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- Nominal logit models vs ordinal logit models

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08-05-2011 06:30 AM

Please allow me to give a discussion on the nomial logit models and ordinal logit models.

I ran analysis for a data using both methods. But the results are pretty much different. The dependent variable has 3 categories: 1 (loss<$1000), 2 ($1000<=loss<=$10000) and 3 (loss>$10000). There is a list of variables to predict the dependent variable. Two approaches of nominal logit model and ordinal logit model are used to compare the difference of parameter estimates.

The 1st approach treates the dependent variable as nominal which resulted in 12 significant varables, and the 2nd approach treates the dependent variable as ordinal which resulted in only 10 significant variables. Besides, the coefficients produced are pretty incompatible.

The difference between these two approaches leads to an open questinon: which result is more trusted? Personally, I prefer the nominal approach. But this approach produces two sets of coeffcients for respectively comparing group 1 vs group 3, and group 2 vs group 3. The ordinal approach added one strict constraint that the two sets of coefficients (group 1 vs group 2 + 3, group 1 + 2 vs group 3) are equal. So it is more neat and easy for interpretation. However, it is just because of this constraint which sometimes compromised the result.

Any comments?

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08-08-2011
11:27 AM

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08-08-2011 11:27 AM

My 2 cents-

it think you should use the method that is most appropriate for your dependent variable. in this case since your dependent variable is ordinal i think the ordinal logit is approriate. exploiting the ordinal nature of the dependent variable gives you more power for your hypothesis test (since you have more residual df available by not having to estimate 2 sets of coefficients for each variable) - this may be why the 2 variables are not significant in the ordinal model. unless you have strong reason to believe that the ordinal model assumptions (essentially that the 3 categories of the dependent variable are arbritary cutpoints for the underlying latent variable they are measuring) are violated, then an ordinal model is appropriate. finally you can test if a nominal model offers a significantly better fit than the ordinal model by performing a likelihood ratio test for the 2 models

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08-08-2011
11:27 AM

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08-08-2011 11:27 AM

My 2 cents-

it think you should use the method that is most appropriate for your dependent variable. in this case since your dependent variable is ordinal i think the ordinal logit is approriate. exploiting the ordinal nature of the dependent variable gives you more power for your hypothesis test (since you have more residual df available by not having to estimate 2 sets of coefficients for each variable) - this may be why the 2 variables are not significant in the ordinal model. unless you have strong reason to believe that the ordinal model assumptions (essentially that the 3 categories of the dependent variable are arbritary cutpoints for the underlying latent variable they are measuring) are violated, then an ordinal model is appropriate. finally you can test if a nominal model offers a significantly better fit than the ordinal model by performing a likelihood ratio test for the 2 models

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08-09-2011 06:44 AM

trekvana,

yours is a complete good answer. Thanks for the guide. I believe the choice is to test both models and see whether they significantly differ in terms of results and goodness-of-fit. If there is no big difference, then clearly cumulative model is a better choice.

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08-08-2011 02:35 PM

What type of comparison are you looking to do?

The group 1 vs group 2+3 compares the lower level to higher levels, while group 1+2 vs group 3 does the same, lower to higher. If you're not interested in doing those types of comparisons then run the nominal. To me its a question of what's your question and interest.

And if you're doing nominal do you want a comparison of group 1 to group 2? Or is that not of interest?

The results should be different, you're answering different questions in each one.

My 2 cents

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08-09-2011 06:43 AM

Hi Reeza,

Yours is a good point. I am not interested at all to compare group 1 vs group 2.

I tested and compared the two models: cumulative vs multinomial, and found the latter has a much better fit than the first one. So I decided to keep the multinomial one. Anyway, my key interest is on the comparion between group 1 and group 3 (reference group).

Glad to learn and practice.

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08-09-2011 09:10 AM

excellent point by reeza-

statistical methods should be chosen to address the question/hypothesis of interest as best as possible. however, one thing that i've seen in practice is people chasing significance and using whichever methods (including inapproriate ones) will give them a p-value to their liking. the methods and hypothesis should be chosen before hand and the approriate method should be determined before running the analysis.

in this case bncoxok, the nominal model is appropriate given that you want a direct comparison of group 1 with group 3. if you wanted to say something about how lower levels of the dependent variable compared to higher levels as a whole and not specifcally group 1 vs 2 or group 2 vs 3 etc. then the ordinal model (in my opinion, given the assumptions are tenable) would be a better choice. lastly aside from a likelihood test, you can also check the AIC and BIC of the two models to see if adding all those additional parameters in the nominal model has its advantages over the ordinal model

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08-09-2011 12:05 PM

You never specified what your sample sizes are for each group.

If your dealing with smaller numbers then having a large group (group2+3) vs group 1 will always give you a better fit because you're using more data.

Just something to keep in mind.