# glmertree

##### (Generalized) Linear Mixed Model Trees

Model-based recursive partitioning based on (generalized) linear mixed models.

- Keywords
- tree

##### Usage

```
lmertree(formula, data, weights = NULL, cluster = NULL,
ranefstart = NULL, offset = NULL, joint = TRUE,
abstol = 0.001, maxit = 100, dfsplit = TRUE, verbose = FALSE,
plot = FALSE, REML = TRUE, lmer.control = lmerControl(), …)
```glmertree(formula, data, family = "binomial", weights = NULL,
cluster = NULL, ranefstart = NULL, offset = NULL, joint = TRUE,
abstol = 0.001, maxit = 100, dfsplit = TRUE, verbose = FALSE,
plot = FALSE, nAGQ = 1L, glmer.control = glmerControl(), …)

##### Arguments

- formula
formula specifying the response variable and a three-part right-hand-side describing the regressors, random effects, and partitioning variables, respectively. For details see below.

- data
data.frame to be used for estimating the model tree.

- family
family specification for

`glmtree`

and`glmer`

. See`glm`

documentation for families.- weights
numeric. An optional numeric vector of weights. Can be a name of a column in data or a vector of length

`nrow(data)`

.- cluster
optional vector of cluster IDs to be employed for clustered covariances in the parameter stability tests. Can be a name of a column in

`data`

or a vector of length`nrow(data)`

. If`cluster = NULL`

(the default), observation-level covariances are employed in the parameter stability tests. If partitioning variables are measured on the cluster level, this will likely yield spurious splits, which can be mitigated by specification of the cluster argument, which results in cluster-level covariances being employed in the parameter stability tests.- ranefstart
`NULL`

(the default),`TRUE`

, or a numeric vector of length`nrow(data)`

. Specifies the offset to be used in estimation of the first tree.`NULL`

by default, yielding a zero offset initialization. If`ranefstart = TRUE`

is specified, the random effects will be estimated first and the first tree will be grown using the random-effects predictions as an offset.- offset
optional numeric vector to be included in the linear predictor with a coeffcient of one. Note that

`offset`

can be a name of a column in`data`

or a a numeric vector of length`nrow(data)`

.- joint
logical. Should the fixed effects from the tree be (re-)estimated jointly along with the random effects?

- abstol
numeric. The convergence criterion used for estimation of the model. When the difference in log-likelihoods of the random-effects model from two consecutive iterations is smaller than

`abstol`

, estimation of the model tree has converged.- maxit
numeric. The maximum number of iterations to be performed in estimation of the model tree.

- dfsplit
logical or numeric.

`as.integer(dfsplit)`

is the degrees of freedom per selected split employed when extracting the log-likelihood.- verbose
Should the log-likelihood value of the estimated random-effects model be printed for every iteration of the estimation?

- plot
Should the tree be plotted at every iteration of the estimation? Note that selecting this option slows down execution of the function.

- REML
logical scalar. Should the fixef-effects estimates be chosen to optimize the REML criterion (as opposed to the log-likelihood)? Will be passed to funtion

`lmer()`

. See`lmer`

for details.- nAGQ
integer scalar. Specifies the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood, to be passed to function

`glmer()`

. See`glmer`

for details.- lmer.control, glmer.control
list. An optional list with control parameters to be passed to

`lmer()`

and`glmer()`

, respectively. See`lmerControl`

for details.- …
Additional arguments to be passed to

`lmtree()`

or`glmtree()`

. See`mob_control`

documentation for details.

##### Details

(G)LMM trees learn a tree where each terminal node is associated with different fixed-effects regression coefficients while adjusting for global random effects (such as a random intercept). This allows for detection of subgroups with different fixed-effects parameter estimates, keeping the random effects constant throughout the tree (i.e., random effects are estimated globally). The estimation algorithm iterates between (1) estimation of the tree given an offset of random effects, and (2) estimation of the random effects given the tree structure. See Fokkema et al. (2018) for a detailed introduction.

