Two Factor Copula Model in Health Measurement

• Autorzy: Martyna Kobus , Olga Półchłopek

Warianty tytułu

Dwuwskaźnikowy model kopuł czynnikowych w ocenie stanu zdrowia

• Języki publikacji: EN

Abstrakty

EN

Researchers emphasize the need to include broad information on health in health analyses (Conti et al. 2010, Heckman et al. 2011). This is mostly because single health indicators are not efficient in describing a person's health, and detailed information on health is increasingly available via e.g. ageing surveys. This, however, calls for a joint analysis of health indicators, taking into account the dependencies between various health variables. It is not self-evident how one should model such a multidimensional distribution, and in our previous paper (Kobus and Półchłopek, 2016) we offer a method for ordinal health data that models them in a flexible and computationally efficient way, the so-called factor copula models (Nikoloulopoulos and Joe 2015). Here we continue research in this area. We use 2-factor models to estimate 24-dimensional health distribution and show that they provide a highly accurate description of health data and perform better than standard analyses based on multivariate normal distribution. We find that a 2-factor model which is a combination of the t(5)+t(4) copulas gives the highest likelihood. Based on this, we identify two major factors which govern the 24 health variable distributions and based on the estimated copula parameters we give them interpretation. Factor one relates to the general mood and attitude in life, whereas factor two describes physical health.(original abstract)

Analiza łącznych rozkładów wskaźników zdrowia jest konieczna do zrozumienia stanu zdrowia starzejących się społeczeństw i efektywnej polityki zdrowotnej (Conti et al., 2010; Heckman et al., 2011). W poprzednim artykule (Kobus and Półchłopek, 2016) zaproponowałyśmy metodę modelowania porządkowych zmiennych zdrowotnych, tj. tak zwane kopuły czynnikowe (Nikoloulopoulos and Joe, 2015). W niniejszym artykule rozwijamy nasze badania w tym zakresie, wykorzystując modele dwuczynnikowe do estymacji 24-wymiarowych rozkładów i pokazując, że pozwalają one na bardzo precyzyjny opis rozkładów zdrowia. Wykazujemy również, że kopuły czynnikowe oparte na kombinacjach rozkładów i spisują się lepiej niż standardowe podejście oparte na wielowymiarowych rozkładach gaussowskich. Dodatkowo identyfikujemy dwa główne czynniki, które wpływają na rozkład 24 zmiennych, jak również interpretujemy je na podstawie uzyskanych parametrów. Pierwszy czynnik związany jest z usposobieniem i podejściem do życia, a drugi ze zdrowiem fizycznym.(abstrakt oryginalny)

Słowa kluczowe

EN

Health; Modeling of health care; Health status of the population

PL

Zdrowie; Modelowanie ochrony zdrowia; Stan zdrowia ludności

• Czasopismo: Studia Ekonomiczne / Polska Akademia Nauk. Instytut Nauk Ekonomicznych
• Rocznik: 2017
• Numer: nr 1 (92)
• Strony: 84--112

