Hello, Jolien van Dijk

Yes there are differences :

1- Cumulative logistic regression models :are used to predict an ordinal response(eg: opinion, satisfaction (based on Likert scale ...), and have the condition of proportional odds (POd) . Proportional odds means that the coefficients for each predictor category must be consistent, or have parallel slopes, across all levels of the response. So, The cumulative logit model is a direct extension of the usual logistic model.

2- Ordinal Logistic is equivalent to Ordered Logistic Regresson: they are base on proportional Odds assumption.

Best regards.

Thank you for your answer Chellai Fatih .

I still don't quite understand the difference though if (1) both are for ordinal response data, (2) both are based on logistic regressions and (3) both are based on the Proportional Odds Assumption. Am I missing something obvious?

Yes of course Jolien van Dijk ,

all are for : ordinal data , and all are an extension (or a cas of Logisitic regression) and all them requere the Proportional Odds Assumption.

« Ordered » and « Ordinal » logistic regression are, I guess, the same thing. Just a matter of preferred term to describe a qualitative variable with ordered levels. [I guess you may say that « ordered » logistic regression may be applied to non-ordered qualitative variables, assuming an arbitrary order, whereas « ordinal » just apply to really ordinal variable, but conceptually that's absurd so...]

The idea of ordinal logistic regression is to try to use the information that levels are ordered to answer questions of the kind « does the outcome *increase* with X » instead of the more general question « does the outcome *change* with X », which is the question answered by the more general multinomial logistic regression.

To achieve this, assumptions are done.

One possible assumption is that

1) you use cumulative probabilities instead of point probabilities to define the ratios used in the model — that is, if levels are A < B < C, you use p(Y ≤ A)/p(Y > A), then p( Y ≤ B ) / p( Y > B ). Cumulative probabilities only exist in an ordered case, for the inequality to mean something... Usual multinomial mode would use instead p(Y = B)/p(Y = A) and p(Y=C)/p(Y=A).

=> this is the « cumulative logistic regression » model

2) eventually, make the additional assumption that the coefficients of the linear model between ln( ratio ) and X are the same for all ratios. This is the "proportional odds" assumption. It is not mandatory for cumulative logistic regression, but very common.

Note that other assumptions exist, for instance using the ratios of successive levels — p(Y=B)/p(Y=A) and p(Y=C)/p(Y=B) using the previous example, usually with adding assumption 2) of identical coefficients for all ratios [but that's not proportional odds]. This is also an ordinal logistic regression model, but not a cumulative one; it is known as adjacent categories logistic regression. With more than 3 levels, other choices also exist.

So, basically, ordinal = ordered logistic is a supercase of cumulative logistic regression and a subcase of multinomial logistic regression.

Hope this helps,

yes,they are different for the same thing

Yes, there are differences and they are all use to predict responses. The Cumulative logistic regression models are used to predict an ordinal response and have the assumption of proportional odds. For example: In the Dublin attitudinal questionnaire survey, the respondents were asked to express how strongly they agreed or disagreed that they will use the LUAS to travel to work in future. The responses categories were: strongly agreed, agreed, neutral, disagreed and strongly disagreed, with a scores of +2, +1, 0, -1, -2 respectively. Also, the cumulative logistic regression models have the assumption of proportional odds which means the coefficients for each predictor category must be consistent across all levels of the response.

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https://oapub.org/soc/index.php/EJSSS/article/view/316