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RE: st: Time Series Poisson


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Time Series Poisson
Date   Mon, 31 Oct 2011 07:27:34 -0400

Rich,
I also assume you must be modeling some type of aggregate (US-level) count, so I wonder if an ecological growth curve could be fit to the series:
Yang, C.C., Yang, C.C., & Yeh, K.H. (2005). Ecological-Inference-Based Latent Growth Models: Modeling Changes of Alienation. Quality & Quantity, 39(2), 125-135. 
I have some other papers that you might want to take a peak at, but unfortunately the nifty, pre-programmed Stata-specific solution seems elusive. :) For example, Wu and Cao (2011) apply their blockwise empirical likelihood approach to analyze counts on polio cases in the US and daily non-accidental deaths in Toronto -- so a bit similar to your case in having only one geographic area and one outcome (they also have one or two time-varying covariates but I don't think these would be required to use the approach). 
Schmidt, A.M., & Pereira, J.B.M. (2011). Modelling Time Series of Counts in Epidemiology. International Statistical Review, 79(1), 48–69.
Wu, R., & Cao, J. (2011). Blockwise empirical likelihood for time series of counts. Journal of Multivariate Analysis, 102(3), 661-673.
Franke, J., Kirch, C., & Kamgaing, J.T. (May 15, 2011). Changepoints in Times Series of Counts.http://mspcdip.mathematik.uni-karlsruhe.de/~ckirch/papers/pp_INARCH_CP.pdf
Thomas, S.J. (May 2010). Model-based clustering for multivariate time series of counts. Doctoral Dissertation. Houston, TX: Rice University.http://scholarship.rice.edu/bitstream/handle/1911/62066/3421317.PDF?sequence=1
Freeland, R.K., & McCabe, B.P.M. (2004). Analysis of low count time series data by poisson autoregression. Journal of Time Series Analysis, 25(5), 701-722.
Davis, R.A., Dunsmuir, W.T.M., & Wang, Y. (2000). On Autocorrelation in a Poisson Regression Model. Biometrika, 87(3), 491-505. 
Jung, R.C., & Tremayne, A.R. (2003). Testing for serial dependence in time series models of counts. Journal of Time Series Analysis, 24(1), 65–84.
Hay, J.L., & Pettitt, A.N. (2001). Bayesian analysis of a time series of counts with covariates: an application to the control of an infectious disease. Biostatistics, 2(4), 433-444.http://biostatistics.oxfordjournals.org/content/2/4/433.full.pdf
Fokianos, K. (2001). Truncated Poisson Regression for Time Series of Counts. Scandinavian Journal of Statistics, 28(4), 645–659.
Brandt, P.T., Williams, J.T., Fordham, B.O., & Pollins, B. (2000). Dynamic Modeling for Persistent Event-Count Time Series. American Journal of Political Science, 44(4), 823-843. 
Shen, H., & Huang, J.Z. (2008). Forecasting time series of inhomogenous poisson processes with application to call center workforce management. The Annals of Applied Statistics, 2(2), 601–623.http://www.unc.edu/~haipeng/publication/poissonSVD.pdf
Boucher, J.-P., & Guillen, M. (2009). A survey on models for panel count data with applications to insurance. RACSAM, 103(2), 277–294.http://www.rac.es/ficheros/doc/00698.pdf
Sparks, R.S., Keighley, T., & Muscatello, D. (2009). Improving EWMA Plans for Detecting Unusual Increases in Poisson Counts. Journal of Applied Mathematics and Decision Sciences, 2009, Article ID 512356.
FrüHwirth-Schnatter, S., & Wagner, H. (2006). Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling. Biometrika, 93(4), 827-841.
Best,
Cam

