I am using negative binomial regression where the sample has been split into quartiles based on values for a particular variable. Is there is formal way to test for the equality of coefficients across the four separate models? Paternoster et al.'s (1998) test seemingly is only appropriate when using OLS regression. The coefficients across the four quartiles are as follows:
Q1: b = -.0188595 SE = .0579923
Q2: b = .0273382 SE = .0367739
Q3: b = .0350463 SE = .0251663
Q4: b = .0565013 SE = .0143621
I am not quite sure why Paternoster's test cannot be applied for the coefficients of the negative binomial regression, since the point of interest is the equation's sampling distribution, which should still be the z distribution. In any case, you may consider restructuring your model and just perform one analysis with dummy variables and interaction terms (conditional). I think the latter is also a more appropriate approach since you have just one dataset.
Hi Ryan,
You can use the Clogg et al test (advocated by Paternoster et al) because Brame and colleagues (1998) showed that it applies to maximum likelihood estimation. Additionally, MacKinnon and colleagues have some good stuff on this issue that may help. They advocate for the use of slightly different tests. The two references below may be useful. Hope this helps--good luck!
Scott
Brame, R., Paternoster, R., Mazerolle, P., & Piquero, A. (1998). Testing for the equality of maximum-likelihood regression coefficients between two independent equations. Journal of Quantitative Criminology, 14(3), 245-261.
MacKinnon, D.P., Lockwood, C.M., Hoffman, J.M., West, S.G. & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7(1), 83-104.
Hey Ryan -- I believe Scott has provided the correct answer to your question -- I am not clear, however, whether or not the manner in which your samples were produced violates any assumptions for the Brame application.
Hi Ryan,
as far as I know you should not use the Paternoster test for a comparison of NB regression coefficients, although the authors claim the opposite. But you may use the test for a comparison of the NB marginal effects at representative values. For more details see
Greene, W. (2010). Testing Hypotheses About Interaction Terms in Nonlinear Models. Economic Letters 107: 291-296.
Mood, C. (2010). Logistic Regression: Why We Cannot Do What We Think We Can Do, And What We Can Do About It. European Sociological Review 26: 67–82.
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