# reb_bootstrap: REB Bootstrap for Two-Level Nested LMEs In lmeresampler: Bootstrap Methods for Nested Linear Mixed-Effects Models

 reb_bootstrap.lmerMod R Documentation

## REB Bootstrap for Two-Level Nested LMEs

### Description

Generate random effect block (REB) bootstrap replicates of a statistic for a two-level nested linear mixed-effects model.

### Usage

## S3 method for class 'lmerMod'
reb_bootstrap(model, .f, B, reb_type, .refit = TRUE)

## S3 method for class 'lme'
reb_bootstrap(model, .f, B, reb_type, .refit = TRUE)

reb_bootstrap(model, .f, B, reb_type, .refit = TRUE)


### Arguments

 model The model object you wish to bootstrap. .f A function returning the statistic(s) of interest. B The number of bootstrap resamples. reb_type Specification of what random effect block bootstrap version to implement. Possible values are 0, 1 or 2. .refit a logical value indicating whether the model should be refit to the bootstrap resample, or if the simulated bootstrap resample should be returned. Defaults to TRUE.

### Details

The random effects block (REB) bootstrap was outlined by Chambers and Chandra (2013) and has been developed for two-level nested linear mixed-effects (LME) models. Consider a two-level LME of the form

y = X β + Z b + ε

The REB bootstrap algorithm (type = 0) is as follows:

1. Calculate the nonparametric residual quantities for the fitted model

• marginal residuals r = y - Xβ

• predicted random effects \tilde{b} = (Z^\prime Z)^{-1} Z^\prime r

• error terms \tilde{e} = r - Z \tilde{b}

2. Take a simple random sample, with replacement, of the predicted random effects, \tilde{b}.

3. Draw a simple random sample, with replacement, of the group (cluster) IDs. For each sampled cluster, draw a random sample, with replacement, of size n_i from that cluster's vector of error terms, \tilde{e}.

4. Generate bootstrap samples via the fitted model equation y = X \widehat{β} + Z \tilde{b} + \tilde{e}

5. Refit the model and extract the statistic(s) of interest.

6. Repeat steps 2-5 B times.

Variation 1 (type = 1): The first variation of the REB bootstrap zero centers and rescales the residual quantities prior to resampling.

Variation 2 (type = 2): The second variation of the REB bootstrap scales the estimates and centers the bootstrap distributions (i.e., adjusts for bias) after REB bootstrapping.

### Value

The returned value is an object of class "lmeresamp".

### References

Chambers, R. and Chandra, H. (2013) A random effect block bootstrap for clustered data. Journal of Computational and Graphical Statistics, 22, 452–470.

• Examples are given in bootstrap
• parametric_bootstrap, resid_bootstrap, case_bootstrap, reb_bootstrap, wild_bootstrap for more details on a specific bootstrap.
• bootMer in the lme4 package for an implementation of (semi-)parametric bootstrap for mixed models.