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RE: st: Model for Poisson-shaped distribution but with non-count data


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Model for Poisson-shaped distribution but with non-count data
Date   Mon, 5 Dec 2011 23:39:23 -0500

Hi again Owen,

In thinking about this further, it seems quite possible that you may be dealing with a mixture/unobserved heterogeneity given the wonky distribution on that DV. Now, there are some debates in the literature about whether mixture models always uncover substantively meaningful latent groups, or just capitalize on bumpy distributions that don't really have any substantive relevance, and this argument would be important to consider carefully here... but it may be well worth checking out this literature and seeing if a mixture regression might be suitable for your data (the multilevel version may be a good option in your case, as you noted the need to include random intercepts):

Grün, B., & Leisch, F. (2008). Finite Mixtures of Generalized Linear Regression Models. In Shalabh & C. Heumann (Eds.), Recent Advances in Linear Models and Related Areas: Essays in Honour of Helge Toutenburg (pp. 205-239). Heidelberg: Physica-Verlag. http://epub.ub.uni-muenchen.de/2087/1/tr013.pdf

Kaplan, D. (2005). Finite Mixture Dynamic Regression Modeling of Panel Data with Implications for Dynamic Response Analysis. Journal of Educational and Behavioral Statistics, 30, 169-187.

Khalili, A., & Chen, J. (2007). Variable Selection in Finite Mixture of Regression Models. Journal of the American Statistical Association, 102(479), 1025-1038.http://www.stat.ubc.ca/~khalili/Abbas_Khalili_Paper_JASA1.pdf

Jang, D.-H., & Anderson-Cook, C.M. (2010). Fraction of Design Space Plots for Evaluating Ridge Estimators in Mixture Experiments. Quality and Reliability Engineering International, 27(1),  27-34.  http://onlinelibrary.wiley.com/doi/10.1002/qre.1104/pdf

Kettaneh-Wold, N. (1992). Analysis of mixture data with partial least squares. Chemometrics and Intelligent Laboratory Systems, 14, 57-69. 
ftp://124.42.15.59/ck/2011-01/165/008/922/249/Analysis%20of%20mixture%20data%20with%20partial.pdf

Ding, C.S. (2006). Using regression mixture analysis in educational research. Practical Assessment, Research and Evaluation, 11(11). http://pareonline.net/pdf/v11n11.pdf

Muthén, B. & Asparouhov, T. (2009). Multilevel regression mixture analysis. Journal of the Royal Statistical Society, Series A, 172, 639-657. http://www.gseis.ucla.edu/faculty/muthen/articles/Article_128.pdf

Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338–363.

Muthén, B.O. (2003). Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran (2003). Psychological methods, 8(3), 369-377.

Cam
 

> From: cnm100@hotmail.com
> To: statalist@hsphsun2.harvard.edu
> Subject: RE: st: Model for Poisson-shaped distribution but with non-count data
> Date: Mon, 5 Dec 2011 21:32:30 -0500
> 
> Hi Owen,
> It might help further if we knew exactly what your DV was.  I don't know about a transformation... what about robust standard errors and rescaled fit statistics?
> 
> Maas, C.J.M., & Hox, J.J. (2004a). The influence of violations of assumptions on multilevel parameter estimates and their standard errors. Computational Statistics & Data Analysis, 46, 427–440.http://igitur-archive.library.uu.nl/fss/2007-1004-200713/Maas(2004)_influence%20of%20violations.pdf
> 
> Maas, C.J.M., & Hox, J.J. (2004b). Robustness issues in multilevel regression analysis. Statistica Neerlandica, 58, 127–137.http://joophox.net/publist/sn04.pdf
> 
> Zhou, J., Zhu, H. (2003). Robust Estimation and Design Procedures for the Random Effects Model. The Canadian Journal of Statistics,  31(1), 99-110.
> 
> Yuan, K.-H., & Bentler, P.M. (2002). On normal theory based inference for multilevel models with distributional violations. Psychometrika, 67(4), 539-561.http://www.springerlink.com/content/833158k606754897/fulltext.pdf
> 
> Dedrick, R.F., Ferron, J.M., Hess, M.R., Hogarty, K.Y., Kromrey, J.D., Lang, T.R., Niles, J.D., & Lee, R.S. (2009). Multilevel Modeling: A Review of Methodological Issues and Applications. Review of Educational Research, 79(1), 69-102.
> 
> Best,
> Cam
> 
> > Date: Mon, 5 Dec 2011 15:34:09 -0800
> > Subject: st: Model for Poisson-shaped distribution but with non-count data
> > From: ogallupe@gmail.com
> > To: statalist@hsphsun2.harvard.edu
> > 
> > Hello,
> > 
> > Does anyone know what type of regression model I should use? I've been
> > searching and have not been able to find a modeling approach designed
> > to meet the distributional properties of a variable I am hoping to
> > analyse.
> > 
> > The dependent variable has what looks like a Poisson distribution, but
> > with non-count data. About 28% of the sample scores somewhere between
> > 0 and 1. The highest value is 182.6. Skew = 2.256; kurtosis = 10.002.
> > N=2776.
> > 
> > I have tried bootstrapped linear regressions and linear regressions
> > after employing a normalizing transformation using lnskew0 (though the
> > normalization is not perfect and results in a bimodal residual
> > distribution).
> > 
> > One further complication is that I need to include random intercepts.
> > 
> > If anyone could help, it would be very  much appreciated.
> > 
> > Regards,
> > 
> > Owen Gallupe
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