Visual check of model assumptions

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

Usage

check_model(x, ...)

# S3 method for default
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.

Value

The data frame that is used for plotting.

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.

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.

Examples

# \donttest{
m <- lm(mpg ~ wt + cyl + gear + disp, data = mtcars)
check_model(m)


data(sleepstudy, package = "lme4")
m <- lme4::lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
check_model(m, panel = FALSE)
# }