Talk:Ordinal regression

Merge discussion

There is considerable overlap between ordered logit and ordered probit, and it all could be conveniently placed in this article {possibly renamed as ordered ....). Melcombe (talk) 21:46, 21 May 2012 (UTC)

I agrree User:PeterLFlomPhD

I agree user:hopf

I agrree User:Rawal Khirodkar — Preceding unsigned comment added by Rawalkhirodkar (talk • contribs) 17:21, 25 February 2015 (UTC)

I agree user:Benjamin Schlegel — Preceding undated comment added 10:55, 3 April 2014 (UTC)

I disagree. A composite article titled "Ordinal regression" would be confusing, as this is not the everyday language that is used to talk about these models. Better to keep two separate articles and tolerate some element of duplication. There are a whole series of articles on probit models, and another series on logit models, which would also be disrupted by such a change. - Anonymous (31 March 2015) — Preceding unsigned comment added by 158.143.68.250 (talk) 14:43, 31 March 2015 (UTC)

I've begun expanding the stub Ordinal regression. I'll see if I merge in the other two articles; so far, it seems like most literature explains ordinal regression by either starting from ordered logit and then discussing ordered probit as a variant, or by discussing a general model and then deriving the logit and probit models from it by plugging in a link function. QVVERTYVS (hm?) 17:48, 16 July 2015 (UTC)

There are quite a number of variations of analysis for ordinal data (see Agresti's book, which I added) although not all of these are regression. I am new to editing Wikipedia. How can I help with this article without getting in Qwertyus' way? PeterLFlomPhD (talk) 14:14, 23 July 2015 (UTC)

Just edit — but what exactly do you mean by "not all of these are regression"? I've noticed different definitions of regression being in use in different fields. QVVERTYVS (hm?) 14:34, 23 July 2015 (UTC)

For instance, there are methods of analyzing crosstabs (frequency tables) that use ordinal ideas but do not have a dependent variable. PeterLFlomPhD (talk) 14:45, 23 July 2015 (UTC)

Right. I would say that would be fitting for a separate article, to which I don't have much to contribute; I was actually steering this page toward the models developed for ordinal regression in machine learning, where predicting the dependent variable is the problem of interest, not modeling or other kinds of inference. QVVERTYVS (hm?) 17:13, 23 July 2015 (UTC)

Proportional odds vs. hazard

Re: this edit: isn't proportional odds an alternative model for ordered logit, rather than proportional hazard? QVVERTYVS (hm?) 17:17, 23 July 2015 (UTC)

You are correct. The Proportional hazards model is a model for survival analysis, e.g., the Cox PH model. Both are talked about in the reference cited, but they are generally different models for different purposes. --Mark viking (talk) 21:03, 23 July 2015 (UTC)

I don't have McCullagh and Nelder handy; do they use "hazards" when talking about the ordered logit? I vaguely recall seeing this model called "proportional hazards" but I think "proportional odds" is much more common -- PeterLFlomPhD (talk) 21:31, 23 July 2015 (UTC)

McCullagh 1980, §4:

The proportional odds and the proportional hazards models have the same general form namely

$\operatorname {link} \{\gamma _{j}(x)\}=\theta _{j}-\beta ^{T}x,$ (4.1)

where "link" is the logit or complementary log-log function

... so I guess the article is wrong in asserting that the inverse link function of prop haz is exp. I don't know how I got that idea, it should be exp(-exp(x)), the inverse of log(-log(x)). QVVERTYVS (hm?) 21:42, 23 July 2015 (UTC)

So it seems to me that it should be "proportional odds" here; also, the Wikipedia article for proportional hazards says it is for survival analysis == PeterLFlomPhD (talk) 23:18, 23 July 2015 (UTC)

The formulas given by McCullagh match those of the article Proportional hazards model. I changed the inverse link function for proportional hazards. QVVERTYVS (hm?) 06:07, 24 July 2015 (UTC)