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

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  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?
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  • $\begingroup$ Just as a sidenote OLS refers to Ordinary Least Square. Not to Ordinal Logistic (Regression) en.wikipedia.org/wiki/Ordinary_least_squares $\endgroup$
    – Janosch
    May 20 at 8:13
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    $\begingroup$ 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? $\endgroup$
    – frank
    May 20 at 13:27
  • $\begingroup$ Thanks for the corrections to the title and table $\endgroup$ May 20 at 18:39

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In logistic regression you linearly regress the log odds, so the fitted coefficients are the "beta weights" for the log odds. So you can say that the "IV1 effect on the log odds of the DV is 11%, compared to IV2".

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.

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  • $\begingroup$ Thanks Frank. The issue is that I need a general solution, i.e., a formula that I can automate. $\endgroup$ May 21 at 5:25

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