nparLD (version 2.2)

summary.nparLD: Object Summary for nparLD

Description

This function prints out a summary of the object returned by the function nparLD. The summary includes the model and the corresponding formula, the relative treatment effect (RTE), the Wald-type statistic (WTS), and the ANOVA-type statistic (ATS).

Usage

# S3 method for nparLD
summary(object, ...)

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 time1, time2, and group 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, the degrees of freedom (df) of the central chi-squared distribution, and the corresponding p-value of the Wald-type test.

ANOVA.test

the test statistic, the numerator degrees of freedom (df) of the central F distribution, and the corresponding p-value of the ANOVA-type test; the denominator degrees of freedom is set to infinity.

covariance

the covariance matrix.

Conf.Int

the (pointwise) 100(1-alpha) percent confidence intervals. See ld.ci for details.

...

Other function-specific outputs. For example, ANOVA.test.mod.Box which is applicable to designs with whole-plot factor(s).

Arguments

object

an nparLD class object generated by nparLD (see examples).

...

further arguments passed to or from other methods.

On the Test Statistics

Although we provide both Wald-type statistic (WTS, see Wald.test) and ANOVA-type statistic with the denominator degrees of freedom set to infinity (ATS, see ANOVA.test), ATS is typically preferred to WTS as it requires less assumptions on the covariance matrix and it has superior small sample performances. Moreover, for the main effects and interactions involving only the whole-plot factors, the modified ANOVA-type statistic with Box (1954) approximation (ANOVA.test.mod.Box) is preferred to ATS. See Brunner et al. (2002) for more details.

Author

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

Details

The Fx-LD-Fy design refers to the experimental design with x whole-plot factor and y sub-plot factors. A whole-plot (between-subjects) factor refers to a factor effective for each subject at all times. A sub-plot (within-subjects) factor refers to a factor effective at a single time point for all time curves and all subjects. The LD-Fy design refers to the experimental design with no whole-plot factor. See Brunner et al. (2002) for more examples.

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, f2.ld.f1, ld.ci, amylase, edema, shoulder, tree, panic, panic2, plasma, dental, rat, respiration

Examples

## Example with the "Panic disorder study I" data (LD-F1 design) ##
data(panic)
ex.f1.np<-nparLD(resp~time, data=panic, subject="subject", description=FALSE, 
order.warning=FALSE)
summary.nparLD(ex.f1.np)

#Model: 
#LD F1 Model 
 
#Call: 
#resp ~ time

#Relative Treatment Effect (RTE):
#      RankMeans Nobs       RTE
#time0  66.09375   16 0.8199219
#time2  50.50000   16 0.6250000
#time4  41.28125   16 0.5097656
#time6  25.62500   16 0.3140625
#time8  19.00000   16 0.2312500

#Wald-Type Statistc (WTS):
#     Statistic df    p-value
#time  126.6946  4 1.9822e-26

#ANOVA-Type Statistc (ATS):
#     Statistic       df      p-value
#time  36.93664 2.234135 1.975781e-18