Heterogeneity - terrible - probit model - how to solve

[Elise Sobrie]

Dear all,

For my master thesis, I am using a probit model.

my model:
probit Rejected i.WLB1 i.Industry i.COUNTRY i.Sole Sales Size FirmAge Experience

Rejected is a dummy equal to 1 when the firm is rejected in their loan request, zero otherwise
WLB is a dummy equal to 1 when the firm is a woman-led-business, zero otherwise
Industry ranges from 1 to 6, as there are six kinds of industry, if a firm is e.g. in industry 3, it gets a dummy value 1
COUNTRY ranges from 1 to 3, here also, e.g. firm is located in country2, gets dummy value 1
Sole is a dummy equal to 1 when there is sole proprietorship, zero otherwise
Sales, Experience, FirmAge and Size are numeric

When I was testing for heterogeneity, I got Pr > F = 0.000 (both for the Breush-Pagan test and White test), so it couldn't be worse. Also, when I do a scatter plot with the fitted values and the squared residuals, you can see a pattern (so no random distribution). I already saw that there exist the option 'robust' for linear regression, but unfortunately, I use probit. Is there a command that I can use similar to 'robust'? Or how do I solve this?
Currently I am trying non-linearity tests (e.g. testing for polynomiality of dependent var, logging), because I thought that when I change my model a bit, the problem could be solved. However, when I do these tests, my model doesn't improve (p values and chi² are getting worse). Also, as my dependent variable is a binary variable, it is (I think) useless to do scatter plots between the y variable and the numeric independent variables, as you only see bullet points around the line of the 1 and 0 values of the y variable and you cannot see a clear pattern (to see if the variable is eg has a exponential pattern).
Also, am I correct that I cannot transform my dummy independent variables, that this is only possible with numeric ones?

Thank you in advance!

[Clyde Schechter]

You can get robust standard errors in probit by adding the -vce(robust)- option to your command.

Also, am I correct that I cannot transform my dummy independent variables, that this is only possible with numeric ones?

Well, there are two aspects to this. There are some transformations that can't be applied, such as log-transformation, because log(0) is undefined. But, most transformations can be applied to 0/1 variables. The other, more important aspect, is that it is useless to apply transformations to indicator variables. No matter how you transform them, you still have only two distinct values, and whatever problems that presents when those values are 0 and 1 will plague you in the same or some related form when they are two other numbers. (Correction: you can transform them so they collapse into one value, which then makes the variable unusable altogether.) Moreover, the transformation of the variable just makes interpreting the coefficients more difficult to interpret. There is perhaps one exception to this: some people like to code their dichotomous variables as -0.5/0.5 and they have various arguments for why this is helpful. Other than that, though, transforming indicator variables is just a waste of time.

[Elise Sobrie]

[QUOTE=Clyde Schechter;n1432432]You can get robust standard errors in probit by adding the -vce(robust)- option to your command.

Dear Mr. Schechter

Thank you very much for your reply!
So if I use the vce(robust) option, I won't have heteroscedasticity?

Also, do you know other possibilities - except for logging and adding polynomial terms (because these I have tested and don't make a difference) - to improve my model? Because except for the heteroscedasticity, we don't have significant independent variables and our chi² is around 0.10, which is not good.

Thank you in advance!

[Wessel de Kroo]

1. Yes standard errors will be robust after using the

vce(robust)

command. This will take of your data for a logit regression, as stated

as for your comments on transforming indicator variables , also see Clydes comment..


2.
in addition with respect to your results.

- you could try expanding your sample period in order to gain more statistical significance of your independent variables.

- you could expand your independent variables in your dataset

- statement above will probably result in a different chi square score. As for right now, you accept your null hypothesis.

[Clyde Schechter]

So if I use the vce(robust) option, I won't have heteroscedasticity?

I wouldn't put it that way. The data are what they are and you still have heteroscedasticity. But if you use -vce(robust)- you won't have a heteroscedasticity problem. That is, the standard errors will be correct in spite of the heteroscedasticity.

[Elise Sobrie]

Thank you both for your helpful answers!