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This vignette can be referred to by citing the package:

citation("see")

Introduction

A crucial aspect when building regression models is to evaluate the quality of modelfit. It is important to investigate how well models fit to the data and which fit indices to report. Functions to create diagnostic plots or to compute fit measures do exist, however, mostly spread over different packages. There is no unique and consistent approach to assess the model quality for different kind of models.

The primary goal of the performance package in easystats ecosystem is to fill this gap and to provide utilities for computing indices of model quality and goodness of fit. These include measures like r-squared (R2), root mean squared error (RMSE) or intraclass correlation coefficient (ICC) , but also functions to check (mixed) models for overdispersion, zero-inflation, convergence or singularity.

For more, see: https://easystats.github.io/performance/

Checking Model Assumptions

Let’s load the needed libraries first:

Binned Residuals

(related function documentation)

Example where model is not a good fit.

model <- glm(vs ~ wt + mpg, data = mtcars, family = "binomial")
result <- binned_residuals(model)
result

plot(result)

Example where model is a good fit.

model <- glm(am ~ mpg + vs + cyl, data = mtcars, family = "binomial")
result <- binned_residuals(model)
result

plot(result)

Check for Multicollinearity - Variance Inflation Factor

(related function documentation)

m <- lm(mpg ~ wt + cyl + gear + disp, data = mtcars)
result <- check_collinearity(m)

result
plot(result)
library(glmmTMB)
data(Salamanders)

# create highly correlated pseudo-variable
set.seed(1)
Salamanders$cover2 <-
  Salamanders$cover * runif(n = nrow(Salamanders), min = 0.7, max = 1.5)

# fit mixed model with zero-inflation
model <- glmmTMB(
  count ~ spp + mined + cover + cover2 + (1 | site),
  ziformula = ~ spp + mined,
  family = truncated_poisson,
  data = Salamanders
)

result <- check_collinearity(model)

result
plot(result)

Check for Outliers

(related function documentation)

# select only mpg and disp (continuous)
mt1 <- mtcars[, c(1, 3, 4)]
# create some fake outliers and attach outliers to main df
mt2 <- rbind(mt1, data.frame(mpg = c(37, 40), disp = c(300, 400), hp = c(110, 120)))
# fit model with outliers
model <- lm(disp ~ mpg + hp, data = mt2)
result <- check_outliers(model)

result

There are two visualization options

dot-plot with contour lines

plot(result, type = "dots")

bars indicating influential observations

plot(result, type = "bars")

Check for Normal Distributed Residuals

(related function documentation)

model <- lm(mpg ~ wt + cyl + gear + disp, data = mtcars)
result <- check_normality(model)

Density Plot

plot(result)

QQ Plot

plot(result, type = "qq")

PP Plot

plot(result, type = "pp")

Check for Normal Distributed Random Effects

(related function documentation)

model <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
result <- check_normality(model, effects = "random")
plot(result)

Check for Heteroscedasticity

(related function documentation)

model <- lm(mpg ~ wt + cyl + gear + disp, data = mtcars)
result <- check_heteroscedasticity(model)
plot(result)

Check for Homogeneity

(related function documentation)

model <- lm(len ~ supp + dose, data = ToothGrowth)
result <- check_homogeneity(model)
plot(result)

Posterior Predictive Checks

(related function documentation)

model <- lm(mpg ~ wt + cyl + gear + disp, data = mtcars)
check_posterior_predictions(model)

To check if the model properly captures the variation in the data, use check_range = TRUE:

model <- lm(mpg ~ wt + cyl + gear + disp, data = mtcars)
check_posterior_predictions(model, check_range = TRUE)

Overall Model Check

(related function documentation)

The composition of plots when checking model assumptions depends on the type of the input model. E.g., for logistic regression models, a binned residuals plot is used, while for linear models a plot of homegeneity of variance is shown instead. Models from count data include plots to inspect overdispersion.

Checks for generalized linear models

Logistic regression model

model <- glm(am ~ mpg + vs + cyl, data = mtcars, family = "binomial")
check_model(model)

Modelling count data

model <- glm(
  count ~ spp + mined + cover,
  family = poisson(),
  data = Salamanders
)
check_model(model)

Checks for linear (mixed) models

model <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
check_model(model)
check_model(model, panel = FALSE)

Note that not all checks supported in performance will be reported in this unified visual check. For example, for linear models, one needs to check the assumption that errors are not autocorrelated, but this check will not be shown in the visual check.

check_autocorrelation(lm(formula = wt ~ mpg, data = mtcars))

Compare Model Performances

(related function documentation)

compare_performance() computes indices of model performance for different models at once and hence allows comparison of indices across models. The plot()-method creates a “spiderweb” plot, where the different indices are normalized and larger values indicate better model performance. Hence, points closer to the center indicate worse fit indices.

data(iris)
lm1 <- lm(Sepal.Length ~ Species, data = iris)
lm2 <- lm(Sepal.Length ~ Species + Petal.Length, data = iris)
lm3 <- lm(Sepal.Length ~ Species * Sepal.Width, data = iris)
lm4 <- lm(Sepal.Length ~ Species * Sepal.Width + Petal.Length + Petal.Width, data = iris)
result <- compare_performance(lm1, lm2, lm3, lm4)

result

plot(result)

Model and Vector Properties

(related function documentation)

model <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
result <- check_distribution(model)

result
plot(result)
vec <- bayestestR::distribution_poisson(n = 500, lambda = 2.5)
result <- check_distribution(vec)

result
plot(result)

ROC curves

(related function documentation)

data(iris)
set.seed(123)
iris$y <- rbinom(nrow(iris), size = 1, 0.3)

folds <- sample(nrow(iris), size = nrow(iris) / 8, replace = FALSE)
test_data <- iris[folds, ]
train_data <- iris[-folds, ]

model <- glm(y ~ Sepal.Length + Sepal.Width, data = train_data, family = "binomial")
result <- performance_roc(model, new_data = test_data)

result
plot(result)

You can also compare ROC curves for different models.

set.seed(123)
library(bayestestR)

# creating models
m1 <- glm(vs ~ wt + mpg, data = mtcars, family = "binomial")
m2 <- glm(vs ~ wt + am + mpg, data = mtcars, family = "binomial")

# comparing their performances using the AUC curve
plot(performance_roc(m1, m2))