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Hi, I am not understanding what the difference is between model convergence (as in a multivariable logistic regression model), versus the fit of a model.

In SAS, does QIC tell us the fit of a model?

In SAS, does QIC tell us the fit of a model?

Model Convergence- the model is estimated in a way that uses multiple runs (think successive approximations). If a solution is available, the model will converge on a solution. If, for one reason or another, the model cannot converge, then it means that an "appropriate" solution was not found during the estimation procedure. Be cautious, though, because some programs will still give you model output with an error message for nonconvergence (the solutions aren't appropriate, so you need to figure out what's going on).

Model Fit- the degree of how "compatible" the model is with the data (maybe thought of as how well the model explains or predicts the outcome variable).

QIC is similar to the AIC for model fit-- smaller is better. The QIC, as I understand it (from a text I just referenced), is utilized to help determine the correlation structure with better fit. However, caution should be applied, as the book (Allison's Logitic Regression in SAS) indicates that the QIC can be misleading in that nonsensical correlation structures (per theory or prior knowledge) can appear to fit the data "better". Use subject matter knowledge when using the QIC to evaluate the correlation structure if there is a disagreement between structures.

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One question would be: what can cause a model to not converge? Am I correct in saying that sparsity in data would potentially cause convergence problems since the model is not populated with enough data to work properly/to converge on a solution?

In terms of AIC to assess model fit, is it only used as a relative measure like QIC i.e. must compare it to AICs from other models, and lowest AIC is the model with the best fit?

Lastly, I am using proc genmod in SAS for modified Poisson multivariable regression (with a binary outcome), and I heard that model fit cannot be assessed in this scenario. Are you aware of the reason for this?

Similarly, I heard that the assumptions of proc genmod for modified poisson regression cannot actually be verified using SAS. Do you why this is? Couldn't identify anything related to this in the literature.

Thanks, that was really helpful!

One question would be: what can cause a model to not converge? Am I correct in saying that sparsity in data would potentially cause convergence problems since the model is not populated with enough data to work properly/to converge on a solution?

One question would be: what can cause a model to not converge? Am I correct in saying that sparsity in data would potentially cause convergence problems since the model is not populated with enough data to work properly/to converge on a solution?

In terms of AIC to assess model fit, is it only used as a relative measure like QIC i.e. must compare it to AICs from other models, and lowest AIC is the model with the best fit?

Lastly, I am using proc genmod in SAS for modified Poisson multivariable regression (with a binary outcome), and I heard that model fit cannot be assessed in this scenario. Are you aware of the reason for this?

Similarly, I heard that the assumptions of proc genmod for modified poisson regression cannot actually be verified using SAS. Do you why this is? Couldn't identify anything related to this in the literature.

If you have access to a copy of Paul Allison's "Logistic Regression Using the SAS System: Theory and Application" (2nd edition), I would recommend looking through the Poisson chapter. (I haven't had the chance to read it fully as of yet.) The book, however, is rated well and is very conversational (and it uses SAS for it's examples), so this seems like it might be useful for you if you can access it (unless another user is able to clarify these points for you).

Sorry I couldn't be of further assistance. Convergence issues crop up in different methods that use iterative estimation processes, so I thought I would make an attempt to help out.

Thanks again, very helpful info.

I was wondering if you could describe how the model is estimated as it converges on a solution. What is the mechanism at work behind that estimation process (for modified poisson for instance). Are you referring to MLE for instance?

I was wondering if you could describe how the model is estimated as it converges on a solution. What is the mechanism at work behind that estimation process (for modified poisson for instance). Are you referring to MLE for instance?