why is log-gamma default shape parameter set to 2.5 rather than 2?

[Ben Bolker]

The Chung et al. Psychometrika paper discusses a $\textrm{log-gamma}(\alpha = 2, \lambda \to 0)$ setting for the prior (as the least-informative prior that will guarantee variance > 0). Yet the code uses shape = 2.5. Can you say what the justification was? (e.g., does setting the value to exactly 2.0 lead to numeric problems in some cases, and you decided to make it 2.5 rather than [say] 2.001) ?

[Vincent Dorie]

I really don't remember. It's probably because I wrote the code before the paper and alpha = 2.5 cancels out the first order bias. I think 2 was used for the paper because of its linear behavior near 0.

…

On Fri, May 3, 2024 at 8:24 PM Ben Bolker ***@***.***> wrote: The Chung et al. *Psychometrika* paper discusses a $\textrm{log-gamma}(\alpha = 2, \lambda \to 0)$ setting for the prior (as the least-informative prior that will guarantee variance > 0). Yet the code <https://github.com/vdorie/blme/blob/2f2d55c26f30fb0e4398aefc74f590c17c75caf6/R/dist.R#L169> uses shape = 2.5. Can you say what the justification was? (e.g., does setting the value to exactly 2.0 lead to numeric problems in some cases, and you decided to make it 2.5 rather than [say] 2.001) ? — Reply to this email directly, view it on GitHub <#15>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAE5P4GH2KI7BSW6AMUCPO3ZAQTD5AVCNFSM6AAAAABHGKUK2GVHI2DSMVQWIX3LMV43ASLTON2WKOZSGI3TQNRRGMZDQMY> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>