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)
::install_github("aloy/HLMdiag") devtools
```

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()`

combines`hlm_influence()`

and`hlm_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")
<- lme4::lmer(Reaction ~ Days + (Days|Subject), data = sleepstudy) sleep.lmer
```

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.