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

In nparLD: Nonparametric Analysis of Longitudinal Data in Factorial Experiments

Nonparametric Tests for the LD-F1 Design

Description

This function performs several tests for the relative treatment effects with global or patterned alternatives for the LD-F1 design (see Details for the definition). For the experiments with LD-F1 design, the Wald-type statistic (WTS), Hotelling's F (T-squared) statistic, and the ANOVA-type statistic (ATS) are calculated for the global alternatives. The hypothesis can also be tested against patterned alternatives to detect various trends. For the design with two time points where no data are missing, tests under Behrens-Fisher and homogeneous variance situations can be performed.

Usage

ld.f1(y, time, subject, w.pat=NULL, time.name="Time", description=TRUE, 
time.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.
subject	a vector of individual subjects
w.pat	a vector of pattern for the pattern alternatives; the default option is NULL. The length, if specified, must be equal to the number of time levels.
time.name	a character vector specifying the name of the time vector; the default option is "Time".
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, 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 LD-F1 design refers to the experimental design with one sub-plot factor (longitudinal data for one homogeneous group of subjects). 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 number of time vector levels; 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.
Hotelling.test	the test statistic, numerator and denominator degrees of freedom (df1, df2), respectively, for the central F distribution, and corresponding p-value of the Hotelling's F (T-squared) 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.
two.sample.test	the test statistic and corresponding p-values (approximated by standard normal and Student's t distributions) of the test under homogeneous variance situation.
two.sample.BF.test	the test statistic and corresponding p-values (approximated by standard normal (N) and Student's t distributions (T)) of the test under the Behrens-Fisher situation where variances of the two samples are not assumed to be equal.
pattern.test	the test statistic and corresponding p-values (approximated by standard normal (N) and Student's t distributions (T)) of the test with patterned alternatives where the patterns are specified by w.pat.
covariance	the covariance matrix.
model.name	the name of the model used.

Note

If there are more than two time points in the data, or if there is a missing observation, two.sample.test and two.sample.BF.test return NULL. If the denominator degrees of freedom (df2) is less than 1, Hotelling.test returns NULL.

Author(s)

Kimihiro Noguchi, Mahbub Latif, Frank Konietschke, Yulia Gel, Edgar Brunner

References

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.f2, f1.ld.f1, f1.ld.f2, f2.ld.f1, ld.ci, panic

Examples

## Example with the "Panic disorder study I" data ##
data(panic)
attach(panic)
w.pat<-c(5,4,3,2,5)
ex.f1<-ld.f1(y=resp, time=time, subject=subject, w.pat=w.pat, time.name="Week", 
description=FALSE, time.order=c(0,2,4,6,8))
# LD F1 Model 
# ----------------------- 
# Check that the order of the time level is correct.
# Time level:   0 2 4 6 8 
# If the order is not correct, specify the correct order in time.order.

## Wald-type statistic 
ex.f1$Wald.test

#     Statistic df p-value
#Week  126.6946  4 1.9822e-26

## ANOVA-type statistic
ex.f1$ANOVA.test

#     Statistic       df p-value
#Week  36.93664 2.234135 1.975781e-18

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