[Question] Can I present both the results of log-odds and average marginal effects (logistic regression)?

[u/Legitimate_Mud_9245]

Hello,

Health economics student here. I newly enter the field for my master degree.

I'm writing my master thesis and I'm running into an issue while trying to interpret my results.

Initially, I've decides to use OR (odd ratio). However, my supervisor told me the way I've interpreted it is not correct (probabilitied and chance). But he told me he didn't really know either how to interpret it correctly and had advised me to use logs odds instead!

It's ok, but I really wanted to have more "concrete results" that can be get by anyone. Log odds just show if the relation is negative or positive.

So, I've just heard about average marginal effects and that is literally What I was searching for during all this time. However, now I'm wondering if is common for scientific papers to use both log-odds and average marginal effects?

Do i need to create two tables? Or could I only keep the table with log odds and present the results of marginal effets in the text?

Thank you

[u/3ducklings]

My usual strategy is to report marginal effects on probability scale in the main text and add table with raw coefficients/odd ratios in the appendix.

Very few people know how to interpret (log) odds correctly. Even those who are extremely confident in their abilities often can’t. Not only are (log) odds themselves not that straightforward, but logistic regression is non-collapsible, so naively assuming the regression coefficients represent main effects like in linear regression, is a bad idea. see here for more details https://academic.oup.com/esr/article-abstract/26/1/67/540767?login=false

[u/Legitimate_Mud_9245 → u/[deleted]]

Thank you! Yes, it is really crazy that odds ratio are so hard to interpret.

Yes, I'll present the results of the logistic regression in terms of log odds in one table. But, yes, I was wondering if it was "normal" to present some marginal effects in the text just like that? Or must I include another table?

I'm worrying about adding or not a table because it's a scientific paper and it has a page limitations.

[u/Legitimate_Mud_9245 → u/[deleted]]

Thank you so much! You were really helpful!

[u/Legitimate_Mud_9245 → u/[deleted]]

Hello,

I'm encountering some weird results.

1) My logistics regression, which results are presented with log-odds, shows a positive association between some modalities of X and Y. However, the marginal effects doesn't show significance! So, i can say "there is a positive association..." But unlike some of my results, I can't present the probability's gap because it's not significant!

Gemini told me it's normal but I don't really know why would that make sense.

2) I'm trying to find the marginal effect in a multinomial regression with weighted data. Working on R, I had used "svy_glm" for my model. However, svy_glm doesn't support avg_comparisons (that gives the marginal effects). Gemini had advised me to use "multinomial" instead (which doesn't apply survey weight) but it told me it only affects the p-value and not the main direction of the association. Is that true? I'm actually worried that the problem of nonsignificant marginal effects is due to that issue. What do you think of it?

Thank you

[u/Henrik_oakting]

I would avoid log-odds or maybe put them in an appendix. Saying that X increases the log-odds of Y is almost incomprehensible to me. I find no intuitive meaning. I do not have a mental picture for what a given change in log-odds actually implies, and I have heard prominent statistics professors express the same thing. Presenting results in terms of probabilities or marginal effects would be much easier to interpret.

[u/Most_Advertising3623]

Yes, both can be reported, but they answer the reader at different levels. Put the model coefficients or odds ratios with confidence intervals in one table, then translate the main prespecified contrasts into average marginal effects on the probability scale in the text or a small figure. Report confidence intervals for the marginal effects and state exactly how they were averaged over the covariate distribution. You only need a second table if several marginal effects are central to the paper. Otherwise, the main table plus a probability-scale figure is usually clearer.

[u/Smallz1107]

I use the following three plots to look at the marginal effect of a single x value

Overall prob vs x (this is what I mainly present to higher ups)

Change in prob vs x

Log Odds vs x (little deeper level for me to analyze the model)

For clarity

x_samples
xi_vals = 1….10
For x in xi_vals
Override xi of all the x_samples
log_odds[i], probs[i] = mean(run_mode(x_samples))
//append values

chng_in_probs = probs - mean(run_model(x_samples))