A hierarchical latent class model for predicting disability small area counts from survey data
We consider the estimation of the number of severely disabled people by using data from the Italian survey on 'Health conditions and appeal to Medicare'. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the...
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| Published in | Journal of the Royal Statistical Society. Series A, Statistics in society Vol. 179; no. 1; pp. 103 - 131 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Blackwell Publishing Ltd
01.01.2016
John Wiley & Sons Ltd Oxford University Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0964-1998 1467-985X |
| DOI | 10.1111/rssa.12112 |
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| Abstract | We consider the estimation of the number of severely disabled people by using data from the Italian survey on 'Health conditions and appeal to Medicare'. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the ability of a person to accomplish everyday tasks. Latent class models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey is designed to provide reliable estimates at the level of administrative regions ('Nomenclature des unités territoriales statistiques', level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a latent class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data by using penalized splines. Demmler-Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors. |
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| AbstractList | We consider the estimation of the number of severely disabled people by using data from the Italian survey on ‘Health conditions and appeal to Medicare’. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the ability of a person to accomplish everyday tasks. Latent class models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey is designed to provide reliable estimates at the level of administrative regions (‘Nomenclature des unités territoriales statistiques’, level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a latent class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data by using penalized splines. Demmler–Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors. We consider the estimation of the number of severely disabled people by using data from the Italian survey on 'Health conditions and appeal to Medicare'. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the ability of a person to accomplish everyday tasks. Latent class models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey is designed to provide reliable estimates at the level of administrative regions ('Nomenclature des unites territoriales statistiques', level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a latent class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data by using penalized splines. Demmler-Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors. [web URL: http://onlinelibrary.wiley.com/doi/10.1111/rssa.12112/abstract] We consider the estimation of the number of severely disabled people by using data from the Italian survey on 'Health conditions and appeal to Medicare'. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the ability of a person to accomplish everyday tasks. Latent class models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey is designed to provide reliable estimates at the level of administrative regions ('Nomenclature des unites territoriales statistiques', level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a latent class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data by using penalized splines. Demmler-Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors. Summary We consider the estimation of the number of severely disabled people by using data from the Italian survey on ‘Health conditions and appeal to Medicare’. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the ability of a person to accomplish everyday tasks. Latent class models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey is designed to provide reliable estimates at the level of administrative regions (‘Nomenclature des unités territoriales statistiques’, level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a latent class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data by using penalized splines. Demmler–Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors. |
| Author | Fabrizi, Enrico Giovanna Ranalli, M. Montanari, Giorgio E. |
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| Cites_doi | 10.1016/j.csda.2009.03.024 10.1111/1467-9868.00353 10.1111/j.1467-985X.2006.00419.x 10.1001/jama.1963.03060120024016 10.1002/0471722189 10.1017/CBO9780511499531 10.1093/pan/mph001 10.1111/j.1467-9868.2007.00635.x 10.1016/j.jspi.2009.07.022 10.1007/s11136-008-9313-x 10.1017/CBO9780511755453 10.1002/0471249688 10.1007/s10260-010-0148-6 10.1002/env.680 10.1111/j.1541-0420.2010.01502.x 10.1214/08-AOAS205 10.1007/s11336-013-9368-7 10.1214/12-STS395 10.1214/ss/1038425655 |