> Date: Sun, 30 Oct 2011 23:46:55 -0500
> To: statalist@hsphsun2.harvard.edu
> From: richardwilliams.ndu@gmail.com
> Subject: RE: st: Time Series Poisson
> 
> Thanks Cameron and Tirthankar. Many of these look 
> promising. To be clear, there is only 1 country 
> involved here, with separate records for each of 
> 45 years. Some of these sources sound like they 
> might be designed for cross-sectional time series 
> rather than time series, but I don't understand 
> either well enough to really say. (And I am still 
> hoping for that nifty Stata-specific solution, 
> since I am not sure how far we will get if we 
> have to figure out how to program this ourselves!)
> 
> At 08:42 PM 10/30/2011, Cameron McIntosh wrote:
> >Hi Richard, Tirthankar
> >I might also suggest:
> >Oh, M.-S., & Lim, Y.B. (2001). Bayesian analysis 
> >of time series Poisson data. Journal of Applied Statistics, 28(2), 259-271.
> >Drescher, D. (2008). Testing for presence of a 
> >latent process in count series. Journal of 
> >Statistical Computation and Simulation, 78(7), 595-607.
> >Jung, R.C., Kukuk, M., & Liesenfeld, R. (2006). 
> >Time series of count data: modeling, estimation 
> >and diagnostics. Computational Statistics & Data Analysis, 51(4), 2350-2364.
> >Jorgensen, B., Lundbye-Christensen, S., Song, 
> >P.X-K., & Sun, Li. (1999). A State Space Model 
> >for Multivariate Longitudinal Count Data. Biometrika, 86(1), 169-181.
> >Knape, J., Jonzén, N., Sköld, M., & Sokolov, L. 
> >(2009). Multivariate state-space modelling of 
> >bird migration count data. Environmental and 
> >Ecological Statistics, 3(Section I), 59-79.
> >Knape et al. (2009) model a 54-year time series 
> >of various bird species counts, your student 
> >might follow their Bayesian strategy... I was 
> >also thinking that it might be possible to fit a 
> >latent growth curve or multilevel model to this 
> >type of data, with Poisson links on the 45 indicators:
> >Liu, H. (2007). Growth Curve Models for 
> >Zero-Inflated Count Data: An Application to 
> >Smoking Behavior. Structural Equation Modeling, 14(2), 247-279.
> >Alosh, M. (2009). Modeling longitudinal count 
> >data with dropouts. Pharmaceutical Statistics, 9(1), 35-45.
> >Min, Y., & Agresti, A. (2005). Random effect 
> >models for repeated measures of zero-inflated 
> >count data. Statistical Modelling, 5(1), 1-19. 
> >Coelho-Barrosa, E.A., Achcar, J.A., & Mazucheli, 
> >J. (2010). Longitudinal Poisson modeling: an 
> >application for CD4 counting in HIV-infected 
> >patients. Journal of Applied Statistics, 37(5), 865-880.
> >My two cents,
> >Cam
> > > Date: Sun, 30 Oct 2011 18:04:46 -0700
> > > Subject: Re: st: Time Series Poisson
> > > From: tirthankar.chakravarty@gmail.com
> > > To: statalist@hsphsun2.harvard.edu
> > >
> > > Richard,
> > >
> > > See chapter 4 in this book:
> > > http://amzn.com/0471363553
> > >
> > > T
> > >
> > >
> > > On Sun, Oct 30, 2011 at 6:53 PM, Richard Williams
> > > <richardwilliams.ndu@gmail.com> wrote:
> > > > One of my students (a political scientist 
> > of course -- they always bring up
> > > > these weird problems I have never 
> > encountered myself!) has a data set that
> > > > consists of 45 yearly records for the 
> > United States. The dependent variable
> > > > is a count. It sounded to me like the sort 
> > of thing that should be analyzed
> > > > by a time series poisson model. But, 
> > unfortunately, I wasn't even sure that
> > > > such a thing existed - I was hoping there was a tspoisson command, but no
> > > > such luck.
> > > >
> > > > However, I found this Stata Technical 
> > Bulletin for a very old user-written
> > > > command called nwest. 
> > http://www.stata.com/products/stb/journals/stb39.pdf.
> > > > It says "This article discusses the 
> > calculation of standard errors that are
> > > > robust to heteroscedasticity and serial 
> > correlation for probit, logit, and
> > > > poisson regression models."
> > > >
> > > > I also found this slightly newer post from 2003:
> > > > http://www.stata.com/statalist/archive/2003-06/msg00258.html.
> > > >
> > > > What I take from this is that he should -tsset- his data and use -glm- to
> > > > estimate a Poisson model with Newey-West standard errors, e.g. something
> > > > like
> > > >
> > > > glm y x1 x2 x3, family(poisson) link(log) vce(hac nwest)
> > > >
> > > > Does this sound right, and if so is this 
> > the best he can do, at least with
> > > > Stata?
> > > >
> > > >
> > > > -------------------------------------------
> > > > Richard Williams, Notre Dame Dept of Sociology
> > > > OFFICE: (574)631-6668, (574)631-6463
> > > > HOME:   (574)289-5227
> > > > EMAIL:  Richard.A.Williams.5@ND.Edu
> > > > WWW:    http://www.nd.edu/~rwilliam
> > > >
> > > > *
> > > > *   For searches and help try:
> > > > *   http://www.stata.com/help.cgi?search
> > > > *   http://www.stata.com/support/statalist/faq
> > > > *   http://www.ats.ucla.edu/stat/stata/
> > > >
> > >
> > >
> > >
> > > --
> > > Tirthankar Chakravarty
> > > tchakravarty@ucsd.edu
> > > tirthankar.chakravarty@gmail.com
> > >
> > > *
> > > *   For searches and help try:
> > > *   http://www.stata.com/help.cgi?search
> > > *   http://www.stata.com/support/statalist/faq
> > > *   http://www.ats.ucla.edu/stat/stata/
> >
> >*
> >*   For searches and help try:
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> >*   http://www.stata.com/support/statalist/faq
> >*   http://www.ats.ucla.edu/stat/stata/
> 
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME:   (574)289-5227
> EMAIL:  Richard.A.Williams.5@ND.Edu
> WWW:    http://www.nd.edu/~rwilliam
> 
> 
> *
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> *   http://www.ats.ucla.edu/stat/stata/
 		 	   		  
*
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