Need help with constraint dropped when testing for equality coefficients and joint significance of two variables

[Vi Dinh]

Hi all,

Currently, I'm doing a multiple regression, with the totalcases as the dependent variable, while other 6 variables (border, PM, health, popu, totalphy, GDP) are independent. GDP, totalphy (total physicians in a country), health (health expenditure of a country) are calculated using population * per capita or per 1000 indicators (GDP per capita, health expenditure per capita, physicians per 1000) by generating new variable.

The problem is that when I tried to test the equality of coefficients of health and GDP, the result is constraint 1 dropped and there was no F value nor Prob > F. I also test joint significance for 15 pairs of variables and many pairs suffered from constraint dropped.

Can anyone provide me with a detailed explanation and solution? I appreciate every answer given to me.

[Clyde Schechter]

As you don't provide any example data, I can't play with this to try to figure it out. Here's my best guess. Regressions and related commands often encounter numerical instabilities when there are marked differences in the scale of the variables involved. We see that in your output here in that the coefficients of health and GDP are numbers of the order of magnitude 10^-5 and 10^-6. I suspect that the health and GDP coefficients are close enough to zero that Stata is misunderstanding the command as something like -test 0 = 0- and considering that to be a meaningless constraint. I also would guess that health and GDP expenditures are highly correlated with each other--and that will add further numerical instability to this kind of test.

I suggest that you rescale (change the units of) those variables. Instead of whatever currency unit they are in, change it to units of 1,000 currency units. That will make the values of those variables smaller, and that in turn will make the coefficients larger and more similar in magnitude to the other coefficients in your model. See if that fixes the problem.

If it does not, when you post back, be sure to post an example of your data set that reproduces this problem. Be sure to use the -dataex- command to do that. If you are running version 17, 16 or a fully updated version 15.1 or 14.2, -dataex- is already part of your official Stata installation. If not, run -ssc install dataex- to get it. Either way, run -help dataex- to read the simple instructions for using it. -dataex- will save you time; it is easier and quicker than typing out tables. It includes complete information about aspects of the data that are often critical to answering your question but cannot be seen from tabular displays or screenshots. It also makes it possible for those who want to help you to create a faithful representation of your example to try out their code, which in turn makes it more likely that their answer will actually work in your data.

All of that said, I do wonder whether a linear regression model is really the best approach here, as opposed to perhaps a Poisson regression with population as an exposure variable. But that's a discussion for another day.