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| Copyright | Copyright © 2016 The Royal Statistical Society and John Wiley & Sons Ltd. 2015 Royal Statistical Society Copyright Blackwell Publishing Ltd. Jan 2016 |
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| References | Aitkin, M., Liu, C. and Chadwick, T. (2009) Bayesian model comparison and model averaging for small-area estimation. Ann. Appl. Statist., 3, 199-221. Opsomer, J. D., Claeskens, G., Ranalli, M. G., Kauermann, G. and Breidt, F. J. (2008) Non-parametric small area estimation using penalized spline regression. J. R. Statist. Soc. B, 70, 265-286. Ruppert, D., Wand, M. P. and Carroll, R. J. (2003) Semiparametric Regression. New York: Cambridge University Press. Gelman, A. (2006) Prior distributions for variance parameters in hierarchical models. Baysn Anal., 1, 515-533. Ghosh, J., Herring, A. H. and Siega-Riez, A. M. A. (2011) Bayesian variable selection for latent class models. Biometrics, 67, 917-925. Pfeffermann, D. (2013) New important developments in small area estimation. Statist. Sci., 28, 40-68. Statistics Canada (2007) 2005 Survey of Financial Security-Public Use Microdata File User Guide. Ottawa: Statistics Canada. (Available from http://www.statcan.gc.ca/pub/13f0026m/13f0026m2007001-eng.htm.) Eilers, P. H. C. and Marx, B. D. (1996) Flexible smoothing with B-splines and penalties. Statist. Sci., 11, 89-121. Katz, S., Ford, A. B., Moskowitz, R. W., Jackson, B. A. and Jaffe, M. W. (1963) Studies of illness in the aged-the index of ADL: a standardized measure of biological and psychosocial function. J. Am. Med. Ass., 185, 914-919. Pan, J.-C. and Huang, G.-H. (2014) Bayesian inferences of latent class models with an unknown number of classes. Psychometrika, 79, 621-646. Hagenaars, J. A. and McCutcheon, A. L. (2002) Applied Latent Class Analysis. Cambridge: Cambridge University Press. Nychka, D. and Cummins, D. (1996) Flexible smoothing with B-splines and penalties-comment. Statist. Sci., 11, 104-105. Montanari, G. E., Ranalli, M. G. and Eusebi, P. (2011) Latent variable modeling of disability in people aged 65 or more. Statist. Meth. Applic., 20, 49-63. Thomas, A., O'Hara, B., Ligges, U. and Sturz, S. (2006) Making bugs open. R News, 6, 12-17. Crespi, C. and Boscardin, W. (2009) Bayesian model checking for multivariate outcome data. Computnl Statist. Data Anal., 53, 3765-3772. Crainiceanu, C., Ruppert, D. and Wand, M. P. (2005) Bayesian analysis for penalized spline regression using winbugs. J. Statist. Softwr., 14, 1-24. Bolck, A., Croon, M. and Hagenaars, J. (2004) Estimating latent structure models with categorical variables: one-step versus three-step estimators. Polit. Anal., 12, 3-27. Agresti, A. (2002) Categorical Data Analysis. New York: Wiley. ISTAT (2008) Condizioni di salute e ricorso di servizi sanitari-Nota metodologica. ISTAT, Rome. (Available from http://www.istat.it/it/archivio/10836.) Mesbah, M. (2004) Measurement and analysis of health related quality of life and environmental data. Envirometrics, 15, 473-481. Fabrizi, E. and Trivisano, C. (2010) Robust linear mixed models for small area estimation. J. Statist. Planng Inf., 140, 433-443. Chung, H., Flaherty, B. P. and Schafer, J. L. (2006) Latent class logistic regression: application to marijuana use and attitudes among high school seniors. J. R. Statist. Soc. A, 169, 723-743. Cabrero-Garcìa, J. and Lòpez-Pina, J. A. (2008) Aggregated measures of functional disability in a nationally representative sample of disabled people: analysis of dimensionality according to gender and severity of disability. Qual. Life Res., 17, 425-436. Rao, J. (2003) Small Area Estimation. New York: Wiley. Lazarsfeld, P. and Henry, N. (1968) Latent Structure Analysis. Boston, Houghton Mifflin. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002) Bayesian measures of model complexity and fit (with discussion). J. R. Statist. Soc. B, 64, 583-639. 1963; 185 2013; 28 2009; 53 2001 2002; 64 2004; 15 2004; 12 2008; 17 2011; 20 2008 2007 2014; 79 2006; 6 2010; 140 2011; 67 2006; 1 2003 2002 2009; 3 2008; 70 1968 2006; 169 2005; 14 1996; 11 Fabrizi (2023022804490710300_) 2010; 140 Thomas (2023022804490710300_) 2006; 6 Chung (2023022804490710300_) 2006; 169 Agresti (2023022804490710300_) 2002 Opsomer (2023022804490710300_) 2008; 70 Hagenaars (2023022804490710300_) 2002 ISTAT (2023022804490710300_) 2008 Cabrero-Garcìa (2023022804490710300_) 2008; 17 Mesbah (2023022804490710300_) 2004; 15 Ruppert (2023022804490710300_) 2003 Montanari (2023022804490710300_) 2011; 20 Pan (2023022804490710300_) 2014; 79 Eilers (2023022804490710300_) 1996; 11 Ghosh (2023022804490710300_) 2011; 67 Brown (2023022804490710300_) 2001 Crespi (2023022804490710300_) 2009; 53 Pfeffermann (2023022804490710300_) 2013; 28 Spiegelhalter (2023022804490710300_) 2002; 64 Crainiceanu (2023022804490710300_) 2005; 14 Bolck (2023022804490710300_) 2004; 12 Gelman (2023022804490710300_) 2006; 1 Nychka (2023022804490710300_) 1996; 11 Rao (2023022804490710300_) 2003 Katz (2023022804490710300_) 1963; 185 Erosheva (2023022804490710300_) 2002 Aitkin (2023022804490710300_) 2009; 3 Statistics Canada (2023022804490710300_) 2007 Lazarsfeld (2023022804490710300_) 1968 |
