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.
See also
Procedure: ORTHPOLYNOMIAL.
Commands for: Calculations and manipulation, Repeated measurements.
Example
CAPTION 'VORTHPOLYNOMIAL example',\
!t('Data from Box, G.E.P. (1950). Problems in the analysis of',\
'growth and wear curves. Biometrics, 6, 362-389.'); STYLE=meta,plain
UNIT [NVALUES= 27]
TEXT [VALUES= Control, Thyroxin, Thiouracil] Labels
FACTOR [LABELS= Labels; VALUES= 10(1), 7(2), 10(3)] Treat
FACTOR [LEVELS= 27] Rat
READ Rat, Weight[1...5]
1 57 86 114 139 172 2 60 93 123 146 177
3 52 77 111 144 185 4 49 67 100 129 164
5 56 81 104 121 151 6 46 70 102 131 153
7 51 71 94 110 141 8 63 91 112 130 154
9 49 67 90 112 140 10 57 82 110 139 169
11 59 85 121 146 181 12 54 71 90 110 138
13 56 75 108 151 189 14 59 85 116 148 177
15 57 72 97 120 144 16 52 73 97 116 140
17 52 70 105 138 171
18 61 86 109 120 129 19 59 80 101 111 122
20 53 79 100 106 133 21 59 88 100 111 122
22 51 75 101 123 140 23 51 75 92 100 119
24 56 78 95 103 108 25 58 69 93 116 140
26 46 61 78 90 107 27 53 72 89 104 122 :
VORTHPOLYNOMIAL Weight; CONTRAST= !P(Mean, Lin, Quad, Cub, Quart)
PRINT Mean, Lin, Quad, Cub, Quart
TREATMENT Treat
ANOVA [FPROBABILITY=yes] Mean, Lin, Quad