To specify all variables in the model a `formula`

such as
`y ~ x1 + x2 | random | z1 + z2 + z3`

is used, where `y`

is the
response, `x1`

and `x2`

are the regressors in every node of the
tree, `random`

is the random effects, and `z1`

to `z3`

are
the partitioning variables considered for growing the tree. If `random`

is only a single variable such as `id`

a random intercept with respect
to `id`

is used. Alternatively, it may be an explicit random-effects
formula such as `(1 | id)`

or a more complicated formula such as
`((1+time) | id)`

. (Note that in the latter two formulas, the brackets
are necessary to protect the pipes in the random-effects formulation.)

In the random-effects model from step (2), two strategies are available:
Either the fitted values from the tree can be supplied as an offset
(`joint = FALSE`

) so that only the random effects are estimated.
Or the fixed effects are (re-)estimated along with the random effects
using a nesting factor with nodes from the tree (`joint = TRUE`

).
In the former case, the estimation of each random-effects model is typically
faster, but more iterations are required.

The code is still under development and might change in future versions.

##### Value

The function returns a list with the following objects:

The final `lmtree`

/`glmtree`

.

The final `lmer`

random-effects model.

The corresponding random effects of `lmer`

.

The corresponding `VarCorr(lmer)`

.

The corresponding `attr(VarCorr(lmer), "sc")^2`

.

The dataset specified with the `data`

argument
including added auxiliary variables `.ranef`

and `.tree`

from the last iteration.

The log-likelihood value of the last iteration.

The number of iterations used to estimate the `lmertree`

.

The maximum number of iterations specified with the `maxit`

argument.

The random effects used as an offset, as specified with
the `ranefstart`

argument.

The formula as specified with the `formula`

argument.

The formula as specified with the `randomformula`

argument.

The prespecified value for the change in log-likelihood to evaluate
convergence, as specified with the `abstol`

argument.

A list containing control parameters passed to
`lmtree()`

, as specified with ….

A list containing control parameters passed to
`lmer()`

, as specified in the `lmer.control`

argument.

Whether the fixed effects from the tree were (re-)estimated jointly along
with the random effects, specified with the `joint`

argument.

##### References

Fokkema M, Smits N, Zeileis A, Hothorn T, Kelderman H (2018). “Detecting Treatment-Subgroup Interactions in Clustered Data with Generalized Linear Mixed-Effects Model Trees”. Behavior Research Methods, 50(5), 2016-2034. https://doi.org/10.3758/s13428-017-0971-x

##### See Also

##### Examples

```
# NOT RUN {
## artificial example data
data("DepressionDemo", package = "glmertree")
## fit normal linear regression LMM tree for continuous outcome
lt <- lmertree(depression ~ treatment | cluster | age + anxiety + duration,
data = DepressionDemo)
print(lt)
plot(lt, which = "all") # default behavior, may also be "tree" or "ranef"
coef(lt)
ranef(lt)
predict(lt, type = "response") # default behavior, may also be "node"
predict(lt, re.form = NA) # excludes random effects, see ?lme4::predict.merMod
residuals(lt)
VarCorr(lt) # see lme4::VarCorr
## fit logistic regression GLMM tree for binary outcome
gt <- glmertree(depression_bin ~ treatment | cluster | age + anxiety + duration,
data = DepressionDemo)
print(gt)
plot(gt, which = "all") # default behavior, may also be "tree" or "ranef"
coef(gt)
ranef(gt)
predict(gt, type = "response") # default behavior, may also be "node" or "link"
predict(gt, re.form = NA) # excludes random effects, see ?lme4::predict.merMod
residuals(gt)
VarCorr(gt) # see lme4::VarCorr
# }
```

*Documentation reproduced from package glmertree, version 0.2-0, License: GPL-2 | GPL-3*