Can random effect only model positive correlations?

[melissap]

Hello,

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).

Example:
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!

 

[hlsmith]

Can you post their exact wording/review. Because I am also not following what their concern may be.

 

[melissap]

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."

 

[hlsmith]

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.

 

[melissap]

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"?

 

[fed2]

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.

 

[melissap]

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?

 

[fed2]

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.

 

[melissap]

I see, thank you very much for your help

 

[fed2]

no problem-o