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Visualisation of linear model assumption diagnostics

Source: R/vis_lm_assumptions.R
vis_lm_assumptions.Rd

Checks the residual diagnostics in the general linear model Student's t-test (t.test,var=EQUAL) Fisher oneway ANOVA (aov) or simple linear regression. Performs the Shapiro-Wilk and Anderson-Darling tests for normality, and for grouped data also levene.test and Bartlett's test for homogeneity of variances. For simple linear regression, heteroscedasticity is assessed with bp.test, the studentised Breusch-Pagan test, which regresses squared raw residuals on fitted values. The normality tests, the grouped variance tests, and the histogram and Q-Q panels are computed from the internally studentised residuals r_i = e_i / (SE_res sqrt(1 - h_i)), which remove the leverage-dependent variance of the raw residuals (Var(e_i) = sigma^2 (1 - h_i)). The residuals-vs-fitted panel (regression mode) uses the z-residuals z_i = e_i / SE_res, which retain the leverage-dependent spread.

Usage

vis_lm_assumptions(
  samples,
  fact,
  cex = 1,
  correlation = FALSE,
  conf.level = 0.95,
  qq_nsim = getOption("visStatistics.qq_nsim", 5000L),
  plot_args = list()
)

Arguments

samples

Numeric vector; the dependent variable.

fact

Factor; the independent variable.

cex

Numeric; scaling factor for plot text and symbols (default: 1).

correlation

Logical. If FALSE and fact is numeric, regression diagnostics are shown. If TRUE, no regression diagnostics are shown. Default is FALSE.

conf.level

Numeric confidence level for the simulated Q-Q envelopes.

qq_nsim

Integer number of simulated refits for the Q-Q envelopes.

plot_args

Optional named list of base graphics parameters.

Value

A list with elements:

summary_anova

Summary of the ANOVA model.

shapiro_test

Result from shapiro.test().

ad_test

Result from nortest::ad.test() or a character message if n < 7.

levene_test

Result from levene.test() (grouped diagnostics only).

bartlett_test

Result from bartlett.test() (grouped diagnostics only).

bp_test

Result from bp.test() (regression diagnostics only).

Details

The Q-Q panel shows the simultaneous and point-wise tolerance bands computed by qq_lm_envelope, which documents their construction and gives the reference for it.

References

Schützenmeister, A., Jensen, U., & Piepho, H.-P. (2012). Checking Normality and Homoscedasticity in the General Linear Model Using Diagnostic Plots. Communications in Statistics - Simulation and Computation, 41(2). doi:10.1080/03610918.2011.582560. (Q-Q simultaneous tolerance band, see qq_lm_envelope.)

See levene.test and bp.test for the references of those two tests.

Examples

ToothGrowth$dose <- as.factor(ToothGrowth$dose)
vis_lm_assumptions(ToothGrowth$len, ToothGrowth$dose, qq_nsim = 100L)