The package HLMdiag was created in order to provide a unified
framework for analysts to diagnose hierarchical linear models (HLMs).
When HLMdiag was created in 2014, it made diagnostic procedures
available for HLMs that had not yet been implemented in statistical
software. Over the past 6 years, other packages have gradually
implemented some of these procedures; however, diagnosing a model still
often requires multiple packages, each of which has its own syntax and
quirks. HLMdiag provides diagnostic tools targeting all aspects and
levels of hierarchical linear models in a single package. HLMdiag
provides wrapper functions to all types of residuals implemented in
lme4 and nlme as well as providing access to the marginal and least
squares residuals. For influence diagnostics, HLMdiag provides
functions to calculate Cook’s distance, MDFFITS, covariance trace and
ratio, relative variance change, and leverage.
If you would like to install the development version of HLMdiag, you
may do so using devtools:
#install.packages("devtools")
library(devtools)
devtools::install_github("aloy/HLMdiag")To instead download the stable CRAN version instead, use:
install.packages("HLMdiag")The functions provided by this package can be separated into three groups: residual analysis, influence analysis, and graphical tools.
The residual functions in HLMdiag allow the analyst to estimate all
types of residuals defined for a hierarchical linear model. They provide
access to level-1, higher-level, and marginal residuals and use both
Least Squares and Empirical Bayes estimation methods to provide the
analyst with more choices in evaluating a model. The hlm_resid method
is inspired by the augment() function in broom and appends all types
of residuals and fitted values for a given level to the model frame;
however, individual types of residuals can be calculated with the
pull_resid method.
The functions available for residual analysis in HLMdiag are:
*hlm_resid() calculates all residual diagnostics for a given level,
returning a tibble with the residuals and fitted values appended to the
original model frame.
*pull_resid() calculates a specified type of residual, returning a
vector and prioritizing computational efficiency.
*hlm_augment() combines hlm_influence() and hlm_resid() to return
a tibble with residual values and influence diagnostics appended to the
original model frame.
The influence analysis functions provide functionality to calculate
Cook’s distance, MDFFITS, covariance ratio, covariance trace, relative
variance change, and leverage. Additionally, two functions to calculate
Cook’s distance, MDFFITS, covariance ratio, and covariance trace are
provided: a one step approximation, and a full refit method that refits
the model and recalculates the fixed and random effects. This
functionality is available through individual functions for each
diagnostic; however, the hlm_influence function can be used to
calculate all available diagnostics for each observation or group of
observations.
The functions available for influence analysis in HLMdiag are:
cooks.distance()calculates Cook’s distance values, which measures the difference between the original fixed effects and the deleted ones.mdffits()calculates MDFFITS, a multivariate version of the DFFITS statistic, which is also a measure of the difference in fixed effects.covtrace()calculates covariance trace, the ratio between the covariance matrices with and without unit i to the identity matrix.covratio()calculate covariance ratio, a comparison of the two covariance matrices with and without unit i using their determinants.rvc()calculates relative variance change, a measurement of the ratio of estimates of the l th variance component with and without unit i.leverage()calculates leverage, he rate of change in the predicted response with respect to the observed response.case_delete()iteratively deletes observations or groups of observations, returning a list of fixed and random components from the original model and the models created by deletion.hlm_influence()calculates all of the influence diagnostics, returning a tibble with the influence values appended to the original model frame.hlm_augment()combineshlm_influence()andhlm_resid()to return a tibble with residual values and influence diagnostics appended to the original model frame.
HLMdiag provides the function dotplot_diag(), which creates dotplots
to visually represent influence diagnostics. It is especially useful
when used with the values returned by hlm_influence(). HLMdiag also
provides grouped Q-Q plots (group_qqnorm()), and Q-Q plots that
combine the functionality of qqnorm and qqline (ggplot_qqnorm()).
We will use the sleepstudy data set from the lme4 package.
library(lme4)
#> Loading required package: Matrix
library(HLMdiag)
#>
#> Attaching package: 'HLMdiag'
#> The following object is masked from 'package:stats':
#>
#> covratio
data(sleepstudy, package = "lme4")
sleep.lmer <- lme4::lmer(Reaction ~ Days + (Days|Subject), data = sleepstudy) We calculate the unstandardized level-1 and marginal residuals for each observation below.
hlm_resid(sleep.lmer)
#> # A tibble: 180 x 10
#> id Reaction Days Subject .resid .fitted .ls.resid .ls.fitted .mar.resid
#> <dbl> <dbl> <dbl> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 250. 0 308 -4.10 254. 5.37 244. -1.85
#> 2 2 259. 1 308 -14.6 273. -7.25 266. -3.17
#> 3 3 251. 2 308 -42.2 293. -36.9 288. -21.5
#> 4 4 321. 3 308 8.78 313. 12.0 309. 38.6
#> 5 5 357. 4 308 24.5 332. 25.6 331. 63.6
#> 6 6 415. 5 308 62.7 352. 61.7 353. 111.
#> 7 7 382. 6 308 10.5 372. 7.42 375. 68.0
#> 8 8 290. 7 308 -101. 391. -106. 397. -34.5
#> 9 9 431. 8 308 19.6 411. 12.3 418. 95.4
#> 10 10 466. 9 308 35.7 431. 26.3 440. 121.
#> # … with 170 more rows, and 1 more variable: .mar.fitted <dbl>For more information and examples of the functionality of hlm_resid(),
see the residual diagnostics vignette.
We calculate influence diagnostics for each observation with the following line:
hlm_influence(sleep.lmer)
#> # A tibble: 180 x 9
#> id Reaction Days Subject cooksd mdffits covtrace covratio
#> <int> <dbl> <dbl> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 1 250. 0 308 1.48e-4 1.47e-4 0.00887 1.01
#> 2 2 259. 1 308 1.10e-3 1.09e-3 0.00558 1.01
#> 3 3 251. 2 308 5.13e-3 5.11e-3 0.00330 1.00
#> 4 4 321. 3 308 1.14e-4 1.14e-4 0.00175 1.00
#> 5 5 357. 4 308 3.93e-4 3.92e-4 0.000778 1.00
#> 6 6 415. 5 308 1.07e-3 1.07e-3 0.000321 1.00
#> 7 7 382. 6 308 3.49e-5 3.49e-5 0.000361 1.00
#> 8 8 290. 7 308 8.81e-3 8.80e-3 0.000944 1.00
#> 9 9 431. 8 308 8.23e-4 8.21e-4 0.00219 1.00
#> 10 10 466. 9 308 5.99e-3 5.96e-3 0.00435 1.00
#> # … with 170 more rows, and 1 more variable: leverage.overall <dbl>For more information and examples of the functionality of
hlm_influence(), see the influence diagnostics vignette.