Which analysis fit better?

[Emanuele Spina]

Hi.

I have a dataset of 60 cases. I want to calculate the effects of some independent variables on my dep - var, comprehensive of 7 levels (a scale from 0 to 6, with a different distances between each levels, so is not properly an ordinal scale).

Would be fair to use a regress command in this case?
Or i must choose multinomial logistic regression (mlogit) to predict the effects of each independent var?

I tried also to treat my dependent as binary (0 < 4; 1 => 4), using subsequently logistic regression command, but i lose some effects observed with linear regression.

Thank you for support

[Weiwen Ng]

If your scale is 0, 1, 2, ..., 6, like what many people call a Likert item, how is it not ordinal? Those scales do not have equal distances between the levels, meaning that we can't think of the item they're measuring as if we are measuring temperature. In that case, it would be much better to use ordinal regression than OLS.

[Carlo Lazzaro]

Emanuele:
about the risk of dichotomizing (mutatis mutandis,as the paper refers to continuous predictor) see https://www.ncbi.nlm.nih.gov/pubmed/16217841.

[Marcos Almeida]

Just to add a small note, after both helpful advices:

Theoretically, in your case, you might think about a multinomial logistic regression. In fact, even under a "fully" ordinal scale, we may decide to give - mlogit - model a try as well. That said, I fear the sample size may end up small enough even for a "crude" model, let alone the inclusion of "some independent variables" as you wish.

[Emanuele Spina]

If your scale is 0, 1, 2, ..., 6, like what many people call a Likert item, how is it not ordinal? Those scales do not have equal distances between the levels, meaning that we can't think of the item they're measuring as if we are measuring temperature. In that case, it would be much better to use ordinal regression than OLS.

Hi weiwen, thank for your reply.
So i can treat as ordinal a scale also with not equal distances between terms?
It would solve any problem!

[Emanuele Spina]

Just to add a small note, after both helpful advices:

Theoretically, in your case, you might think about a multinomial logistic regression. In fact, even under a "fully" ordinal scale, we may decide to give - mlogit - model a try as well. That said, I fear the sample size may end up small enough even for a "crude" model, let alone the inclusion of "some independent variables" as you wish.

I try to run an mlogit but my sample is too small (60 cases for 7 levels, with 4 indep var)!

[Weiwen Ng]

Hi weiwen, thank for your reply.
So i can treat as ordinal a scale also with not equal distances between terms?
It would solve any problem!

Yes, you can treat it as ordinal. In fact, this is exactly the sort of problem that you would use an ordinal regression for.

Just to clarify: as you know (but just saying for completeness), we often ask people to rate something on a 1 to 5 scale, where 1 is poor, 2 is fair, 3 is good, 4 is very good, 5 is excellent. Imagine that health status is a continuous variable, and that as your health status increases, the probability of making a higher response increases. That is the setup behind ordered probability models.

We can't observe health status, but we've got no way to be sure that, when it comes to the underlying latent variable, the distance between responses of 1 and 2 and between responses 4 and 5 are the same. The numeric difference on the Likert item is 1, obviously, but it won't mean the same thing.

Now, ordered logit regressions (both logit and probit) require the proportional odds assumption, which is the assumption that the covariates affect the relationships between any pair of responses equally (e.g. being female affects the probability of 1 vs 2 and 4 vs 5 equally). (I hope I have explained that correctly.) That's a relatively strong assumption. The multinomial regression will separately estimate coefficients between each pair, which is a weak assumption. There are ordered regression models that are in between these assumptions, which I am not personally familiar with, but some examples are generalized ordered logit (user written command gologit2, hat tip to Richard Williams, link below) and stereotype logit (slogit, native to Stata 13 at least). Personally, I would start with ordered logit/probit and work from there.

http://www3.nd.edu/~rwilliam/gologit2/

[Emanuele Spina]

Ok, thank you. It will help us make easier treating our analysis.

[Andrew Musau]

A general point about likert scales: As the number of points tend to infinity, ordered logit estimates approach those of OLS. Therefore, it is not unusual to see studies that treat a likert scale with 11+ distinct points as an interval scale (approximately). Even with 7 points, you should not be surprised to see that OLS and ordered logit estimates do not divert much. Estimate both and compare!