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What to do When Your Hessian is Not Invertible: Alternatives to Model Respecification in Nonlinear Estimation
Gill, Jeff
King, Gary

Uploaded 05-14-2002
Keywords Hessian
generalized inverse
maximum likelihood
statistical computing
importance sampling
generalized linear model
singular normal
Abstract What should a researcher do when statistical analysis software terminates before completion with a message that the Hessian is not invertable? The standard textbook advice is to respecify the model, but this is another way of saying that the researcher should change the question being asked. Obviously, however, computer programs should not be in the business of deciding what questions are worthy of study. Although noninvertable Hessians are sometimes signals of poorly posed questions, nonsensical models, or inappropriate estimators, they also frequently occur when information about the quantities of interest does exist in the data, through the likelihood function. We explain the problem in some detail and lay out two preliminary proposals for ways of dealing with noninvertable Hessians without changing the question asked.

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