nparLD

nparLD

nparLD provides nonparametric methods for the analysis of longitudinal and repeated-measures data in factorial experiments. The package implements procedures for hypotheses in marginal distribution functions and in unweighted relative marginal effects. It supports crossed factorial designs, missing observations, dependent replicate measurements, rank- and pseudo-rank-based inference, Wald-type and ANOVA-type statistics, multiple contrast procedures, and simultaneous confidence intervals.

Installation

You can install the development version locally with:

devtools::install()

Basic example

library(nparLD)

set.seed(123)

T <- 4
n <- c(10, 10, 10)
N <- sum(T * n)

y <- rnorm(N)
times <- c(rep(1:T, n[1]), rep(1:T, n[2]), rep(1:T, n[3]))
grp <- c(rep(1, n[1] * T), rep(2, n[2] * T), rep(3, n[3] * T))
subjects <- c(
  sort(rep(1:n[1], T)),
  sort(rep((n[1] + 1):(n[1] + n[2]), T)),
  sort(rep((n[1] + n[2] + 1):(n[1] + n[2] + n[3]), T))
)

data <- data.frame(times, grp, subjects, y)

fit <- nparLD(
  y ~ grp * times,
  data = data,
  subject = "subjects",
  hypothesis = "H0p",
  contrast = list("grp:times")
)

fit
plot(fit)
plot(fit$MCTP)

Weighted and unweighted relative effects

The package distinguishes between weighted and unweighted relative marginal effects.

Weighted effects are based on the sample-size weighted reference distribution. They describe relative positions with respect to the empirical distribution obtained by pooling the marginal samples according to their observed sample sizes. Weighted effects are useful as descriptive summaries and correspond to ordinary rank-based estimators.

Unweighted effects are based on an equally weighted reference distribution over the factorial cells. Each cell contributes equally to the reference distribution, independently of its sample size. These effects are the inferential target for hypotheses in relative marginal effects, selected by hypothesis = "H0p", and are estimated using pseudo-ranks.

Consequently, tests of hypotheses in relative marginal effects are performed for unweighted effects. Weighted effects are reported descriptively, but they are not used as the target of H0p tests because their interpretation depends on the sample-size allocation across cells.

````markdown The following example illustrates how the two effect concepts are requested.

data(panic2)

fit_weighted <- nparLD(
  resp ~ group * time,
  data = panic2,
  subject = "subject",
  effect = "weighted",
  hypothesis = "H0F"
)

fit_unweighted <- nparLD(
  resp ~ group * time,
  data = panic2,
  subject = "subject",
  effect = "unweighted",
  hypothesis = "H0F"
)

fit_weighted
fit_unweighted

The first analysis reports weighted effects as descriptive summaries together with tests in marginal distribution functions. The second analysis targets unweighted relative marginal effects and therefore provides the appropriate effect scale for H0p.

Hypothesis types

Use hypothesis = "H0F" to test hypotheses in marginal distribution functions. These tests compare marginal distribution functions either using classical ranks with the argument effect="weighted" or using pseudo-ranks using the argument effect = "unweighted".

Use hypothesis = "H0p" to test hypotheses in unweighted relative marginal effects. These effects describe the relative position of each marginal distribution with respect to a common unweighted reference distribution and are useful for interpretation, contrasts, simultaneous confidence intervals, and plots.

Dependent replicates

Dependent replicate measurements can be specified with the replicate argument.

datensatz2 <- datensatz[rep(seq_len(nrow(datensatz)), each = 3), ]
datensatz2$rep <- rep(1:3, times = nrow(datensatz))
datensatz2$y <- rnorm(nrow(datensatz2))

fit_rep <- nparLD(
  y ~ grp * times,
  data = datensatz2,
  subject = "subjekte",
  replicate = "rep",
  hypothesis = "H0p",
  cell.weights = "subjects"
)

fit_rep

For relative marginal effects, cell.weights = "subjects" targets a typical subject-condition cell, while cell.weights = "observations" targets a typical replicate observation.

Classical longitudinal designs

Earlier versions of nparLD used design-specific functions such as ld.f1(), f1.ld.f1(), or f2.ld.f1(). In the redesigned package, these designs are specified through one general formula interface.

Typical examples are:

For example, the shoulder data correspond to an F2-LD-F1 design:

data(shoulder)

fit <- nparLD(
  resp ~ group1 * group2 * time,
  data = shoulder,
  subject = "subject",
  hypothesis = "H0p",
  contrast = list("group1:time")
)

fit
plot(fit)
plot(fit$MCTP)