RM: Tests for Repeated Measures in Semi-Parametric Factorial Designs

Description

The RM() function calculates the Wald-type statistic (WTS), the ANOVA-type statistic (ATS) as well as resampling versions of these test statistics for semi-parametric repeated measures designs.

Usage

RM(
  formula,
  data,
  subject,
  within,
  no.subf,
  iter = 10000,
  alpha = 0.05,
  resampling = "Perm",
  para = FALSE,
  CPU,
  seed,
  CI.method = "t-quantile",
  dec = 3
)

Value

An RM 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, the mean and 100*(1-alpha)% confidence intervals (based on t-quantiles).
Covariance: The estimated covariance matrix.
WTS: The value of the WTS along with degrees of freedom of the central chi-square distribution and corresponding p-value.
ATS: The value of the ATS, degrees of freedom of the central F distribution and the corresponding p-value.
resampling: p-values for the test statistics based on the chosen resampling approach.

Arguments

formula: A model formula object. The left hand side contains the response variable and the right hand side contains the factor variables of interest. The within-subject factor(s) must be the last factor(s) in the formula, e.g. outcome ~ 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. Either this or no.subf must be specified.
no.subf: The number of within-subject factors in the data. Must be specified if within is omitted.
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 "Perm" (randomly permute all observations), "paramBS" (parametric bootstrap approach) and "WildBS" (wild bootstrap approach with Rademacher weights). Except for the Wild Bootstrap, all methods are applied to the WTS only.
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.
CI.method: The method for calculating the quantiles used for the confidence intervals, either "t-quantile" (the default) or "resampling" (the quantile of the resampled WTS).
dec: Number of decimals the results should be rounded to. Default is 3.

Details

The RM() function provides the Wald-type statistic as well as the ANOVA-type statistic for repeated measures designs with metric data as described in Friedrich et al. (2017). These are even applicable for non-normal error terms and/or heteroscedastic variances. It is implemented for designs with an arbitrary number of between-subject (whole-plot) and within-subject (sub-plot) factors and allows for different sample sizes. In addition to the asymptotic p-values, it also provides p-values based on resampling approaches. NOTE: The number of within-subject factors or their labels need to be specified in the function call. If only one factor is present, it is assumed that this is a within-subject factor (e.g. time).

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. Example: Consider a study with one between-subject factor "treatment" with levels verum and placebo and one within-subject factor "time" (4 measurements). If subjects in the placebo group are labeled 1-20 and subjects in the verum group have the same labels, the program erroneously assumes 20 individuals with 8 measurements each instead of 40 individuals with 4 measurements each.

References

Friedrich, S., Konietschke, F., and Pauly, M. (2019). Resampling-Based Analysis of Multivariate Data and Repeated Measures Designs with the R Package MANOVA.RM. The R Journal, 11(2), 380-400.

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.

Examples

Run this code

data(o2cons)
if (FALSE) {
oxy <- RM(O2 ~ Group * Staphylococci * Time, data = o2cons, 
            subject = "Subject", no.subf = 2, iter = 1000,
            resampling = "Perm")
summary(oxy)
plot(oxy, factor = "Group") 
 
# For more details including the output of the examples also refer to the 
# package vignette.

# using the EEG data, consider additional within-subjects factors 'brain region' 
# and 'feature'
data(EEG)
EEG_model <- RM(resp ~ sex * diagnosis * feature * region, 
               data = EEG, subject = "id", within = c("feature", "region"),
               resampling = "WildBS",
               iter = 1000,  alpha = 0.01, seed = 987, dec = 2)
summary(EEG_model)
}

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