# More than one outcome (dependent) variables in ordinal logistic regression

I want to run ordinal logistic regression (OLR) in SPSS. My data include 6 predictor variable (two continuous and 4 categorical ) but my outcome variables are also 6 (categorical-likert scale). e.g my dependent variable is Business development and 6 likert scale questions were asked for this, increase in profit, sales, size, asset, marketing and labour.

1-If I composite these 6 variable into one by first sum all the 6 variables and then recode them into again five categories like before (In SPSS in Transform, Compute variable and then recode into different variables). I think in this way I lost my original data and may categorize them wrong.

2-If I think of using Categorical Principle component analysis for reducing the dependent variables, it will give results (object scores) in continuous form on which I have to run linear regression. I do not want to run linear regression as my original data is categorical.

3-So option left is to run OLR without combining the dependent variable on each DV. It means that there is no model for Business development and 6 models for profit, sales....

My question is that

• Is it preferable to run OLR with each DV and then summarize the results
• OR Is there any other method for reducing DV and running OLR.

• OR Is there any better method than ordinal logistic regression for this data.

Among the many possible ways to analyze this dataset, a one that I would try first is multivariate linear regression. Multivariate means that you have multiple outcome variables (the six Likert scales). Linear, rather than logistic, means that you treat each Likert scale as a continuous output. (It's true that ordinal logistic methods are more appropriate theoretically for rating scales, but that seems like overkill for a first attempt.) Rencher, "Methods of Multivariate Analysis" seems like a decent introduction.

• thanks Jack. Could I use Rasch model on my data?
– wxa
Jan 18, 2012 at 12:17
• OR ANY IRT Model
– wxa
Jan 18, 2012 at 12:22
• i believe you've already asked the IRT / Rasch question elsewhere stats.stackexchange.com/questions/21268/… Jan 18, 2012 at 17:51

One approach to analyzing data of this form is to utilize an item-response-theory framework. "Business Development" is poorly defined. You have 6 items which ostensibly relate to Business Development, but according to the description you have no idea how they should be combined, if at all, to form a usable scale.

Parceling is the simplest approach: add the 6 likert items together and compose a single sum score. This is surprisingly adequate in a number of situations. It is helpful to verify all 6 items are positively correlated as a rudimentary dimensionality analysis.

A more flexible approach is fitting an item response theory model which treats business development as a latent trait which is input to the six likert scale manifest variables according to a proportional odds model with a set of intercepts and slopes. The R package mirt is capable of fitting these models. This is a more general approach to combining these measures. The "ability" is a generalized concept of a sum-score which accounts for the fact that some questions may have very low or very high prevalence, and that differences may be of varying weights in that regard. This is a rough, high level explanation, but you should be able to conduct some self-directed research to see if this is a useful approach to combining multiple ordinal measures.