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Say I have a dataset containing age, gender, race, selected field of study, and selected competence level in selected field of 15,000 people.

I wish to see how and if age, gender, and/or race (and the interactions between these variables) influence the selected field of study and competence level.

I was thinking maybe I could use a 2-way ANOVA, but I believe ANOVA would not be applicable here since there are 3 independent variables (age, gender, race) and 2 dependent variables which are qualitative (categorical). So, I am not sure what do to.

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Usually in designs like yours where you would use multiple categorical predictor variables with a categorical DV (dependent variable) you would indeed not go for ANOVA (since this requires a higher measurement level for your dependent variable), but 'loglinear analysis' instead is commonly used for this and will be appropriate here.
Hope this helps and good luck with your research!

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  • $\begingroup$ Note that there are two categorical dependent variables. $\endgroup$
    – chl
    Commented Oct 30, 2020 at 12:22

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