Bartolucci, Francesco and Giorgio E., Montanari and Pandolfi, Silvia (2012): Item selection by an extended Latent Class model: An application to nursing homes evaluation.
Download (296kB) | Preview
The evaluation of nursing homes and the assessment of the quality of the health care provided to their patients are usually based on the administration of questionnaires made of a large number of polytomous items. In applications involving data collected by questionnaires of this type, the Latent Class (LC) model represents a useful tool for classifying subjects in homogenous groups. In this paper, we propose an algorithm for item selection, which is based on the LC model. The proposed algorithm is aimed at finding the smallest subset of items which provides an amount of information close to that of the initial set. The method sequentially eliminates the items that do not significantly change the classification of the subjects in the sample with respect to the classification based on the full set of items. The LC model, and then the item selection algorithm, may be also used with missing responses that are dealt with assuming a form of latent ignorability. The potentialities of the proposed approach are illustrated through an application to a nursing home dataset collected within the ULISSE project, which concerns the quality-of-life of elderly patients hosted in Italian nursing homes. The dataset presents several issues, such as missing responses and a very large number of items included in the questionnaire.
|Item Type:||MPRA Paper|
|Original Title:||Item selection by an extended Latent Class model: An application to nursing homes evaluation|
|Keywords:||Expectation-Maximization algorithm, Polytomous items, Quality-of-life, ULISSE project|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
I - Health, Education, and Welfare > I1 - Health > I11 - Analysis of Health Care Markets
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C33 - Panel Data Models ; Spatio-temporal Models
|Depositing User:||Francesco Bartolucci|
|Date Deposited:||13 May 2012 17:13|
|Last Modified:||07 Feb 2016 16:47|
Akaike, H. (1973). Information theory and an extension of the Maximum Likelihood prin- ciple. In Petrov, B. and Csaki, F., editors, Second International Symposium on Information Theory, Budapest. Akademiai Kiado.
Andersen, E. (1977). Sufficient statistics and latent trait models. Psychometrika, 42:69–81. Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43:561–573.
Bandeen-Roche, K., Miglioretti, D. L., Zeger, S. L., and Rathouz, P. J. (1997). Latent variable regression for multiple discrete outcomes. Journal of the American Statistical Association, 92:1375–1386.
Bandeen-Roche, K., Xue, Q.-L., Ferrucci, L., Walston, J., Guralnik, J. M., Chaves, P., Zeger, S. L., and Fried, L. P. (2006). Phenotype of frailty: characterization in the women’s health and aging studies. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 61:262–266.
Bartolucci, F., Lupparelli, M., and Montanari, G. E. (2009). Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes. Annals of Applied Statistics, 3:611–636.
Baum, L. E. and Petrie, T. (1966). Statistical inference for probabilistic functions of finite state Markov chains. The Annals of Mathematical Statistics, 37:1554–1563.
Baum, L. E., Petrie, T., Soules, G., and Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. The Annals of Mathematical Statistics, 41:164–171.
Biernacki, C., Celeux, G., and Govaert, G. (1999). An improvement of the NEC criterion for assessing the number of clusters in a mixture model. Non-Linear Analysis, 20:267–272.
Biernacki, C., Celeux, G., and Govaert, G. (2003). Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics & Data Analysis, 41:561–575.
Breyer, F., Costa-Font, J., and Felder, S. (2010). Ageing, health, and health care. Oxford Review of Economic Policy, 26:674–690.
Celeux, G. and Soromenho, G. (1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classification, 13:195–212.
Dean, N. and Raftery, A. (2010). Latent class analysis variable selection. Annals of the Institute of Statistical Mathematics, 62:11–35.
Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum Likelihood from in- complete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39:1–38.
Dias (2006). Model selection for the binary latent class model: A Monte Carlo simulation. In Data Science and Classification, pages 91–99. Springer Berlin Heidelberg.
Erosheva, E. (2002). Grade of membership and latent structure models with application to disability survey data. PhD thesis, Carnegie Mellon University, Department of Statistics.
Erosheva, E., Fienberg, S., and Joutard, C. (2007). Describing disability through individual- level mixture models for multivariate binary data. Annals of Applied Statistics, 1:502–537.
Erosheva, E. A. (2006). Latent class representation of the grade of membership model. Technical report, University of Washington, Seattle.
Fraley, C. and Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97:611–631.
Gajewski, B., Thompson, S., Dunton, N., Becker, A., and Wrona, M. (2006). Inter-rater re- liability of nursing home surveys: a Bayesian latent class approach. Statistics in Medicine, 25:325–344.
Galasso, V. and Profeta, P. (2007). How does ageing affect the welfare state? European Journal of Political Economy, 23:554–563.
Goodman, L. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61:215–231.
Grabowski, D., Angelelli, J., and Mor, V. (2004). Medicaid payment and risk-adjusted nursing home quality measures. Health Affairs, 23:243–252.
Harel, O. and Schafer, J. L. (2009). Partial and latent ignorability in missing-data problems. Biometrika, 96:37–50.
Hawes, C., Morris, J. N., Phillips, C. D., Fries, B. E., Murphy, K., and Mor, V. (1997). Development of the nursing home resident assessment instrument in the USA. Age and Agening, 26:19–25.
Hirdes, J. P., Zimmerman, D., Hallman, K. G., and Soucie, P. S. (1998). Use of the MDS quality indicators to assess quality of care in institutional settings. Canadian Journal for Quality in Health Care, 14:5–11.
Howell, D. (2008). The treatment of missing data. In Outhwaite, W. and Turner, S., editors, The Sage handbook of Social Science Methodology, pages 208–224. London: Sage.
