I have two ordinal variables, ranked on a 1-5 Likert scale, and a categorical variable of age groups. What I would like to is extract significant (or determine and identify the existence of) homogeneous groups from the categorical variable. A simple example would be:
Variable_1 (Likert 1-5): Do you like chocolate?
Variable_2 (Likert 1-5): Do you like fruit?
Variable_3 (Categorical 15-25,26-35,36-45, etc.): Please select your age.
From this I'm looking for significant relationships between the responses of Variable_1 and Variable_2 based upon the age group. Examples could be subjects between 16-25 liked chocolate but do not like fruit; conversely subjects between 56-65 liked fruit and not chocolate.
What statistical test / method could I use in this circumstance?
Note 1: at the moment I believe that cross-tabs is probably my best bet here with possibly the recoding Variable_1 and Variable_2 into a dichotomous dependant variables - which appears to simplify the results.
Note 2: for those that are interested, I posted this question yesterday and by all account it was rather confusing and placed on hold, although feel free to check it out.
Note 3: using SPSS (if that helps)
Univariate (regressing one on another), a bivariate ordinal correlation can be done in SPSS. In crosstabs, you click statistics and under ordinal, click gamma (Google the options and decide if another is appropriate).
Multivariate, click analyze, regression, ordinal, put one on top and two independent below. On output, click on the test of parallell lines and cell information. Multivariate ordinal regression assumes an adequate cell count (in a 3 by 3 table, 80% of cells should be >5) and none should be zero. If breached, categories can be collapsed. Ordinal regression is also called a proportional odds model, as it assumes that odds are proportional for being at or below or above a certain category.
Consider Discriminant Analysis. Target variable is AgeGroup and your two rating scales are predictors. This will give you a model that may give you the joint effects that you want.
Also, Ordinal Logistic Regression will give you a formula which is a combination of your two rating scales that predicts AgeGroup.
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