Fractional response variable with many 0s and 1s

[Robert Wagner]

Hello Together,

I would like to carry out some analyses to investigate the drivers for the proportion of training places filled at company level. The values of the dependent variable are distributed as follows:

I wonder what type of analysis is suitable for this kind of distribution structure of the dependent variable.

The following options have already been tested:

Fractional response logit: depvar specified by the share of filled positions

fracreg logit share_positions_filled x1 x2 x2

GLM binomial response: depvar specified by number of sucesses (total_positions_filled) in a series of binomial trials (total_positions_offered)

glm total_positions_filled y x1 x2 x3, family(binomial total_positions_offered) link(logit) robust

GLM binomial response: depvar specified by the share of filled positions

glm share_positions_filled y x1 x2 x3, family(binomial) link(logit)

Logit: depvar specified as Dummy (0 = below-average share of positions filled; 1 = above-average share of positions filled)

logit above_avg_positions_filled y x1 x2 x3

As I am very unsure which of the estimation methods is suitable, I would be pleased if some of you could give your thoughts on this.


Thank you very much for your help & Have a good one

[Maarten Buis]

I would either go fracreg or zoib (from SSC). The binomial regression with the number of trials is equivalent to binreg could work if there is a really strong explanatory variable that can explain the bimodal distribution. Binomial response without the number of trials should almost be like fracreg except that you are missing the vce(robust) option. That option is not optional in this case. logit is not appropriate in this case as it only compares the 0 versus non-0 values.You might be interested in this: http://www.maartenbuis.nl/publications/prop.html

[Robert Wagner]

Thank you very much for your very helpful answer Mr Buis. I will try out your suggestions.