# leverage.mer: Leverage for HLMs In HLMdiag: Diagnostic Tools for Hierarchical (Multilevel) Linear Models

## Description

This function calculates the leverage of a hierarchical linear model fit by lmer.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 ## Default S3 method: leverage(object, ...) ## S3 method for class 'mer' leverage(object, level = 1, ...) ## S3 method for class 'lmerMod' leverage(object, level = 1, ...) ## S3 method for class 'lme' leverage(object, level = 1, ...) 

## Arguments

 object fitted object of class mer of lmerMod ... do not use level the level at which the leverage should be calculated: either 1 for observation level leverage (default) or the name of the grouping factor (as defined in flist of the mer object) for group level leverage. leverage assumes that the grouping factors are unique; thus, if IDs are repeated within each unit, unique IDs must be generated by the user prior to use of leverage.

## Details

Demidenko and Stukel (2005) describe leverage for mixed (hierarchical) linear models as being the sum of two components, a leverage associated with the fixed (H_1) and a leverage associated with the random effects (H_2) where

H_1 = X (X^\prime V^{-1} X)^{-1} X^\prime V^{-1}

and

H_2 = ZDZ^{\prime} V^{-1} (I - H_1)

Nobre and Singer (2011) propose using

H_2^* = ZDZ^{\prime}

as the random effects leverage as it does not rely on the fixed effects.

For individual observations leverage uses the diagonal elements of the above matrices as the measure of leverage. For higher-level units, leverage uses the mean trace of the above matrices associated with each higher-level unit.

## Value

leverage returns a data frame with the following columns:

overall

The overall leverage, i.e. H = H_1 + H_2.

fixef

The leverage corresponding to the fixed effects.

ranef

The leverage corresponding to the random effects proposed by Demidenko and Stukel (2005).

ranef.uc

The (unconfounded) leverage corresponding to the random effects proposed by Nobre and Singer (2011).

## References

Demidenko, E., & Stukel, T. A. (2005) Influence analysis for linear mixed-effects models. Statistics in Medicine, 24(6), 893–909.

Nobre, J. S., & Singer, J. M. (2011) Leverage analysis for linear mixed models. Journal of Applied Statistics, 38(5), 1063–1072.

cooks.distance.mer, mdffits.mer, covratio.mer, covtrace.mer, rvc.mer

## Examples

  1 2 3 4 5 6 7 8 9 10 data(sleepstudy, package = 'lme4') fm <- lme4::lmer(Reaction ~ Days + (Days | Subject), sleepstudy) # Observation level leverage lev1 <- leverage(fm, level = 1) head(lev1) # Group level leverage lev2 <- leverage(fm, level = "Subject") head(lev2) 

### Example output

Attaching package: ‘HLMdiag’

The following object is masked from ‘package:stats’:

covratio

overall       fixef      ranef  ranef.uc
1 0.22930404 0.019191919 0.21011212 0.9345897
2 0.16972999 0.013804714 0.15592528 1.0174683
3 0.12682372 0.009764310 0.11705941 1.2074459
4 0.10058520 0.007070707 0.09351449 1.5045226
5 0.09101445 0.005723906 0.08529055 1.9086983
6 0.09811147 0.005723906 0.09238756 2.4199730
overall      fixef     ranef ranef.uc
1 0.161234 0.01111111 0.1501229 2.592732
2 0.161234 0.01111111 0.1501229 2.592732
3 0.161234 0.01111111 0.1501229 2.592732
4 0.161234 0.01111111 0.1501229 2.592732
5 0.161234 0.01111111 0.1501229 2.592732
6 0.161234 0.01111111 0.1501229 2.592732


HLMdiag documentation built on May 2, 2021, 9:06 a.m.