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My dependent variable is Likert data (strongly agree, agree, neutral, disagree, strongly disagree). My independent variables include age and 3 categorical variables (one has 3 levels, two are binomial).

I want to see which independent variables are associated differences in agreement with X, Y, and Z statements. Would I first run a Pearson's chi-square for test of independence for each statement for each independent variable? Or should I do an ordinal logistic regression? I would also like to say something like older people are more likely to strongly disagree/disagree with this statement.

I don't mind turning age into a categorical variable and I don't mind condensing my Likert data into strongly/agree vs. neutral vs. strongly disagree/disagree.

I'm obviously a non-statistician and am drawing from minimal experience during college years ago! I would appreciate any help I could get.

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You can run ordinal regression models (e.g., ordinal logistic or probit regression) to examine the relationships between the covariates and your outcome. Standard ordinal regression models work by assuming there is an underlying, unobserved continuous variable (in your case, agreement) that has been discretized into several bins at various thresholds. These methods model the relationship between this underlying variable and the predictors you've specified. The coefficients can be interpreted as the effect of the predictors on the underlying outcome, just like in standard regression, though there are some additional interpretational complexities with this practice.

With two predictors, you can run univariable and multivariable regression models. Univariable regression models answer the question of to what degree the predictor is associated with the outcome. Multivariable regression models answer the question of to what degree each predictor is associated with the outcome over and above the other predictor(s).

See Bürkner and Vuorre (2019) for a nice introduction and tutorial of ordinal regression for psychology researchers.

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