qq_lm_envelope

Computes pointwise and simultaneous Q-Q envelopes for internally
studentised residuals from an unweighted <code>lm</code> or <code>aov</code> 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 Schuetzenmeister et al. (2012,
doi:10.1080/03610918.2011.582560).

Automated test selection, visualised. 'visStatistics'
automatically selects and visualises statistical hypothesis tests
comparing two vectors, based on their class and distribution. Visual
outputs, including box plots, bar charts, regression
lines with confidence bands, mosaic plots, residual plots, and Q-Q
plots, are annotated with relevant test statistics, assumption checks,
and post-hoc analyses where applicable. The algorithmic workflow
shifts attention from ad-hoc test selection to visual diagnostic
assessment and statistical interpretation. It is particularly suited
for server-side R applications, where end users interact solely
through a web interface to select data groups and receive a complete
visual statistical analysis automatically. The same automation makes
it useful in time-constrained contexts such as statistical consulting,
where it reduces effort spent on test selection and leaves more room
for interpretation. The implemented tests cover the most frequently
applied inferential methods in biomedical research (Hayat et al.
(2017) <doi:10.1371/journal.pone.0179032>). The test selection
algorithm proceeds as follows: Input vectors of class numeric or
integer are considered numerical; those of class factor are considered
categorical; those of class ordered are considered ordinal.
Assumptions of residual normality and homogeneity of variances are
considered met if the corresponding test yields a p-value greater than
the significance level alpha = 1 - conf.level. (1) When the response
is numerical and the predictor is categorical, a test comparing
central tendencies is selected. In the default setting (group_test =
NULL), residual normality is assessed at every group size using
shapiro.test() applied to the standardised residuals of lm(). If
normality is not met, wilcox.test() is used when the predictor has two
levels and kruskal.test() followed by pairwise.wilcox.test()
otherwise. If normality is met, levene.test() assesses variance
homogeneity. For two-level predictors, Student's t.test(var.equal =
TRUE) is applied if variances are homogeneous and Welch's t.test()
otherwise. For predictors with more than two levels, aov() followed by
TukeyHSD() is applied if variances are homogeneous, and oneway.test()
followed by games.howell() otherwise. Setting group_test to "welch" or
"rank" bypasses these assumption tests and fixes the analysis to
Welch-type or to rank-based tests, respectively.
(2) When both vectors are numerical, lm() is fitted by
default (correlation = FALSE). If correlation = TRUE, Spearman rank
correlation is performed. (3) When the response is ordinal, it is
converted to numeric ranks and the non-parametric path from (1) is
followed (Wilcoxon or Kruskal-Wallis). When both variables are
ordinal and correlation = TRUE, Kendall's tau_b is used instead. (4)
When both vectors are categorical, Cochran's rule (Cochran (1954)
<doi:10.2307/3001666>) is applied to test independence either by
chisq.test() or fisher.test().

Sabine Schilling

visStatistics

Automated Selection and Visualisation of Statistical Hypothesis
Tests

Peter Kauf

qq_lm_envelope function

<dl><dt>model</dt>
<dd>An unweighted <code>lm</code> or <code>aov</code> object.</dd>
<dt>conf.level</dt>
<dd>Numeric confidence level for the envelopes.</dd>
<dt>nsim</dt>
<dd>Integer number of simulated refits.</dd>
<dt>q.type</dt>
<dd>Integer quantile type passed to <code><a href="/link/stats%3A%3Aquantile()?package=visStatistics&version=0.3.0" data-mini-rdoc="visStatistics::stats::quantile()">stats::quantile()</a></code>.</dd>
<dt>tol</dt>
<dd>Numeric tolerance for the simultaneous-band coverage search.</dd>
<dt>max.iter</dt>
<dd>Integer maximum number of bisection iterations.</dd></dl>

Arguments

Simulated Q-Q envelopes for linear model residuals — qq_lm_envelope

<dl>

<dt>model</dt>
<dd>An unweighted <code>lm</code> or <code>aov</code> object.</dd>


<dt>conf.level</dt>
<dd>Numeric confidence level for the envelopes.</dd>


<dt>nsim</dt>
<dd>Integer number of simulated refits.</dd>


<dt>q.type</dt>
<dd>Integer quantile type passed to <code><a href='https://rdrr.io/r/stats/quantile.html'>stats::quantile()</a></code>.</dd>


<dt>tol</dt>
<dd>Numeric tolerance for the simultaneous-band coverage search.</dd>


<dt>max.iter</dt>
<dd>Integer maximum number of bisection iterations.</dd>

</dl>

qq_lm_envelope: Simulated Q-Q envelopes for linear model residuals

Description

Usage

Value

Arguments

Examples