# GLMMadaptive: Generalized Linear Mixed Models using Adaptive Gaussian Quadrature

## Description

GLMMadaptive fits mixed effects models for grouped/clustered outcome variables for which the integral over the random effects in the definition of the marginal likelihood cannot be solved analytically. The package approximates these integrals using the adaptive Gauss-Hermite quadrature rule.

Multiple random effects terms can be included for the grouping factor (e.g., random intercepts, random linear slopes, random quadratic slopes), but currently only a single grouping factor is allowed.

## Basic Features

- The package contains a single model-fitting function named
`mixed_model()`

with four

required arguments, `fixed`

a formula for the fixed effects, `random`

a formula for the
random effects, `family`

a family object specifying the type of response variable, and
`data`

a data frame containing the variables in the previously mentioned formulas.

- Methods for standard generics are provided, i.e.,
`coef()`

,`fixef()`

,`ranef()`

,

`vcov()`

, `logLik()`

, `summary()`

, `anova()`

, `confint()`

, `fitted()`

, `residuals()`

,
`predict()`

, and `simulate()`

.

- Negative binomial mixed models can be fitted using the
`negative.binomial()`

family

object.

- Zero-inflated Poisson and negative binomial models using the
`zi.poisson()`

and

`zi.negative.binomial()`

family objects.

- Hurdle Poisson and negative binomial models using the
`hurdle.poisson()`

and

`hurdle.negative.binomial()`

family objects.

- Two-part/hurdle mixed models for semi-continuous normal data using the

`hurdle.lognormal()`

family object.

Mixed models for censored normal data using the

`censored.normal()`

family object.Continuation ratio mixed models for ordinal data using functions

`cr_setup()`

and`cr_marg_probs()`

.Beta and hurdle Beta mixed effects models using

`beta.fam()`

and`hurdle.beta.fam()`

family objects.

Gamma mixed effects models using the

`Gamma()`

or`Gamma.fam()`

family object.Linear mixed effects models with right and left censored data using the

`censored.normal()`

family object.Users may also specify their own log-density function for the repeated measurements

response variable, and the internal algorithms will take care of the optimization.

- Calculates the marginalized coefficients using the idea of Hedeker et al. (2017) using

function `marginal_coefs()`

.

- Predictions with confidence interval for constructing effects plots are provided by

function `effectPlotData()`

.

## Basic Use

Let `y`

denote a grouped/clustered outcome, `g`

denote the grouping factor, and `x1`

and
`x2`

covariates. A mixed effects model with `y`

as outcome, `x1`

and `x2`

as fixed effects,
and random intercepts is fitted with the code:

```
fm <- mixed_model(fixed = y ~ x1 + x2, random = ~ 1 | g, data = DF,
family = poisson())
summary(fm)
```

In the `data`

argument we provide the data frame `DF`

, which contains the aforementioned
variables. In the family argument we specify the distribution of the grouped/clustered
outcome conditional on the random effects. To include in the random-effects part
intercepts and `x1`

, we update the call to `mixed_model()`

as

```
gm <- mixed_model(fixed = y ~ x1 + x2, random = ~ x1 | g, data = DF,
family = poisson())
summary(gm)
```

## Installation

The development version of the package can be installed from GitHub using the **devtools**
package:

`devtools::install_github("drizopoulos/GLMMadaptive")`

and with vignettes

`devtools::install_github("drizopoulos/GLMMadaptive", build_opts = NULL)`

Hex-sticker courtesy of Greg Papageorgiou @gr_papageorgiou.