HOW DO SAS compute standard error in Proc Logistic

[desireatem]

Please can some one explain to me how SAS compute standard error is proc logistic

[stat_sas]

Using MLE.

[SteveDenham]

The estimated standard error is sigma(eta), which can be computed as the square root of the quadratic form (1, x') (Vhat sub b) (1, x')'

where (Vhat sub b)  is the estimated covariance matrix of the parameter estimates.

Note that these are all calculated in the so-called transformed space, which depends on the link used.

Steve Denham

[stat_sas]

Thanks Steve - What is the estimation procedure behind this calculation please?

[SteveDenham]

Just as you said--it is maximum likelihood

There are several pages of matrix algebra in the Details section of the PROC LOGISTIC documentation that can be fought through.

But in the end, the key facts to know are: maximum likelihood techniques are used to find the point estimates, estimates of the covariance matrix, the gradient matrix and the Hessian matrix.  Appropriate matrix manipulation results in the quadratic form I mentioned.  The standard errors are then calculated from that quadratic form.  The estimates and standard errors are on the "link" scale.  The point estimates on the original scale are obtained by applying the inverse link function, while the standard errors are obtained by using the delta method (a Taylor series expansion around the point estimate).

Steve Denham

[stat_sas]

Thanks agian Steve - This is a very comprehensive explaination about the MLE estimation. Just to learning more, does Newton-Raphson algorithm play any role in this process?

[SteveDenham · Accepted solution]

The optimization process may be Newton-Raphson, although there are other possible methods. The NLOPTIONS statement will allow for selection of optimization algorithms.  In PROC LOGISTIC this is seldom used, however.  The default methodology in LOGISTIC depends on the number of parameters to be estimated: <40 - Newton Raphson with ridging, 40 to 400 - quasi-Newton, >400 - conjugate gradient.

Steve Denham

[stat_sas]

Thanks so much Steve.

[desireatem]

Thanks Steve