Twórcy

autor

Martyna Kobus

• Polish Academy of Sciences

autor

Olga Półchłopek

• Vistula University, Warsaw

Bibliografia

• Aas K., Czado C., Frigessi A., and Bakken H. (2009), Pair-Copula Constructions of Multiple Dependence, "Insurance, Mathematics and Economics", 44: 182-198.
• Abul Naga R.H., Yalcin T. (2008), Inequality measurement for ordered response health data, "Journal of Health Economics", 27(6): 1614-1625.
• Abul Naga R.H., Stapenhurst Ch. (2015), Estimation of inequality indices of the cumulative distribution function, "Economics Letters", 130: 109-112.
• Allison R.A., Foster J.E. (2004), Measuring health inequality using qualitative data, "Journal of Health Economics", 23(3): 505-524.
• Apouey B. (2007), Measuring health polarization with self-assessed health data, "Health Economics", 16: 875-894.
• Apouey B., Silber J. (2013), Inequality and bi-polarization in socioeconomic status and health: ordinal approaches, "SSRN Electronic Journal".
• Atkinson A.B. (1970), On the measurement of inequality, "Journal of Economic Theory", 2(3): 244-263.
• Atkinson A.B. (2011), On lateral thinking, "Journal of Economics Inequality", 9: 319-328.
• Atkinson A.B., Bourguignon F. (1982), The Comparison of Multi Dimensioned Distributions of Economic Status, "Review of Economic Studies", 49(2):183-201.
• Bedford T., Cooke R.M. (2002), Vines - a new graphical model for dependent random variables, "Annals of Statistics", 30: 1031-1068.
• Duclos J.Y., Echevin D. (2012), Health and income: A robust comparison of Canada and the US, "Journal of Health Economics", 30: 293-302.
• Conti G., Heckman J., Urzua S. (2010), The education-health gradient, "American Economic Review", 100(2): 234-238.
• Cowell F., Flachaire E. (2015), Inequality with ordinal data, STICERD 130226 Working Paper.
• Cutler D.M., Huang W., Lleras-Muney A. (2015), When does education matter? The protective effect of education for cohorts graduating in bad times, "Social Science & Medicine", 127: 63-73.
• Cutler D., Lleras-Muney A., Vogl T. (2011), Socioeconomic status and health: dimensions and mechanisms, The Oxford Handbook of Health Economics.
• Genest C., MacKay J. (1986), The joy of copulas: bivariate distributions with uniform marginals, "The American Statistician", 40: 280-283.
• Genest C., Nešlehová J. (2007), A Primer on Copulas for Count Data, "ASTIN Bulletin", 37: 475-515.
• Gibbons R., Hedeker D. (1992), Full-information item bi-factor analysis, "Psychometrika", 57: 423-436.
• Gravel N., Magdalou B., Moyes P. (2015), Ranking distributions of an ordinal attribute,
• Heckman J., Humphries J.E., Urzua S., Veramendi G. (2011), The effects of educational choices on labor market, health, and social outcomes, University of Chicago, unpublished manuscript.
• Holzinger K.J., Swineford F. (1937), The bi-factor method, "Psychometrika", 2: 41-54.
• Hua L., Joe H. (2014), Strength of tail dependence based on conditional tail expectation, "Journal of Multivariate Analysis", 123: 143-159.
• Hult H., Lindskog F. (2002), Multivariate extremes, aggregation and dependence in elliptical distributions, "Advances in Applied Probability", 34: 587-608.
• Joe H. (2005), Asymptotic efficiency of the two-stage estimation method for copula-based models, "Journal of Multivariate Analysis", 94: 401-419.
• Joe H. (2015), Dependence modelling with copulas, Taylor & Francis Group.
• Kaiser H.F. (1958), The varimax criterion for analytic rotation in factor analysis, "Psychometrika", 23: 187-200.
• Krupskii P., Joe H. (2013), Factor copula models for multivariate data, "Journal of Multivariate Analysis", 120: 85-101.
• Krupskii P., Joe H. (2015), Structured factor copula models: Theory, inference and computation, "Journal of Multivariate Analysis", 138: 53-73.
• Kunst A.E., Bos V., Lahelma E., Bartley M., Lissau I., Regidor E., et al. (2004), Trends in socioeconomic inequalities in sefl-assessed health in 10 European countries, "International Journal of Epidemiology", 34: 295-305.
• Lazar A., Silber J. (2013), On the cardinal measurement of health inequality when only ordinal information is available on individual health status, "Health Economics", 22(1): 106-113.
• Mackenbach J.P., Stirbu I., Roskam A.J.R., Schaap M.M., Menvielle G., Leinsalu M., Kunst A.E. (2008), Socioeconomic inequalities in health in 22 European countries, "New England Journal of Medicine", 358: 2468-2481.
• Lv G., Wang Y., Xu Y. (2015), On a new class of measures for health inequality based on ordinal data, "Journal of Economic Inequality", 13: 465-477.
• Makdisi P., Yazbeck M. (2014), Measuring socioeconomic health inequalities in the presence of multiple categorical information, "Journal of Health Economics", 34: 84-95.
• Marmot M., Oldfield Z., Clemens S., Blake M., Phelps A., Nazroo J., Steptoe A., Rogers N., Banks J. (2016), English Longitudinal Study of Ageing, Waves 0-7, 1998- 2015 [data collection], 24th Edition, UK Data Service, SN: 5050, http://dx.doi. org/10.5255/UKDA-SN-5050-11
• Nelsen R.B. (2006), An Introduction to Copulas, 2nd ed., Springer.
• Nikoloulopoulos A.K., Joe H. (2015), Factor copula models for item response data, "Psychometrika".
• Nikoloulopoulos A.K., Karlis D. (2010), Regression in a copula model for bivariate count data, "Journal of Applied Statistics", 37(9): 1555-1568.
• Panagiotelis A., Czado C., Joe H. (2012), Pair Copula Constructions for Multivariate Discrete Data, "Journal of the American Statistical Association", 107-499.
• Oh D.H., Patton A.J. (2015), Modelling Dependence in High Dimensions with Factor Copulas, Finance and Economics Discussion Series 2015-051, Board of Governors of the Federal Reserve System.
• Sklar A. (1959), Fonctions de répartition à n dimensions et leursmarges, Publications de l'Institut de Statistique de l'Université de Paris, 8: 229-231.
• Schweizer B., Wolff E.F. (1981), On nonparametric measures of dependence for random variables, "Annals of Statistics", 9: 870885.
• van Doorslaer E., Koolman X. (2004), Explaining the differences in income-related health inequalities across European countries, "Health Economics", 13: 609-628.
• van Doorslaer E., Wagstaff A., Bleichrodt H., Calonge S., Gerdtham U.G., Gerfin M., Geurts J., Gross L., Hakkinen U., Leu R.E., O'Donnell O., Propper C., Puffer F., Rodriguez M., Sundberg G., Winkelhake O. (1997), Income-related inequalities in health: some international comparisons, "Journal of Health Economics", 16: 93-112.