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I am struggling with something that seems like it should be relatively straight forward, but my searches thus far have not yielded results.

Earlier guidance on the site suggests that when using a logit regression for a binomial variable, the samples should be weighted based on how many trials took place.

It seems like this process of weighting rows based on the number of trials will bias the regression to better fit the rows with more trials. Are there situations where one should not weight the rows based on the number of trials?

It may be easier to explain through the specific question I am trying to address now:

My data set consists of county-level data: exogenous demographic variables, and a proportion for the endogenous variable (the proportion of events that took place in that county were about a specific topic). The endogenous variable is a binomial variable, but counties vary in how many events took place. My aim is to measure of the effect of the exogenous demographic variables on this proportion.

To construct the logit GLM, there seem to be two approaches:

(1) Based on the linked question, I can weight or repeat rows for each county based on how many events took place. In this scenario, $y_i$ will be either $0$ or $1$ depending on whether the event was about the topic in question. $x_i$ will be the same demographics for each event in the county.

(2) I can use one sample (row) per county with $y$ as the proportion, $\vec{x}$ as the control variables, and no weights.

My inclination is to use approach (2). It seems like this approach will weight counties consistently, regardless of the number of events, while approach (1) will cause the regression to be skewed to reflect the relationship in counties with more events.

Is it appropriate to perform a logit regression with the endogenous variable being a proportion, and no weights?

Can anyone provide guidance on this situation? Is one approach correct? Or are there reasons to favor one or the other? (Or maybe a totally different approach?)

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