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Simulated Q-Q envelopes for linear model residuals

Source: R/qq_lm_envelope.R
qq_lm_envelope.Rd

Computes pointwise and simultaneous Q-Q envelopes for internally studentised residuals from an unweighted lm or aov object by repeatedly simulating responses from the fitted normal-error model and refitting the model. The simultaneous envelope follows the Monte Carlo tolerance-band idea of Schützenmeister et al. (2012); see vis_lm_assumptions and visstat for where these bands are drawn.

Usage

qq_lm_envelope(
  model,
  conf.level = 0.95,
  nsim = getOption("visStatistics.qq_nsim", 5000L),
  q.type = 2L,
  tol = 1e-04,
  max.iter = 100L
)

Arguments

model

An unweighted lm or aov object.

conf.level

Numeric confidence level for the envelopes.

nsim

Integer number of simulated refits.

q.type

Integer quantile type passed to stats::quantile().

tol

Numeric tolerance for the simultaneous-band coverage search.

max.iter

Integer maximum number of bisection iterations.

Value

A list of class qq_lm_envelope with the observed sorted residuals, theoretical quantiles, pointwise bounds, simultaneous bounds, the simulated sorted residual matrix, and the achieved simultaneous coverage.

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.

Examples

fit <- lm(mpg ~ wt, data = mtcars)
env <- qq_lm_envelope(fit, nsim = 100)
str(env)
#> List of 10
#>  $ expected          : num [1:32] -2.15 -1.68 -1.42 -1.23 -1.08 ...
#>  $ observed          : Named num [1:32] -1.52 -1.31 -1.24 -1.16 -1.07 ...
#>   ..- attr(*, "names")= chr [1:32] "Ford Pantera L" "Duster 360" "AMC Javelin" "Camaro Z28" ...
#>  $ sim_orders        : num [1:100, 1:32] -1.76 -2.16 -2.37 -1.92 -2.06 ...
#>  $ conf.level        : num 0.95
#>  $ nsim              : int 100
#>  $ q.type            : int 2
#>  $ pointwise         : num [1:2, 1:32] -2.87 -1.65 -2.21 -1.28 -1.81 ...
#>  $ global            : num [1:2, 1:32] -3.22 -1.39 -2.32 -1.21 -1.87 ...
#>  $ global_coverage   : num 1
#>  $ global_local_alpha: num 0.02
#>  - attr(*, "class")= chr "qq_lm_envelope"