VORTHPOLYNOMIAL procedure

Forms orthogonal polynomials over time for repeated measures (J.T.N.M. Thissen).

Options

TIMEPOINTS = variate

Variate of timepoints; default uses the suffixes of the DATA pointer

MAXDEGREE = scalar

The number of contrasts (excluding the mean); default is the number of identifiers in the CONTRAST pointer minus 1

Parameters

DATA = pointers

Each pointer contains the data variates (observed at successive times); must be set

CONTRAST = pointers

To save the calculated contrasts: the first variate contains the means, the second the linear polynomial contrasts, the third the quadratic polynomial contrasts etc; must be set

Description

A repeated measures experiment is one in which the same set of units, or subjects, is observed at a sequence of times to investigate treatment effects over a period of time. VORTHPOLYNOMIAL calculates orthogonal polynomial contrasts in time for each experimental unit. These contrasts can then be analysed given the block and treatment structure at each timepoint.

The observed data is specified in a pointer containing a set of variates, each one containing the measurements made on the subjects at one of the occasions on which they were observed, and input to the procedure using the DATA parameter. The variate in option TIMEPOINTS specifies the actual times when the measurements were taken. If this is not specified, the suffixes of the DATA pointer are taken as values for the timepoints.

The calculated contrasts are saved in a pointer which must be specified by the CONTRAST parameter. This points to a list of variates: the first variate saves the means over the DATA variates, the second variate saves the linear polynomial contrast, the third the quadratic polynomial, and so on. Provided the MAXDEGREE option is specified, the CONTRAST need not be declared in advance. The suffixes of the pointer are then defined to be 0, 1, 2 ...

The number of contrasts can be specified using option MAXDEGREE and should be less than the number of timepoints. The default setting is the number of identifiers in the pointer specified by the CONTRAST parameter minus 1. If MAXDEGREE is set, and the CONTRAST pointer has been declared to be of length less than MAXDEGREE+1, a fault message is produced.

If an experimental unit has a missing value in one of the DATA variates each contrast in the CONTRAST pointer (including the mean) gets a missing value for this unit.

Options: TIMEPOINTS, MAXDEGREE.

Parameters: DATA, CONTRAST.

Method

Procedure ORTHPOLYNOMIAL gets orthogonal polynomial coefficients which are used to form the contrasts.

Action with RESTRICT

Each variate in the DATA pointer should be restricted in the same way. The saved orthogonal polynomial contrasts are restricted accordingly. The TIMEPOINTS variate must not be restricted.