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