Timeline for Comparing two regression model (Beta regression and linear regression)
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 4 at 2:57 | comment | added | usεr11852 | (I still remember that when I first tried to answer this answer I had the same intuition as you) In the AIC calculation we care to have valid (negative) log-likelihood for each model. Both (maximised) likelihood values we attain are equally valid, thus comparable, despite not sharing the same support. Finally, particular to your last point: A KL divergence is between our model and a "real" model, not between two different candidate models. And the only information about a real model comes from the observations themselves, which are common for both candidate models. | |
| Apr 4 at 1:45 | comment | added | user45765 | @usεr11852 Why AIC can be used in this case? The linear model assumes unbounded responses and beta regression model assumes bounded response in (0,1). The distributions do not even live with the same support. Had AIC been approximation to KL divergence, under this situation KL would be infinite. | |
| Feb 9, 2020 at 0:30 | vote | accept | Oberon | ||
| Jan 10, 2019 at 23:17 | comment | added | usεr11852 | Pleasure! If you find this answer helpful you could consider upvoting it or if it answers your question, accept it as an answer. If you need further clarifications you are welcome to ask. | |
| Jan 8, 2019 at 5:49 | comment | added | usεr11852 | Cool. I am glad I could help. In many cases we might be tempted to us a single metric to choose a model. Or maybe two or $N$ metrics, etc. The point is that a model encapsulates our assumptions. We should not choose a model automatically but instead choose it in such that if facilitates our research question. AIC, $p$-values, etc. help us test or quantify certain assumptions but should not be our biggest factors on this. CV has some great threads on the perils of automatic model selection (eg. here). | |
| Jan 8, 2019 at 5:12 | comment | added | Oberon | Thank you for the answer. One question I would ask is about the second note. You mentioned about not using "single number approach", do you mean, I have to compare more than one number (Ex. comparing AIC, BIC.....)? | |
| Jan 7, 2019 at 22:57 | history | answered | usεr11852 | CC BY-SA 4.0 |