| References_xml | – reference: Chung, H., Flaherty, B. P. and Schafer, J. L. (2006) Latent class logistic regression: application to marijuana use and attitudes among high school seniors. J. R. Statist. Soc. A, 169, 723-743. – reference: Statistics Canada (2007) 2005 Survey of Financial Security-Public Use Microdata File User Guide. Ottawa: Statistics Canada. (Available from http://www.statcan.gc.ca/pub/13f0026m/13f0026m2007001-eng.htm.) – reference: Pan, J.-C. and Huang, G.-H. (2014) Bayesian inferences of latent class models with an unknown number of classes. Psychometrika, 79, 621-646. – reference: Ruppert, D., Wand, M. P. and Carroll, R. J. (2003) Semiparametric Regression. New York: Cambridge University Press. – reference: Cabrero-Garcìa, J. and Lòpez-Pina, J. A. (2008) Aggregated measures of functional disability in a nationally representative sample of disabled people: analysis of dimensionality according to gender and severity of disability. Qual. Life Res., 17, 425-436. – reference: Pfeffermann, D. (2013) New important developments in small area estimation. Statist. Sci., 28, 40-68. – reference: Rao, J. (2003) Small Area Estimation. New York: Wiley. – reference: ISTAT (2008) Condizioni di salute e ricorso di servizi sanitari-Nota metodologica. ISTAT, Rome. (Available from http://www.istat.it/it/archivio/10836.) – reference: Lazarsfeld, P. and Henry, N. (1968) Latent Structure Analysis. Boston, Houghton Mifflin. – reference: Gelman, A. (2006) Prior distributions for variance parameters in hierarchical models. Baysn Anal., 1, 515-533. – reference: Crainiceanu, C., Ruppert, D. and Wand, M. P. (2005) Bayesian analysis for penalized spline regression using winbugs. J. Statist. Softwr., 14, 1-24. – reference: Crespi, C. and Boscardin, W. (2009) Bayesian model checking for multivariate outcome data. Computnl Statist. Data Anal., 53, 3765-3772. – reference: Eilers, P. H. C. and Marx, B. D. (1996) Flexible smoothing with B-splines and penalties. Statist. Sci., 11, 89-121. – reference: Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002) Bayesian measures of model complexity and fit (with discussion). J. R. Statist. Soc. B, 64, 583-639. – reference: Ghosh, J., Herring, A. H. and Siega-Riez, A. M. A. (2011) Bayesian variable selection for latent class models. Biometrics, 67, 917-925. – reference: Thomas, A., O'Hara, B., Ligges, U. and Sturz, S. (2006) Making bugs open. R News, 6, 12-17. – reference: Aitkin, M., Liu, C. and Chadwick, T. (2009) Bayesian model comparison and model averaging for small-area estimation. Ann. Appl. Statist., 3, 199-221. – reference: Montanari, G. E., Ranalli, M. G. and Eusebi, P. (2011) Latent variable modeling of disability in people aged 65 or more. Statist. Meth. Applic., 20, 49-63. – reference: Katz, S., Ford, A. B., Moskowitz, R. W., Jackson, B. A. and Jaffe, M. W. (1963) Studies of illness in the aged-the index of ADL: a standardized measure of biological and psychosocial function. J. Am. Med. Ass., 185, 914-919. – reference: Opsomer, J. D., Claeskens, G., Ranalli, M. G., Kauermann, G. and Breidt, F. J. (2008) Non-parametric small area estimation using penalized spline regression. J. R. Statist. Soc. B, 70, 265-286. – reference: Fabrizi, E. and Trivisano, C. (2010) Robust linear mixed models for small area estimation. J. Statist. Planng Inf., 140, 433-443. – reference: Mesbah, M. (2004) Measurement and analysis of health related quality of life and environmental data. Envirometrics, 15, 473-481. – reference: Bolck, A., Croon, M. and Hagenaars, J. (2004) Estimating latent structure models with categorical variables: one-step versus three-step estimators. Polit. Anal., 12, 3-27. – reference: Agresti, A. (2002) Categorical Data Analysis. New York: Wiley. – reference: Nychka, D. and Cummins, D. 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| SubjectTerms | Appeals Bayesian analysis Classification Computer simulation Counting Demmler-Reinsch bases Disabilities Disability Estimating techniques Health interview survey Markov analysis Mathematical models Medicare Monte Carlo simulation Non-parametric regression Penalized splines Small area estimation Statistics Tasks Unit level model |
| Title | A hierarchical latent class model for predicting disability small area counts from survey data |
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