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I ran into some problems with the interpretation of the parameter estimate of the logistic model recently. When I contacted SAS, here’s their response. Please make sure you specify PARAM=GLM option in the CLASS statement when you want the parameterization to the reference cell coding, ’cause the default is EFFECT. Also I attach the syntax for PARAM below, and you can go to online manual for a better view.
==================== From SAS =======================================
The calculation of the Odds Ratios depends upon the parameterization used for the categorical independent variable. By default, Proc LOGISTIC uses effects coding so the odds ratios are not calculated as EXP(estimate). You can change the parameterization to reference cell coding by using the PARAM=GLM option on the CLASS statement. Using this coding does lead to odds ratios being calculated as EXP(estimate). Note that for continuous variables the odds ratios are always calculated as EXP(estimate). Also note that no matter what parameterization is used, the values of the odds ratios are always the same.
For additional details on this topic, as well as setting the reference levels for the CLASS statement please reference the Syntax section (for the CLASS
statement) and the “Odds Ratio Estimation” portion of the Details section of the LOGISTIC chapter in the SAS/STAT User’s Guide for V8.
==================== Syntax from SAS online manual =========================
PARAM=keyword
specifies the parameterization method for the classification variable or variables. Design matrix columns are created from CLASS variables according to the following coding schemes. The default is PARAM=EFFECT. If PARAM=ORTHPOLY or PARAM=POLY, and the CLASS levels are numeric, then the ORDER= option in the CLASS statement is ignored, and the internal, unformatted values are used.
EFFECT
specifies effect coding
GLM
specifies less than full rank, reference cell coding; this option can only be used as a global option ORTHPOLY specifies orthogonal polynomial coding POLYNOMIAL | POLY specifies polynomial coding REFERENCE | REF specifies reference cell coding
The EFFECT, POLYNOMIAL, REFERENCE, and ORTHPOLY parameterizations are full rank. For the EFFECT and REFERENCE parameterizations, the REF= option in the CLASS statement determines the reference level.
Consider a model with one CLASS variable A with four levels, 1, 2, 5, and 7. Details of the possible choices for the PARAM= option follow.
EFFECT
Three columns are created to indicate group membership of the nonreference levels. For the reference level, all three dummy variables have a value of -1. For instance, if the reference level is 7 (REF=7), the design matrix columns for A are as follows.
Effect Coding
A Design Matrix
1 1 0 0
2 0 1 0
5 0 0 1
7 -1 -1 -1
Parameter estimates of CLASS main effects using the effect coding scheme estimate the difference in the effect of each nonreference level compared to the average effect over all 4 levels.
GLM
As in PROC GLM, four columns are created to indicate group membership. The design matrix columns for A are as follows.
GLM Coding
A Design Matrix
1 1 0 0 0
2 0 1 0 0
5 0 0 1 0
7 0 0 0 1
Parameter estimates of CLASS main effects using the GLM coding scheme estimate the difference in the effects of each level compared to the last level.
ORTHPOLY
The columns are obtained by applying the Gram-Schmidt orthogonalization to the columns for PARAM=POLY. The design matrix columns for A are as follows.
Orthogonal Polynomial Coding
A Design Matrix
1 -1.153 0.907 -0.921
2 -0.734 -0.540 1.473
5 0.524 -1.370 -0.921
7 1.363 1.004 0.368
POLYNOMIAL
POLY
Three columns are created. The first represents the linear term (x), the second represents the quadratic term (x2), and the third represents the cubic term (x3), where x is the level value. If the CLASS levels are not numeric, they are translated into 1, 2, 3, … according to their sorting order. The design matrix columns for A are as follows.
Polynomial Coding
A Design Matrix
1 1 1 1
2 2 4 8
5 5 25 125
7 7 49 343
REFERENCE
REF
Three columns are created to indicate group membership of the nonreference levels. For the reference level, all three dummy variables have a value of 0. For instance, if the reference level is 7 (REF=7), the design matrix columns for A are as follows.
Reference Coding
A Design Matrix
1 1 0 0
2 0 1 0
5 0 0 1
7 0 0 0
Parameter estimates of CLASS main effects using the reference coding scheme estimate the difference in the effect of each nonreference level compared to the effect of the reference level.
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