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12-04-2015 07:38 AM

Hi,

In Proc Logistics , Maximum Likelihood Estimate is received as an output. For each variable , estimate , Standard Error & Chi-Square statistics is obtained. Estimate = Chi-Square statistics / Standard Error.

My question is Chi Square distribution is the distribution of frequencies , so how can it be used in above formula. The formula very well suits , when we calculate estimate from t-statistics in Linear Regression. T- Statistics follows T distribution which is (x- u)/ SE.

How the same fornmula can be used for Logistic and Linear regression is something not clear to me.

Thanks,

Vishal

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12-04-2015 08:22 AM

Sorry if I am misunderstanding, but I cannot reproduce your assertion that "Estimate = Chi-Square statistics / Standard Error". Could you show us what code you are using (and data, if possible)?

Here is an example from the Getting Started example in the PROC LOGISTIC documentation. In this example, the product of the Estimate column and the Standard Error column does not equal the Wald Chi-Square column.

```
data ingots;
input Heat Soak NotReady Freq @@;
datalines;
7 1.0 0 10 14 1.0 0 31 14 4.0 0 19 27 2.2 0 21 51 1.0 1 3
7 1.7 0 17 14 1.7 0 43 27 1.0 1 1 27 2.8 1 1 51 1.0 0 10
7 2.2 0 7 14 2.2 1 2 27 1.0 0 55 27 2.8 0 21 51 1.7 0 1
7 2.8 0 12 14 2.2 0 31 27 1.7 1 4 27 4.0 1 1 51 2.2 0 1
7 4.0 0 9 14 2.8 0 31 27 1.7 0 40 27 4.0 0 15 51 4.0 0 1
;
ods select ParameterEstimates;
proc logistic data=ingots;
model NotReady(event='1') = Heat Soak;
freq Freq;
run;
```

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12-04-2015 10:51 AM

I think your question is statistical, not really related to SAS. You can review the statistical methods behind logistic regression here:

http://www.upa.pdx.edu/IOA/newsom/da2/ho_logistic.pdf

Or in a variety of other places.

http://www.upa.pdx.edu/IOA/newsom/da2/ho_logistic.pdf

Or in a variety of other places.

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12-04-2015 11:57 AM

The chi-squared statistic in the output is just the Wald statistic, (estimate/SE)^2. The square root of the chi-squared statistic for a single parameter estimate is just the t statistic (with infinite denominator df).