I'm fitting a response variable that assume values between 1 (Very Dissatisfied), 2 ,3 ,4 and 5 (Very Satisfied). My explanatory variable assumes also values between 1 and 5, in other words, dependent e independet variables are Likert Scale Variables.
I know that those kind of variables are categorical, therefore is appropriate use a Ordinal Logistic Regression (OLR) instead of Linear Regression (LR). However, for comparasion, I start using a LR method to check the results.
Here comes my doubt:
a) I'm getting high $ R^2 = 0.643$ for the LR. Using the OLR method and applying a $pseudo$ $R^2 $, such Mc Fadden's, the result is $R^2 = 0.153$. How is this possible and what explain that?
Is those results relational with the $R^2=\frac{\sum(x_i-\bar{x})^2}{\sum(y_i-\bar{y})^2}$ formula?