## Interpretation of coefficients in PROC LOGISTIC for reference level encoding

Occasional Contributor
Posts: 5

# Interpretation of coefficients in PROC LOGISTIC for reference level encoding

[ Edited ]

Hello all,

Can some one explain the following question?

The following LOGISTIC procedure output analyzes the relationship between a binary response and an ordinal predictor variable, wrist_size Using reference cell coding, the analyst selects Large (L) as the reference level.

Analysis of Maximum likelihood estimates

Parameter         DF          Estimate    standard error     Wald Chi-sq      Pr>Chisq

Intercept            1            -1.0415      0.4749                  4.8101            0 .0283

wrist_size  M     1            1.1234       0.4989                  5.0697            0.0243

wrist_size S      1             1.6078      0.5478                  8.6133             0.0033

What is the estimated logit for a person with large wrist size?

PROC Star
Posts: 1,288

## Re: Statistics

Always a good idea to post your code. Gives us a lot of information and makes it easier to help you.

You can get the desired quantity by using the ESTIMATE Statement like this

estimate 'Coef for wrist_size L' wrist_size -1 -1;

Occasional Contributor
Posts: 5

## Re: Statistics

The answer to the question is -1.0415 , the value of intercept which is a bit confusing.

Can someone explain this?

Super User
Posts: 10,788

## Re: Statistics

According to SAS documentation about parameterization method.

There is not a column of Large (L), which means its parameter should be zero. Therefore, its logit = parameter estimator of intercept.

Posts: 3,069

## Re: Statistics

[ Edited ]

@Ksharp provides some important information regarding how SAS handles categorical (CLASS) variables in its modeling. One level will always have a coefficient of zero, making the true value of the coefficient for this level = zero + intercept (for a simple one-way design), while the other variables will have a coefficient = (coefficient shown) + intercept (for a simple one-way design).

A better way to estimate the effect of CLASS variables in SAS is to use the LSMEANS command, and then this problem goes away. Each level (even the one with the zero coefficient) is shown with the math above computed for you.

If I may be so bold, you have entitled two recent posts "Statistics", and "Statistics" is a very very very very broad topic, and not a good title. You would be wise to provide more meaningful (and not so broad) title such as "Coefficients in PROC LOGISTIC".

--
Paige Miller
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