Unchanged log likelihood, BIC and AIC when adding additional variable

[Selina Schoen]

Hi there!

I tried to find a solution or reason to my problem, but so far, I found no answer. Maybe someone here can help me?

I run a negative binomial regression because I'm dealing with count data. I checked if negative binomial or Poisson is more appropriated and found out that negative binomial is slightly better. I also use cluster robust standard errors and time fixed and entity fixed effects, which are also appropriated.

Having found the right model, I now turned to play around with including and excluding variables. But the problem is that no matter how many variables I include or exclude, the log likelihood (or the pseudo log likelihood when I include cluster robust or robust standard errors) stays always the same. Therefore, also the BIC and the AIC stay the same.

What does this mean? It seems very odd to me and appears like there is something wrong with the model. Can anyone think of a reason why this is like this?

One example maybe for you to understand better:
I regress oil price, R&D expenditures, control variables (GDP per capita, tax level in each country, propensity of countries to patent) and country and time fixed effects on patent counts. If I then add corn price and corn price is highly statistically significant the log likelihood stays the same. And also if I add then the rape seed oil price the log likelihood stays the same. Or also if I take away the oil price and include a ratio of oil price and corn price.

I hope somebody can help me! Thank you very much

Selina

[Richard Williams]

Welcome to Statalist. Showing your code and output, or providing a replicable example, might really help. Use code tags. See pt 12 of the FAQ.

[Phil Bromiley]

To expand on Richard's comment, you'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. You only need enough to show us your problem.

But it is hard to imagine how adding variables won't change the AIC/BIC even if the likelihood remains the same. It is odd that changing the model doesn't change the likelihood somewhat. Do you have something strange in your data like a perfect fit or something? Are your additional variables totally unrelated to the dv?

[Clyde Schechter]

In addition to Phil Bromiley's suggestion, I wonder if perhaps the variables being added to the model are colinear with the country or time fixed effects (or the combination of them) and therefore the model is, in fact, merely re-parameterized, not changed. The telltale sign of this would be that one or more of the country or time effects would have been omitted from the model when it previously was present.