f2.ld.f1: Nonparametric Tests for the F2-LD-F1 Design

In nparLD: Nonparametric Analysis of Longitudinal Data in Factorial Experiments

Nonparametric Tests for the F2-LD-F1 Design

Description

This function performs several tests for the relative treatment effects with global or patterned alternatives for the F2-LD-F1 design (see Details for the definition). For the experiments with F2-LD-F1 design, the Wald-type statistic (WTS), the ANOVA-type statistic (ATS), and the modified ANOVA-type statistic with Box (1954) approximation are calculated for testing group and time effects, and interaction.

Usage

f2.ld.f1(y, time, group1, group2, subject, time.name="Time", 
group1.name="GroupA", group2.name="GroupB", description=TRUE, 
time.order=NULL, group1.order=NULL, group2.order=NULL,
plot.RTE=TRUE, show.covariance=FALSE, order.warning=TRUE)

Arguments

y	a vector of numeric variable of interest; missing values should be specified as NA.
time	a vector of the sub-plot factor variable. See Details for more explanation.
group1	a vector of the first whole-plot factor variable. See Details for more explanation.
group2	a vector of the second whole-plot factor variable. See Details for more explanation.
subject	a vector of individual subjects
time.name	a character vector specifying the name of the time vector; the default option is "Time".
group1.name	a character vector specifying the name of the group1 vector; the default option is "GroupA".
group2.name	a character vector specifying the name of the group2 vector; the default option is "GroupB".
description	an indicator for whether a short description of the output should be shown; the default option is TRUE.
time.order	a character or numeric vector specifying the order of the time levels; the default option is NULL.
group1.order	a character or numeric vector specifying the order of the time2 levels; the default option is NULL, in which case, the levels are in the order of the original data.
group2.order	a character or numeric vector specifying the order of the group levels; the default option is NULL, in which case, the levels are in the order of the original data.
plot.RTE	an indicator for whether a plot of the relative treatment effect (RTE) should be shown; the default option is TRUE.
show.covariance	an indicator for whether the covariance matrix should be shown; the default option is FALSE, in which case, NULL is returned.
order.warning	an indicator for whether a short description of the warning regarding the ordering of factors should be shown; the default option is TRUE.

Details

The F2-LD-F1 design refers to the experimental design with two whole-plot factors (where group2 is the stratification of group1) and one sub-plot factor. A whole-plot factor refers to a factor effective for each subject at all times. A sub-plot factor refers to a factor effective at a single time point for all time curves and all subjects. See Brunner et al. (2002) for more examples.

Value

A list with the following numeric components.

RTE	summary of the relative treatment effect (RTE) in a n-by-3 matrix form, where n is the total number of time, group1, and group2 levels, and group-time interactions; the summary includes the mean of the ranks (RankMeans) in the 1st column, number of observations without counting the repeated measurements within the cell (Nobs) in the 2nd column, and the relative treatment effect (RTE) in the 3rd column.
Wald.test	the test statistic, degrees of freedom (df) for the central chi-square distribution, and corresponding p-value of the Wald-type test.
ANOVA.test	the test statistic, numerator degrees of freedom (df) for the central F distribution, and corresponding p-value of the ANOVA-type test; denominator degrees of freedom is set to infinity.
ANOVA.test.mod.Box	the test statistic, numerator and denominator degrees of freedom (df1, df2), respectively, for the central F distribution, and corresponding p-value of the ANOVA-type test for the whole-plot factors and their interaction.
covariance	the covariance matrix.
model.name	the name of the model used.

Author(s)

Kimihiro Noguchi, Karthinathan Thangavelu, Frank Konietschke, Yulia Gel, Edgar Brunner

References

Box, G.E.P. (1954). Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics, 25, 290-302.

Brunner, E., Domhof, S., and Langer, F. (2002). Nonparametric Analysis of Longitudinal Data in Factorial Experiments, Wiley, New York.

Brunner, E. and Langer, F. (1999). Nichtparametrische Analyse longitudinaler Daten, R. Oldenbourg Verlag, Munchen Wien.

Noguchi, K., Gel, Y.R., Brunner, E., and Konietschke, F. (2012). nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Journal of Statistical Software, 50(12), 1-23.

See Also

nparLD, ld.f1, ld.f2, f1.ld.f1, f1.ld.f2, ld.ci, shoulder

Examples

## Example with the "Shoulder tip pain study" data ##
data(shoulder)
attach(shoulder)
ex.f2f1<-f2.ld.f1(y=resp, time=time, group1=group1, group2=group2, 
subject=subject, time.name="Time", group1.name="Treatment", 
group2.name="Gender", description=FALSE, time.order=c(1,2,3,4,5,6), 
group1.order=c("Y","N"), group2.order=c("F","M"))
# F2 LD F1 Model 
# ----------------------- 
# Check that the order of the time, group1, and group2 levels are correct.
# Time level:   1 2 3 4 5 6 
# Group1 level:   Y N 
# Group2 level:   F M 
# If the order is not correct, specify the correct order in time.order, 
# group1.order, or group2.order.
#
#
# Warning(s):
# The covariance matrix is singular. 

## Wald-type statistic 
ex.f2f1$Wald.test

#                        Statistic df      p-value
#Treatment             16.40129021  1 5.125033e-05
#Gender                 0.04628558  1 8.296575e-01
#Time                  16.34274332  5 5.930698e-03
#Treatment:Gender       0.03583558  1 8.498554e-01
#Treatment:Time        27.51450085  5 4.527996e-05
#Gender:Time           12.37903186  5 2.994753e-02
#Treatment:Gender:Time  5.11864769  5 4.015727e-01

## ANOVA-type statistic
ex.f2f1$ANOVA.test

#                        Statistic       df      p-value
#Treatment             16.40129021 1.000000 5.125033e-05
#Gender                 0.04628558 1.000000 8.296575e-01
#Time                   3.38218704 2.700754 2.120366e-02
#Treatment:Gender       0.03583558 1.000000 8.498554e-01
#Treatment:Time         3.71077200 2.700754 1.398190e-02
#Gender:Time            1.14434841 2.700754 3.272967e-01
#Treatment:Gender:Time  0.43755394 2.700754 7.054255e-01

## ANOVA-type statistic for the whole-plot factors and 
## their interaction
ex.f2f1$ANOVA.test.mod.Box
#                   Statistic df1      df2      p-value
#Treatment        16.40129021   1 21.86453 0.0005395379
#Gender            0.04628558   1 21.86453 0.8316516274
#Treatment:Gender  0.03583558   1 21.86453 0.8516017168

nparLD documentation built on Aug. 7, 2022, 1:06 a.m.