multRM: Tests for Repeated Measures in Multivariate Semi-Parametric...

In smn74/MANOVA.RM: Resampling-Based Analysis of Multivariate Data and Repeated Measures Designs

Tests for Repeated Measures in Multivariate Semi-Parametric Factorial Designs

Description

The multRM() function calculates the Wald-type statistic (WTS) and the modified ANOVA-type statistic (MATS) as well as resampling versions of these test statistics for multivariate semi-parametric repeated measures designs.

Usage

multRM(
  formula,
  data,
  subject,
  within,
  iter = 10000,
  alpha = 0.05,
  resampling = "paramBS",
  para = FALSE,
  CPU,
  seed,
  dec = 3
)

Arguments

formula	A model formula object. The left hand side contains the matrix of response variables (using cbind()) and the right hand side contains the factor variables of interest. The within-subject factors must be specified last in the formula, e.g. cbind(outcome1, outcome2) ~ between1 * between2 * within1 * within2.
data	A data.frame, list or environment containing the variables in formula. Data must be in long format and must not contain missing values.
subject	The column name of the subjects in the data. NOTE: Subjects within different groups of between-subject factors must have individual labels, see Details for more explanation.
within	Specifies the within-subject factor(s) in the formula.
iter	The number of iterations used for calculating the resampled statistic. The default option is 10,000.
alpha	A number specifying the significance level; the default is 0.05.
resampling	The resampling method to be used, one of "paramBS" (parametric bootstrap approach) and "WildBS" (wild bootstrap approach with Rademacher weights).
para	If parallel computing should be used. Default is FALSE.
CPU	The number of cores used for parallel computing. If not specified, cores are detected via detectCores.
seed	A random seed for the resampling procedure. If omitted, no reproducible seed is set.
dec	Number of decimals the results should be rounded to. Default is 3.

Details

The multRM() function provides the Wald-type statistic as well as the modified ANOVA-type statistic (Friedrich and Pauly, 2018) for repeated measures designs with multivariate metric outcomes. These methods are even applicable for non-normal error terms and/or heteroscedastic variances. Implemented are designs with an arbitrary number of between-subject (whole-plot) and within-subject (sub-plot) factors and the methods allow for different sample sizes. In addition to the asymptotic p-values, p-values based on resampling approaches are provided. NOTE: The within-subject factors need to be specified in the function call (within =).

If subjects in different groups of the between-subject factor have the same id, they will not be identified as different subjects and thus it is erroneously assumed that their measurements belong to one subject. See RM for more explanations and an example.

Value

A MANOVA object containing the following components:

Descriptive	Some descriptive statistics of the data for all factor level combinations. Displayed are the number of individuals per factor level combination and the vector of means (one column per dimension).
Covariance	The estimated covariance matrix.
WTS	The value of the WTS along with degrees of freedom of the central chi-square distribution and p-value.
MATS	The value of the MATS.
resampling	p-values for the test statistic based on the chosen resampling approach.

References

Friedrich, S., Brunner, E. and Pauly, M. (2017). Permuting longitudinal data in spite of the dependencies. Journal of Multivariate Analysis, 153, 255-265.

Bathke, A., Friedrich, S., Konietschke, F., Pauly, M., Staffen, W., Strobl, N. and Hoeller, Y. (2018). Testing Mean Differences among Groups: Multivariate and Repeated Measures Analysis with Minimal Assumptions. Multivariate Behavioral Research, 53(3), 348-359, Doi: 10.1080/00273171.2018.1446320.

Friedrich, S., Konietschke, F., Pauly, M. (2017). GFD - An R-package for the Analysis of General Factorial Designs. Journal of Statistical Software, 79(1), 1-18.

Friedrich, S., and Pauly, M. (2018). MATS: Inference for potentially singular and heteroscedastic MANOVA. Journal of Multivariate Analysis, 165, 166-179.

See Also

RM, MANOVA

Examples

## Not run: 
data(EEG)
library(tidyr)
eeg <- spread(EEG, feature, resp)
fit <- multRM(cbind(brainrate, complexity) ~ sex * region, data = eeg, 
              subject = "id", within = "region")
summary(fit)

## End(Not run)

smn74/MANOVA.RM documentation built on Aug. 30, 2023, 12:01 a.m.