# Transforming ordinal logistic regression coefficients to beta weights

Ordinal logistic regression analysis result in coefficients which are log odds, and not b or beta weights, like in a linear regression. For example:

1. How can I compare the log odds of the DVs? Is it correct to say that DV1 effect on the IV is 11%, compared to DV2 (-0.071/-0.619)?
2. Is there any way to convert the log odds to beta weights?
• Just as a sidenote OLS refers to Ordinary Least Square. Not to Ordinal Logistic (Regression) en.wikipedia.org/wiki/Ordinary_least_squares May 20 at 8:13
• I am a bit confused w.r.t. your choice of abbreviations: If DV abbreviates "dependent variable", you talk about the effect that the dependent variable DV1 has on the independent variable IV? May 20 at 13:27
• Thanks for the corrections to the title and table May 20 at 18:39

Now, the "log odds"-function (or "logit") is nonlinear, and thus is its inverse, the logistic sigmoid function $$\sigma$$. Thus, the effect on the DV, of a unit change in an IV, is not constant but depends on the value of the IV.
So, if you want to know the effect of a change in the IV $$\mathbf x$$ on the DV $$y$$ at the point $$\mathbf x= \mathbf{x_0}$$, you could compute the gradient of $$\sigma(\beta\cdot\mathbf x)$$ at $$\mathbf{x_0}$$, which gives you the linear approximation of the effects of all your scalar IVs at this particular value $$\mathbf{x_0}$$. Recall, that, if you have $$k$$ IVs, then $$\mathbf x \in \mathbb{R}^{k+1}$$, because an extra dimension is added for the intercept.