Kane, R. A., Kling, K. C., Bershadsky, B., Kane, R. L., Giles, K., Degenholtz, H. B., Liu, J., and Cutler, L. J. (2003). Quality of life measures for nursing home residents. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 58:240–248.
Karlis, D. and Xekalaki, E. (2003). Choosing initial values for the EM algorithm for finite mixtures. Computational Statistics & Data Analysis, 41:577–590.
Kass, R. and Raftery, A. (1995). Bayes factors. Journal of the American Statitical Association, 90:773–795.
Kenward, M. G. and Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statistical Science, 13:236–247.
Kohler, H., Billardi, F. C., and Ortega, J. (2002). The emergence of lowest-low fertility in Europe during the 1990s. Population and Development review, 28:641–680.
Lafortune, L., Beland, F., Bergman, H., and Ankri, J. (2009). Health status transitions in community-living elderly with complex care needs: a latent class approach. BMC Geriatrics, 9:6.
Lattanzio, F., Mussi, C., Scafato, E., Ruggiero, C., Dell’Aquila, G., Pedone, C., Mammarella, F., Galluzzo, L., Salvioli, G., Senin, U., Carbonin, P. U., Bernabei, R., and Cherubini, A. (2010). Health care for older people in Italy: The U.L.I.S.S.E. project (un link informatico sui servizi sanitari esistenti per l’anziano - a computerized network on health care services for older people). J Nutr Health Aging, 14:238–42.
Lazarsfeld, P. F. (1950). The logical and mathematical foundation of latent structure ana- lysis. In S. A. Stouffer, L. Guttman, E. A. S., editor, Measurement and Prediction, New York. Princeton University Press.
Lazarsfeld, P. F. and Henry, N. W. (1968). Latent Structure Analysis. Houghton Mifflin, Boston.
Lin, H., McCulloch, C. E., and Rosenheck, R. A. (2004). Latent pattern mixture models for informative intermittent missing data in longitudinal studies. Biometrics, 60:295–305.
Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data. Wiley Series in Probability and Statistics. Wiley, 2nd edition.
Lu, G. and Copas, J. B. (2004). Missing at random, likelihood ignorability and model completeness. The Annals of Statistics, 32:754–765.
Magidson, J. and Vermunt, J. K. (2001). Latent class factor and cluster models, bi-plots and related graphical displays. Sociological Methodology, 31:223–264.
Manton, K. G. and Woodbury, M. A. (1991). Grade of membership generalizations and aging research. Experimental Aging Research, 17:217–226.
McNamee, P. (2004). A comparison of the grade of membership measure with alternative health indicators in explaining costs for older people. Health Economics, 13:379–395.
Mor, V., Berg, K., Angelelli, J., Gifford, D., Morris, J., and Moore, T. (2003). The quality of quality measurement in U.S. nursing homes. Gerontologist, 43:37–46.
Moran, M., Walsh, C., Lynch, A., Coen, R. F., Coakley, D., and Lawlor, B. A. (2004). Syndromes of behavioural and psychological symptoms in mild Alzheimer’s disease. International Journal of Geriatric Psychiatry, 19:359–364.
Morris, J., Hawes, C., Murphy, K., and et al. (1991). Resident Assessment Instrument Training Manual and Resource Guide. Eliot Press, Natick, MA.
Muthén, B., Kaplan, D., and Hollis, M. (1987). On structural equation modeling with data that are not missing completely at random. Psychometrika, 52:431–462.
Nylund, K., Asparouhov, T., and Muth ́en, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14:535–569.
O’Muircheartaigh, C. and Moustaki, I. (1999). Symmetric pattern models: a latent variable approach to item non-response in attitude scales. Journal of the Royal Statistical Society, Series A, 162:177–194.
Phillips, C. D., Hawes, C., Lieberman, T., and Koren, M. J. (2007). Where should momma go? current nursing home performance measurement strategies and a less ambitious approach. BMC Health Serv Res, 7:93.
Portrait, F., Lindeboom, M., and Deeg, D. (1999). Health and mortality of the elderly: the grade of membership method, classification and determination. Health Economics, 8:441–457.
Prado-Jean, A., Couratier, P., Benissan-Tevi, L. A., Nubukpo, P., Druet-Cabanac, M., and Clement, J. P. (2011). Development and validation of an instrument to detect depression in nursing homes. Nursing homes short depression inventory (NH-SDI). International Journal of Geriatric Psychiatry, 26:853–859.
Reboussin, B. A., Miller, M. E., Lohman, K. K., and Have, T. R. T. (2002). Latent class models for longitudinal studies of the elderly with data missing at random. Journal of the Royal Statistical Society, Series C, 51:69–90.
Roy, J. (2003). Modeling longitudinal data with nonignorable dropouts using a latent dropout class model. Biometrics, 59:829–836.
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63:581–592.
Schafer, J. L. (1997). Analysis of incomplete multivariate data. Chapman & Hall.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6:461– 464.
Tanner, M. (1996). Tools for statistical inference. Springer-Verlag, New York, 3rd ed. edition.
Vermunt, J. K. and Magidson, J. (2002). Latent class cluster analysis. In Hagenaars, J. A. and McCutcheon, A. L., editors, Applied latent class analysis. Cambridge University Press, Cambridge, UK.
Woodbury, M. A., Clive, J., and Jr., A. G. (1978). Mathematical typology: A grade of mem- bership technique for obtaining disease definition. Computers and Biomedical Research, 11:277–298.
Zimmerman, D. R. (2003). Improving nursing home quality of care through outcomes data: the MDS quality indicators. International Journal of Geriatric Psychiatry, 18:250–257.