Visual check of various model assumptions (normality of residuals, normality of random effects, linear relationship, homogeneity of variance, multicollinearity).

## Usage

```
check_model(x, ...)
# Default S3 method
check_model(
x,
panel = TRUE,
check = "all",
detrend = TRUE,
bandwidth = "nrd",
type = "density",
residual_type = NULL,
show_dots = NULL,
dot_size = 2,
line_size = 0.8,
title_size = 12,
axis_title_size = base_size,
base_size = 10,
alpha = 0.2,
dot_alpha = 0.8,
colors = c("#3aaf85", "#1b6ca8", "#cd201f"),
theme = "see::theme_lucid",
verbose = FALSE,
...
)
```

## Arguments

- x
A model object.

- ...
Arguments passed down to the individual check functions, especially to

`check_predictions()`

and`binned_residuals()`

.- panel
Logical, if

`TRUE`

, plots are arranged as panels; else, single plots for each diagnostic are returned.- check
Character vector, indicating which checks for should be performed and plotted. May be one or more of

`"all"`

,`"vif"`

,`"qq"`

,`"normality"`

,`"linearity"`

,`"ncv"`

,`"homogeneity"`

,`"outliers"`

,`"reqq"`

,`"pp_check"`

,`"binned_residuals"`

or`"overdispersion"`

. Note that not all check apply to all type of models (see 'Details').`"reqq"`

is a QQ-plot for random effects and only available for mixed models.`"ncv"`

is an alias for`"linearity"`

, and checks for non-constant variance, i.e. for heteroscedasticity, as well as the linear relationship. By default, all possible checks are performed and plotted.- detrend
Logical. Should Q-Q/P-P plots be detrended? Defaults to

`TRUE`

for linear models or when`residual_type = "normal"`

. Defaults to`FALSE`

for QQ plots based on simulated residuals (i.e. when`residual_type = "simulated"`

).- bandwidth
A character string indicating the smoothing bandwidth to be used. Unlike

`stats::density()`

, which used`"nrd0"`

as default, the default used here is`"nrd"`

(which seems to give more plausible results for non-Gaussian models). When problems with plotting occur, try to change to a different value.- type
Plot type for the posterior predictive checks plot. Can be

`"density"`

,`"discrete_dots"`

,`"discrete_interval"`

or`"discrete_both"`

(the`discrete_*`

options are appropriate for models with discrete - binary, integer or ordinal etc. - outcomes).- residual_type
Character, indicating the type of residuals to be used. For non-Gaussian models, the default is

`"simulated"`

, which uses simulated residuals. These are based on`simulate_residuals()`

and thus uses the**DHARMa**package to return randomized quantile residuals. For Gaussian models, the default is`"normal"`

, which uses the default residuals from the model. Setting`residual_type = "normal"`

for non-Gaussian models will use a half-normal Q-Q plot of the absolute value of the standardized deviance residuals.- show_dots
Logical, if

`TRUE`

, will show data points in the plot. Set to`FALSE`

for models with many observations, if generating the plot is too time-consuming. By default,`show_dots = NULL`

. In this case`check_model()`

tries to guess whether performance will be poor due to a very large model and thus automatically shows or hides dots.- dot_size, line_size
Size of line and dot-geoms.

- base_size, title_size, axis_title_size
Base font size for axis and plot titles.

- alpha, dot_alpha
The alpha level of the confidence bands and dot-geoms. Scalar from 0 to 1.

- colors
Character vector with color codes (hex-format). Must be of length 3. First color is usually used for reference lines, second color for dots, and third color for outliers or extreme values.

- theme
String, indicating the name of the plot-theme. Must be in the format

`"package::theme_name"`

(e.g.`"ggplot2::theme_minimal"`

).- verbose
If

`FALSE`

(default), suppress most warning messages.

## Details

For Bayesian models from packages **rstanarm** or **brms**,
models will be "converted" to their frequentist counterpart, using
`bayestestR::bayesian_as_frequentist`

.
A more advanced model-check for Bayesian models will be implemented at a
later stage.

See also the related vignette.

## Note

This function just prepares the data for plotting. To create the plots,
**see** needs to be installed. Furthermore, this function suppresses
all possible warnings. In case you observe suspicious plots, please refer
to the dedicated functions (like `check_collinearity()`

,
`check_normality()`

etc.) to get informative messages and warnings.

## Posterior Predictive Checks

Posterior predictive checks can be used to look for systematic discrepancies
between real and simulated data. It helps to see whether the type of model
(distributional family) fits well to the data. See `check_predictions()`

for further details.

