GLM: Goodness of fit; Robustness Test; Working with Predictions; Interaction Terms

[Dominik Iseli]

Dear Fellow Researchers

Please excuse my unprofessional wording in advance - it's my first post.
I am currently working on my Bachelor thesis with the intention to publish my work in a B/C Journal. Naturally, a journal article sets higher standards to empirical work than a normal Bachelor thesis. Therefore, I am hoping to find some answers here concerning questions nobody on my campus, whether professor nor PhD student, managed to answer!


Let me first describe my data set. I am empirically investigating the effect of diversification on the fund performance of Private Equity firms. Diversification is measured by a fractional (adapted Hirsch-Herfindahl Index) continous variable. The dependent variable, fund performance is measured fractionally as well, between 0 and 1. I use severall control variables.
Following contemporary research, I used a GLM model. After a Modified Park Test, I am now working with the Poisson model (poisson depvar indepvar, vce(robust)).

QUESTION 1: Goodness of fit
MPT recommends Poisson distribution. Kensel density graph looks alike (for lambda=1). Linktest is okay. The assumption of the Poisson regression is that the mean and the variance of the independent variable are the same. This however is not the case. The mean is around 3 times higher. Therefore, I tested with "estat gof", the results: prob > chi2 = 1, what makes me super suspicious. How come the goodness of fit is that high? Next, I tested for over-dispersion with "nbreg", results are okay I guess, alpha was not significantly different from zero and thus indicates that over-dispersion is not a concern. That's all I tested for. This cannot be it, right? Do you have any hints how I can properly assess the quality of my dataset and regression results?

QUESTION 2: Robustness Test
How can I properly assess the robustness? What is common in research?

QUESTION 3: Working with Predictions
Working with GLM makes predictions a little bit hard to interpret, even after "irr". I am looking for a way to display in 3d the predictions of the depvar and 2 indepvars. Is it possible to safe the predictions of the poisson regression for these 3 variables and plot them with "surface"?

QUESTION 4: Interaction Terms
Now things get juicy. I read several articles about the difficult use of interaction terms in GLM. I felt like these articles were pretty contradictory and not very practical. Do you have any hints on how to use interaction terms? I built an interaction term between a dummy variable and the diversification variable. The Interaction term is significant and sort of the crown jewel of my work. Can I simply build an interaction term by interactionvar=dummyvar*diversification?


Thank you very much for your answers. If you need any more info, please let me know, I will answer instantly!
Best regards from Switzerland!

[Richard Williams]

A couple of thoughts.

Given that you are using Poisson and nbreg, I would take a look at Long and Freese's new book. Besides explaining the models they have suggestions for how to make results more interpretable. See

http://www.stata.com/bookstore/regre...ent-variables/

For 4, you should use factor variable notation, and interpretability can be enhanced via the use of margins. For more, see

http://www3.nd.edu/~rwilliam/stats/Margins01.pdf

On 1, it would help to see actual code and output. Your results sound odd to me.

[Dominik Iseli]

Dear Prof. Williams,

thank you very much for your valuable input. Your presentation about the margins command and factor variable notation is very useful! Do you have anymore of these which could be useful to me? I am currently checking if I can order the book from Long and Freese via my university. As for the code and output, I uploaded commented stata output.
I am very much looking forward to your analysis!

Best,
Dominik

[Franziska Goetze]

Dear Stata Users

I have a problem with calculating the marginal effect and testing the significance of an interaction variable after “glm”.

I am trying to estimate the market share of different organic food products.

I am using the following commands:

glm depvar explvar1 explvar2 explvar3 explvar4 explvar3_explvar4, link(logit) family(binomial) vce(robust)

mfx

I created the interaction term “explvar3_explvar4” by multiplying “explvar3” and “explvar4”.

After “mfx” I want to calculate the marginal effect of the interaction variable “explvar3_explvar4” and test whether it is significant by using the “dy/dx” coefficients from “mfx”.

Using the “nlcom” command seems to work after “regress” but for the “glm”-“mfx”-case I am not sure. It seems to me, that when I use the “nlcom” command after “mfx”

e.g. nlcom _b[explvar4]+_b[explvar3_explvar4]*0.014

Stata still uses the coefficients from “glm” and not the marginal effects coefficients from “mfx”.

My question is: How can I calculate the marginal effect of the interaction variable, e.g.

depvar = … β₃*explvar3 + β₄*explvar4 + β₅* explvar3_explvar4 …
marg. eff.: d(depvar) / d(explvar4) = β₄ + β₅*explvar3

with β₃, β₄ and β₅ being the marginal effects (dy/dx) from “mfx”?

I’d be glad if someone has a tip on how to do this. Thank you very much in advance for your help.

Franziska