# influence.merMod

##### Influence Diagnostics for Mixed-Effects Models

These functions compute deletion influence diagnostics for linear
(fit by `lmer`

and generalized linear mixed-effects models
(fit by `glmer`

). The main functions are methods for the `influence`

generic function. Other functions are provided for
computing `dfbeta`

, `dfbetas`

, `cooks.distance`

, and influence on variance-covariance components based
on the objects computed by `influence.merMod`

- Keywords
- models

##### Usage

```
# S3 method for merMod
influence(model, groups, data, maxfun=1000, do.coef =
TRUE, ...)
# S3 method for influence.merMod
cooks.distance(model, ...)
# S3 method for influence.merMod
dfbeta(model, which = c("fixed", "var.cov"), ...)
# S3 method for influence.merMod
dfbetas(model, ...)
```

##### Arguments

- model
in the case of

`influence.merMod`

, a model of class`"merMod"`

; in the case of`cooks.distance`

,`dfbeta`

, or`dfbetas`

, an object returned by`influence.merMod`

- groups
a character vector containing the name of a grouping factor or names of grouping factors; if more than one name is supplied, then groups are defined by all combinations of levels of the grouping factors that appear in the data. If omitted, then each individual row of the data matrix is treated as a "group" to be deleted in turn.

- data
an optional data frame with the data to which

`model`

was fit;`influence.merMod`

can usually retrieve the data used to fit the model, unless it can't be found in the current environment, so it's usually unnecessary to supply this argument.- maxfun
The maximum number of function evaluations (for

`influence.merMod`

) to perform after deleting each group; the defaults are large enough so that the iterations will typically continue to convergence. Setting to`maxfun=20`

for an`lmer`

model or`100`

for a`glmer`

model will typically produce a faster reasonable approximation. An even smaller value can be used if interest is only in influence on the fixed effects.- which
if

`"fixed.effects"`

(the default), return influence on the fixed effects; if`"var.cov"`

, return influence on the variance-covariance components.- do.coef
if

`FALSE`

, skip potentially time-consuming computations; return just a list containing hat values- …
ignored.

##### Details

`influence.merMod`

start with the estimated variance-covariance components from `model`

and then refit
the model omitting each group in turn, not necessarily iterating to completion. For example, `maxfun=20`

takes up to 20 function evaluations
step away from the ML or REML solution for the full data, which usually provides decent approximations to the fully iterated estimates.

The other functions are methods for the `dfbeta`

, `dfbetas`

, and `cooks.distance`

generics, to be applied to the
`"influence.merMod"`

object produced by the `influence`

function; the `dfbeta`

methods can also return
influence on the variance-covariance components.

##### Value

`influence.merMod`

returns objects of class
`"influence.merMod"`

, which contain the following elements:

`"fixed.effects"`

the estimated fixed effects for the model.

`"fixed.effects[-groups]"`

a matrix with columns corresponding to the fixed-effects coefficients and rows corresponding to groups, giving the estimated fixed effects with each group deleted in turn;

*groups*is formed from the name(s) of the grouping factor(s).`"var.cov.comps"`

the estimated variance-covariance parameters for the model.

`"var.cov.comps[-groups]"`

a matrix with the estimated covariance parameters (in columns) with each group deleted in turn.

`"vcov"`

The estimated covariance matrix of the fixed-effects coefficients.

`"vcov[-groups]"`

a list each of whose elements is the estimated covariance matrix of the fixed-effects coefficients with one group deleted.

`"groups"`

a character vector giving the names of the grouping factors.

`"deleted"`

the possibly composite grouping factor, each of whose elements is deleted in turn.

`"converged"`

for

`influence.merMod`

, a logical vector indicating whether the computation converged for each group.`"function.evals"`

for

`influence.merMod`

, a vector of the number of function evaluations performed for each group.

For plotting `"influence.merMod"`

objects, see `infIndexPlot`

.

##### References

Fox, J. and Weisberg, S. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

##### See Also

##### Examples

```
# NOT RUN {
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
inf_fm1 <- influence(fm1, "Subject")
if (require("car")) {
infIndexPlot(inf_fm1)
}
dfbeta(inf_fm1)
dfbetas(inf_fm1)
gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
data = cbpp, family = binomial)
inf_gm1 <- influence(gm1, "herd", maxfun=100)
gm1.11 <- update(gm1, subset = herd != 11) # check deleting herd 11
if (require("car")) {
infIndexPlot(inf_gm1)
compareCoefs(gm1, gm1.11)
}
## FIXME: dfbetas will fail at present *if* car is available, because
## influence.merMod and dfbetas.influence.merMod methods are being
## gotten from car, which has a sqrt(diag(x)) applied to a dpoMatrix ...
## dfbeta(inf_gm1)
## dfbetas(inf_gm1)
# }
```

*Documentation reproduced from package lme4, version 1.1-21, License: GPL (>= 2)*