orpoly Orthogonal polyomial contrasts (unequal spacing | N) orpoly

# SAS Macro Programs: orpoly

\$Version: 1.1 (10 Jun 2003)
Michael Friendly
York University

## The orpoly macro ( get orpoly.sas)

### Orthogonal polyomial contrasts (unequal spacing | N)

For ANOVA models with quantitative factor variables, it is most useful to describe and analyse the factor effects using tests for linear, quadratic, etc. effects. These tests could be carried out with a regression model, but orthogonal polynomial contrasts provide a way to do the same tests, in an ANOVA framework with PROC GLM (or PROC MIXED). But, you need to find the appropriate contrast coefficients.

The ORPOLY macro finds contrast coefficients for orthogonal polynomials for testing a quantitative factor variable, and constructs CONTRAST (or ESTIMATE) statements (for use with PROC GLM or PROC MIXED) using these values.

This is most useful when either (a) the factor levels are unequally spaced (Trials=1 2 4 10), or (b) the sample sizes at the different levels are unequal. In these cases, the 'standard' orthogonal polynomial coefficients cannot be used. The ORPOLY macro uses the SAS/IML `orpoly()` function to find the correct values, and to construct the required CONTRAST (or ESTIMATE) statements.

When the factor levels are equally spaced, *and* sample sizes are equal, the POLY macro provides a simpler way to generate the contrast coefficients, and the associated INTER macro generates contrasts for interactions among the polynomial contrasts.

### Method

The ORPOLY macro uses the SAS/IML `orpoly()` function to find the correct values, and to construct the required CONTRAST (or ESTIMATE) statements.

## Usage

The ORPOLY macro is defined with keyword parameters. The VAR= parameter must be specified. The arguments may be listed within parentheses in any order, separated by commas. For example:
```  %orpoly(var=A, file=temp);
```

### Parameters

Default values are shown after the name of each parameter.
DATA=
The name of the input data set [Default: `DATA=_LAST_`]
VAR=
The `name(s)` of quantitative factor `variable(s)` for orthogonal polynomial contrasts.
DEG=
Maximum degree of orthogonal polynomial contrasts
FILE=
Fileref for contrast statements. The default, `FILE=PRINT`, simply prints the generated statements in the listing file.

To use the generated contrast statements directly following a PROC GLM step, use the FILE= parameter to assign a fileref and create temporary file, which may be used in a GLM step.

TYPE=
Type of statement generated: CONTRAST, ESTIMATE, or BOTH [Default: `TYPE=CONTRAST`]

### Example

Generate some data, with linear & quad A effects, linear B. Levels of B are unequally spaced;
```  data testit;
do a=1 to 5;
do b=1, 5, 9, 13;
do obs=1 to 2;
y = a + a*a + b + 5*normal(0);
output;
end;
end;
end;
run;
```

Assign a filename for the CONTRAST statements, generate them with ORPOLY, and `%INCLUDE` in the GLM step.

```  filename poly 'orpoly.tst' mod;
%orpoly(data=testit, var=a b, file=poly);
```

```  proc glm data=testit;
class a b;
model y=a b a*b;
%include poly;
```

The ORPOLY macro generates the following lines, which are used in the PROC GLM step:

```  contrast "A-lin" A -0.22361 -0.11180 -0.00000  0.11180  0.22361;
contrast "A-quad" A  0.18898 -0.09449 -0.18898 -0.09449  0.18898;
contrast "A-3rd" A -0.11180  0.22361  0.00000 -0.22361  0.11180;

contrast "B-lin" B -0.21213 -0.07071  0.07071  0.21213;
contrast "B-quad" B  0.15811 -0.15811 -0.15811  0.15811;
```