In my survey data I have two variables: One is an ordinal variable with 5-scale scoring from Agree to Disagree. My second variable is an nominal variable where the participants had to choose from 7 different options. I now want to test if people who showed strong agreement to the ordinal variable are more likely to choose one specific option of the nominal variable. Is there any method to use for this situation? Sorry, if this has been asked many times already.
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1$\begingroup$ Chi-square testing is possible. That ignores the ordering on one variable. There may be other suggestions. $\endgroup$– Nick CoxCommented Apr 12, 2021 at 17:40
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Since you want to determine whether strong agreement is associated with a particular nominal outcome class, you could run polytomous logistic regression with nominal class as the dependent variable and 4 binarized (0,1) dummy variables as predictors, representing the 4 ordinal levels (5-1) with level 1 as the corner point. The results will provide a table of regression coefficients and their significance for 6 of the classes (7-1). In this fashion, you would be able to look at the table of 4 regression coefficients for each nominal outcome class, and determine which Likert scale value contributed positively or negatively to the outcome, and whether each was significant. For coding the four predictors, the x-values for a record would be e.g. $x_i=(0,0,0,1)$ for a subject that strongly agreed - where there is no code for strongly disagree -- as their responses contribute to the y-intercept.
This can also be run using multivariate normal regression (MVN) in which the outcome y-values for an e.g. record are set to $y_i=(-1,-1,1,-1,-1,-1,-1)$ if the outcome class is 3. MVN regression would also provide a table of regression coefficients for each of the nominal classes, which would be interpreted similarly.
In fact, the MVN appraoch is one the best ways to determine if your 7-class problem is linearly separable.