Many regression based tests for single sample repeated measures {Rfast}

Many regression based tests for single sample repeated measures

Description

Many regression based tests for single sample repeated measures.

Usage

rm.lines(y, x, logged = FALSE)
rm.anovas(y, x, logged = FALSE)

Arguments

y

A matrix with the data, where each column refers to a different sample of subjects. For example, the first column is the repeated measurements of a sample of subjects, the second column contains repeated measurements of a second sample of subjects and so on. Within each column, the measurements of each subjects are stacked one upon the other. Say for examples there are n subjects and each of them has been measured d times (in time or at different experimental conditions). We put these in a matrix with just one column. The first d rows are the measurements of subject 1, the next d rows are the measurements of subject 2 and so on.

x

A numerical vector with time (usually) or the the predictor variable. For example the temperature, or the pressure. See the details for more information. Its length is equal to the time points for example, i.e. it must not have the same length as the number of rows of y. For the "rm.lines" this is a continuous variable.

For the "rm.anovas" this is treated as a categorical variable, indicating say the type of experimental condition, but no difference between the points is important. Hence, for this function only, x can also be a facto variable.

logged

Should the p-values be returned (FALSE) or their logarithm (TRUE)?

Details

In order to see whether the repeated measurements are associated with a single covariate, e.g. time we perform many regressions and each time calculate the slope. For each subject, its regression slope with the covariate is calculated. In the end a t-test for the hypothesis that the average slopes is zero is performed. The regression slopes ignore that the measurements are not independent, but note that the slopes are independent, because they come from different subjects. This is a simple, summary statistics based approach found in Davis (2002), yet it can provide satisfactory results.

The second approach ("rm.anovas") found in Davis (2002) is the usual repeated measures ANOVA. In this case, suppose you have taken measurements on one or more variables from the same group of people. See the example below on how to put such data.

Value

A matrix with the test statistic (t-test) and its associated p-value.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[e-mail]> and Manos Papadakis <[e-mail]>.

References

Charles S. Davis (2002). Statistical methods for the analysis of repeated measures. Springer-Verlag, New York.

See Also

rint.regbx, rint.reg, varcomps.mle

Examples

y <- c(74.5,81.5,83.6,68.6,73.1,79.4,
75.5,84.6,70.6,87.3,73.0,75.0,
68.9,71.6,55.9,61.9,60.5,61.8,
57.0,61.3,54.1,59.2,56.6,58.8,
78.3,84.9,64.0,62.2,60.1,78.7,
54.0,62.8,63.0,58.0,56.0,51.5,
72.5,68.3,67.8,71.5,65.0,67.7,
80.8,89.9,83.2,83.0,85.7,79.6)
y <- as.matrix(y)
### the first 6 measurements are from subject 1, measurments 7-12 are from subject 2,
## measurements 13-18 are from subject 3 and so on.
x <- c(-10, 25, 37, 50, 65, 80) ## all subjects were measured at the same time points
res<-rm.lines(y, x) ## Is linear trend between the measurements and the temperature?
res<-rm.anovas(y, x)  ## Tests whether the means of the individuals are the same
## the temperature is treated as categorical variable here.

## fake example
y <- matrnorm(10, 4)
## the y matrix contains 4 repeated measurements for each of the 10 persons.
x <- 1:4
## we stack the measurements of each subject, one under the other in a matrix form.
y1 <- matrix( t(y) )
res<-rm.anovas(y1, x)  ## perform the test
z <- matrix( rnorm(20 * 8), ncol = 2) ## same example, but with 2 sets of measurements.
res<-rm.anovas(z, x)