, data = bacteria))
```

*MASS*version 7.3-60.2 Index]