Can random effect only model positive correlations?


I am a PhD student working in behavioral ecology. I am currently working on reviews for a paper, in which I aim to investigate the influence of mate familiarity on female mate choice. I presented a female with two males (one she already mated with and a "novel" male) and a neutral area, and recorded her behavior. I have a data set with the time the female spent with each male and in the neutral area. Therefore I have three lines per trial (one for each male and one for the neutral area).

I calculated the proportion of time spent with each male (time spent with the previous partner/time spent with both males; and time spent with the novel male/time spent with both males).

Trial___Time spent____Proportion of time___Side
1______3520.002______0.58__________________novel male
1______2501.002______0.42__________________previous partner
1______1535.002______NA___________________neutral area
2______3545.666______0.29__________________novel male
2______8570.965______0.71__________________previous partner
2______1520.002______NA___________________neutral area

I analyzed this using a beta regression model with the proportion of time as the response variable and the familiarity (previous partner or novel male) as fixed effect. I added ID as a random effect since I have two lines per trial (one for each male).

A reviewer commented that "random effect can only model positive correlations of non-independent data" and that I should instead compared the proportion of time spent with one male against 0.5.

Is the reviewer's comment about the random effect true? I did not find any information on that on the internet, is there a paper/book where I could read more about that, or could anyone explain to me what they meant? I am fairly new to stats, so I really want to improve my knowledges to do proper stats.
I chose to analyze my data with beta regression models because it seems to be the best test to use for continuous proportional data (Mangiafico, 2016; Douma & Weedon, 2019), but maybe I'm wrong?

Thanks a lot for your help!


Less is more. Stay pure. Stay poor.
Can you post their exact wording/review. Because I am also not following what their concern may be.
Thanks for taking the time to look over my issue!

Their exact wording was:
"Random effect can only model positive correlations of non-independent data. The proportions of time spent in the sections in a trial are negatively correlated so I don’t think the use of random effect is valid here.

A more standard analysis for a choice assay is to convert the variables into two response variables that describe two independent properties: i) female responsiveness (time with either males/total time in the three sections): this reflects how interested the female is in mating, and ii) preference for novel male (time with novel/time with either male): this reflects the preference for one option over another.

Maybe there are other statistical options, but bottom line is, random effect doesn’t deal with negative correlation.


Less is more. Stay pure. Stay poor.
What do you think they are referencing with negative 'correlations'? Are they writing about model estimates or covariance between values? Unclear to me. I am not an expert in this area, but I wouldn't understand why model estimates couldn't be negative. Beta reg can be used with 0-1 bounded DV data, but can have issues if estimates are near the bottom or top bound, but that isn't their issue.
That's the thing, I really don't know what they mean...From what they write I think they suggest that one cannot use random effects when the response variable is non-independent. The way I see it, I should use the trial as random effect because I have two values of the response variable (proportion of time) per trial (one for the novel male and one for the previous partner). The way they see it, I cannot do that because the two values in the response variable are negatively "correlated"?


Active Member
i think the issue is that you can't have a linear dependance amongst the three outcomes, in this case proportion of time. same as a chi-square only has p-1 degrees of freedom.
Thank you for your answer. Do you mean that I should analyse my data another way? If so, would you have a suggestion of what would be the statistically correct way to do it?


Active Member
same way, but exclude one of the categories:
2______3545.666______0.29__________________novel male
2______8570.965______0.71__________________previous partner

the estimate for the excluded category is jest 1 - the other one, ain't it.

see its technically a negative correlation between these, but that's not the issue per-se, you can totally have negative correlations.