# How to perform regression on a nominal variable using many binary explanatory variables?

I have a dataset:

• Response: categorical, 9 levels.
• 23 predictors: binary, with many 0's.
• Number of samples: 64.

I'm interested to know the dependence of (each level of) the response on predictors.

Grateful for any suggestion to start.

Edit: The topic is related to the analysis of the scientific definitions regarding an ecological concept, for which there exist 9 major terms (the response, in 9 categories). I want to use a method proposed by Delong, 1996: to split the definitions according to some common ecological factors (the 23 binary predictors, which could appear or not in each definition). The predictors (ecological factors) could be combined, but it means also losing detail in the analysis, so if possible, I would like to keep them. The main objective is to find quantitative relationships between the different terms of the concept and the (presence of) ecological factors.

• What's the context of the study? Is the outcome nominal or ordinal (that is, can we assume levels are ordered or not)? Are you interested in a descriptive, explanatory, or predictive approach? – chl Aug 23 '11 at 21:39
• @chl: Thanks. The levels are not ordered. The analysis is just descriptive/explanatory, the date could be not used for prediction. – Marius Aug 24 '11 at 8:36
• Multinomial logistic is good, but with only 64 cases and 9 levels of the DV, you are going to be restricted to only 1 independent variable at a time. Can you combine some levels of the DV? Can you combine some of the IVs? It would help if you provided context to your question. – Peter Flom Aug 24 '11 at 10:23
• @Marius Please, give more context on your study; otherwise, I'm afraid you'll get a lot of possibly not very helpful responses. – chl Aug 24 '11 at 10:51

## 1 Answer

If the response is ordinal then use Ordinal logistic regression see for description here, and if response is nominal then use multinomial logistic regression see for description here.

• Thanks. But, are there enough data (64 records) for a logistic regression (with so many predictors - 23). Could be solved this way in such conditions or must find other approach? – Marius Aug 24 '11 at 8:43
• (-1) You don't really answer the question, do you? Instead of the 'shopping-list' approach, let's wait for OP clarification and provide him with adequate solution. – chl Aug 24 '11 at 10:50
• In theory, 64 records and 23 binary predictors are enough for Ordinal or multinominal logistic regression. But there is one problem can be arise is multi-collinearlity. I would recommend some data reduction methods i.e., Principal Component analysis (PCA) or Partial Least Sqaure or lasso. – love-stats Aug 24 '11 at 15:13