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 Bella posted on Wednesday, July 29, 2009 - 12:33 pm
Dear Linda & Bengt,

I have some quite basic questions. I'm just starting my first GMM and trying to find out how to handle certain missing values.

The data I use are mainly the entries of (officially registered) offenses of a sample consisting of ex-cons. They all started their prison term as juveniles during the same time period, but when they did they were of course not of the same age. The trajectories I want to observe are going to start at their 14th birthday based on the number of entries per year of life, but due to the sample some are only 23 years old when I recently checked their criminal register (in 2008) and some are already 35. Is there any way to mark the missings by a certain value or so, so that mplus registeres that there is not a group who is abstinent since they are 23 (e.g.), but their observation period stops?

My next question also adresses the missings - since I know during which periods in their biographies the observed were convicted and therefore their chance of offending is rather low, what missing value should be used so the growth curves are not distorted, because the number of offenses during the prison term is "0"?

Do You have any idea what would be the best way to handle this?
Thanks a lot in advance!
 Bengt O. Muthen posted on Wednesday, July 29, 2009 - 11:00 pm
For your first question you may want to take a look at our multiple-cohort example in the UG - see ex6.18. Or, you may handle the different age ranges by using a missing data indicator for ages that are not observed for the individual.

Regarding taking incarceration into account in crime curve modeling, we are contacting experts who might have worked on this. - Any reader who knows such work off hand?
 Bella posted on Friday, July 31, 2009 - 7:11 am
Hi Bengt,

thanks for the advice!

Still, if someone has an idea on taking into account the prison terms I'm thankful for any suggestions or hints on papers.

Have a nice weekend,

 Bengt O. Muthen posted on Friday, July 31, 2009 - 6:30 pm
I hear that incarceration modeling may have been attempted by Shawn Bushway at Univ of Albany and Paul Nieuwbeerta in the Netherlands. You may want to Google them. Please let us know if they have any relevant papers.
 Amir Sariaslan posted on Friday, July 31, 2009 - 9:35 pm
You may want to have a look at the following paper:

Eggleston, E. P., Laub, J. H. & Sampson, R. J. (2004): Methodological Sensitivities to Latent Class Analysis of Long-Term Criminal Trajectories. Journal of Quantitative Criminology, vol. 20(1), pp. 1-26.

Tihomir Asparouhov kindly showed how to model the offset component in the Poisson model here:

 Bengt O. Muthen posted on Tuesday, August 04, 2009 - 12:20 am
Here is a response from Hanno Petras at the Univ of Maryland:

In addition to the current response on the discussion board, to my
knowledge exposure time has only been implemented for simple Poisson
Models. I did a little search and the below article is the only one
which integrates ZIP and exposure time. I think that a ZIP model might
be useful for Bellas data where the prob of structural and random zeroes
can vary across time. A two-part model might be interesting as well
where times of incarceration could be used as a time invariant covariate
impacting the probability of being 1 on the u-part. In terms of experts,
Wayne Osgood at PenState comes to mind.

AU: Andy H. Lee
AU: Kui Wang
AU: Kelvin K.W. Yau
TI: Analysis of Zero-Inflated Poisson Data Incorporating Extent of
SO: Biometrical Journal
VL: 43
NO: 8
PG: 963-975
YR: 2001
CP: © 2001 WILEY-VCH Verlag Berlin GmbH, Fed. Rep. of Germany
ON: 1521-4036
PN: 0323-3847
AD: Curtin University of Technology, Australia; City University of Hong
Kong, Hong Kong
DOI: 10.1002/1521-4036(200112)43:8<963::aid-bimj963>3.0.CO;2-K
 Amir Sariaslan posted on Wednesday, August 05, 2009 - 5:54 pm
Professor Muthén,

Thank you for posting Dr. Petras' suggestions. The two-part solution is an interesting one but I am wondering why one would use a time-invariant covariate accounting for the exposure? Assuming that information on incarceration is available for each time point; wouldn't it be more reasonable to use that information as time-varying covariates affecting the u-part of a two-part model? I have a feeling that I might be missing something here.

 Bengt O. Muthen posted on Wednesday, August 05, 2009 - 10:50 pm
Hanno says he will answer you tomorrow.
 Hanno Petras posted on Thursday, August 06, 2009 - 11:29 am
Hi Amir,

sorry for the confusion. Incarceration time is certainly a time variant covariate, but unless that incarceration effects the time specific likelihood to engage in the behavior differently, I would start out with a model where the effect (and not the value of the covariate) is constrained to be invariant (i.e., proportional hazard). Of course, you can relax this constraint either for the entire time span or in a piecewise fashion. Overall, these modeling decisions should also be guided by your specific research questions.

 Amir Sariaslan posted on Thursday, August 06, 2009 - 1:18 pm
Dr. Petras,

Thank you very much for clearing things up. It has indeed opened up my eyes to new ways of modeling incarceration effects.

 Bella posted on Friday, August 07, 2009 - 10:12 am

Thank You all for the very good help and hints.

Indeed, there's a footnote on taking into account the conviction time (Poisson-based models) in:

Blokland, A., Nagin, D. and Nieuwbeerta, P. (2006): Life Span Offending Trajectories of a Dutch Conviction Cohort. In: Blokland, A. & Nieuwbeerta, P. (Eds.): Developmental Studies and Life Course Studies in Delinquency and Crime. A Review of Contemporary Dutch Research.

where they also cite:
Jones,B., Nagin, D. & Roeser, K. (2001). A SAS procedure based on mixture models for estimating developmental trajectories. Sociological Methods and Research 29(3): 374-393.

Maybe that's helpful :-).

I'll google for more papers of Nieuwbeerta and post them here when I cross something helpful! have a great weekend!!
 Bella posted on Saturday, August 15, 2009 - 12:21 pm
Hi there,

this papers was just published and it is also presenting ideas on missing in incarceration samples - think it's the one Bengt meant earlier:

Bushway, S.D., Seeten, G., & Nieuwbeerta, P. (2009). Measuring Long Term Individual Trajectories of Offending Using Multiple Methods. In: Journal of Quantitative Methods.

(published online: )

Have a nice weekend!
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