## Linearity Assumption

The plot **Linearity** checks the assumption of linear relationship.
However, the spread of dots also indicate possible heteroscedasticity (i.e.
non-constant variance, hence, the alias `"ncv"`

for this plot), thus it shows
if residuals have non-linear patterns. This plot helps to see whether
predictors may have a non-linear relationship with the outcome, in which case
the reference line may roughly indicate that relationship. A straight and
horizontal line indicates that the model specification seems to be ok. But
for instance, if the line would be U-shaped, some of the predictors probably
should better be modeled as quadratic term. See `check_heteroscedasticity()`

for further details.

**Some caution is needed** when interpreting these plots. Although these
plots are helpful to check model assumptions, they do not necessarily indicate
so-called "lack of fit", e.g. missed non-linear relationships or interactions.
Thus, it is always recommended to also look at
effect plots, including partial residuals.

## Homogeneity of Variance

This plot checks the assumption of equal variance (homoscedasticity). The desired pattern would be that dots spread equally above and below a straight, horizontal line and show no apparent deviation.

## Influential Observations

This plot is used to identify influential observations. If any points in this
plot fall outside of Cook’s distance (the dashed lines) then it is considered
an influential observation. See `check_outliers()`

for further details.

## Multicollinearity

This plot checks for potential collinearity among predictors. In a nutshell,
multicollinearity means that once you know the effect of one predictor, the
value of knowing the other predictor is rather low. Multicollinearity might
arise when a third, unobserved variable has a causal effect on each of the
two predictors that are associated with the outcome. In such cases, the actual
relationship that matters would be the association between the unobserved
variable and the outcome. See `check_collinearity()`

for further details.

## Normality of Residuals

This plot is used to determine if the residuals of the regression model are
normally distributed. Usually, dots should fall along the line. If there is
some deviation (mostly at the tails), this indicates that the model doesn't
predict the outcome well for that range that shows larger deviations from
the line. For generalized linear models and when `residual_type = "normal"`

,
a half-normal Q-Q plot of the absolute value of the standardized deviance
residuals is shown, however, the interpretation of the plot remains the same.
See `check_normality()`

for further details. Usually, for generalized linear
(mixed) models, a test for uniformity of residuals based on simulated residuals
is conducted (see next section).

## Uniformity of Residuals

Fore non-Gaussian models, when `residual_type = "simulated"`

(the default
for generalized linear (mixed) models), residuals are not expected to be
normally distributed. In this case, the created Q-Q plot checks the uniformity
of residuals. The interpretation of the plot is the same as for the normal
Q-Q plot. See `simulate_residuals()`

and `check_residuals()`

for further
details.

## Overdispersion

For count models, an *overdispersion plot* is shown. Overdispersion occurs
when the observed variance is higher than the variance of a theoretical model.
For Poisson models, variance increases with the mean and, therefore, variance
usually (roughly) equals the mean value. If the variance is much higher,
the data are "overdispersed". See `check_overdispersion()`

for further
details.

## Binned Residuals

For models from binomial families, a *binned residuals plot* is shown.
Binned residual plots are achieved by cutting the the data into bins and then
plotting the average residual versus the average fitted value for each bin.
If the model were true, one would expect about 95% of the residuals to fall
inside the error bounds. See `binned_residuals()`

for further details.

## Residuals for (Generalized) Linear Models

Plots that check the homogeneity of variance use standardized Pearson's
residuals for generalized linear models, and standardized residuals for
linear models. The plots for the normality of residuals (with overlayed
normal curve) and for the linearity assumption use the default residuals
for `lm`

and `glm`

(which are deviance residuals for `glm`

). The Q-Q plots
use simulated residuals (see `simulate_residuals()`

) for non-Gaussian
models and standardized residuals for linear models.

## Troubleshooting

For models with many observations, or for more complex models in general,
generating the plot might become very slow. One reason might be that the
underlying graphic engine becomes slow for plotting many data points. In
such cases, setting the argument `show_dots = FALSE`

might help. Furthermore,
look at the `check`

argument and see if some of the model checks could be
skipped, which also increases performance.

## See also

Other functions to check model assumptions and and assess model quality:
`check_autocorrelation()`

,
`check_collinearity()`

,
`check_convergence()`

,
`check_heteroscedasticity()`

,
`check_homogeneity()`

,
`check_outliers()`

,
`check_overdispersion()`

,
`check_predictions()`

,
`check_singularity()`

,
`check_zeroinflation()`