Hi,

I used the binary logistic regression to do prediction. I got a complete separation result. However, I don't know which coefficients should I choose to interpret my model. In iteration 32, I got the information "Estimation terminated at iteration number 32 because maximum iterations has been reached. Final solution cannot be found." In iteration 33, I got the information "Estimation terminated at iteration number 33 because a perfect fit is detected. This solution is not unique." Can I take the results in iteration 32 and use them as the coefficients in my model?

Thanks.

Best,

Amanda

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Chao Shi
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#SPSSStatistics

Hi Amanda,

When there is a perfect fit, as the message indicates, the solution is not unique. Specifically, maximum likelihood estimates of at least some of the parameters do not exist in that case. So no, it's not valid to use the estimated coefficients from that or the prior iteration. The predicted probabilities from the overall model should however be usable, as any combined set of values that the algorithm produces should result in the same predictions, despite changes in individual parameter estimate values.

One approach to handling situations where maximum likelihood estimates do not exist is to use penalized maximum likelihood estimation. An approach due to David Firth has been implemented in an R package named logistf. SPSS Statistics does not currently have a native procedure that implements this approach, but there is an SPSS Statistics R-based extension named STATS_FIRTHLOG that allows SPSS Statistics users to access this package to obtain reasonable estimates of parameters in situations where standard maximum likelihood estimates are not available. You have to install R, including the logistf package, and install the R Essentials and then the STATS_FIRTHLOG extension, in order to use this.

Best,

Dave

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David Nichols
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Original Message:
Sent: Mon January 06, 2020 10:06 PM
From: Chao Shi
Subject: Binary Logistic Regression-Complete Separation

Hi,

I used the binary logistic regression to do prediction. I got a complete separation result. However, I don't know which coefficients should I choose to interpret my model. In iteration 32, I got the information "Estimation terminated at iteration number 32 because maximum iterations has been reached. Final solution cannot be found." In iteration 33, I got the information "Estimation terminated at iteration number 33 because a perfect fit is detected. This solution is not unique." Can I take the results in iteration 32 and use them as the coefficients in my model?

Thanks.

Best,

Amanda

------------------------------
Chao Shi
------------------------------
#SPSSStatistics