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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?

kjetil b halvorsen
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Arduin
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    This link might be helpful: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/ Also check whuber's answer here: https://stats.stackexchange.com/a/3562/109647 – T.E.G. Aug 27 '18 at 05:24
  • Thank you! It was helpfull. Nevertheless, I still doubt about why categorical variable, when applyied LR, got so hight $R^2$... – Arduin Aug 27 '18 at 19:01

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