On Exact Statistical Properties of Multidimensional Indices Based on Principal Components, Factor Analysis, MIMIC and Structural Equation Models

Recent empirical literature has seen many multidimensional indices emerge as well-being or poverty measures, in particular indices derived from principal components and various latent variable models. Though such indices are being increasingly and widely employed, few studies motivate their use or report the standard errors or confidence intervals associated with these estimators. This paper reviews the different underlying models, reaffirms their appropriateness in this context, examines the statistical properties of resulting indices, gives analytical expressions of their variances and establishes certain exact relationships among them.

[1]  A. Goldberger,et al.  Structural Equation Models in the Social Sciences. , 1974 .

[2]  Clifford C. Clogg,et al.  Handbook of statistical modeling for the social and behavioral sciences , 1995 .

[3]  E. Schokkaert,et al.  Sen’s Concept of the Living Standard applied to the Belgian Unemployed , 1990, Recherches économiques de Louvain.

[4]  A. Goldberger,et al.  Structural Equation Models in the Social Sciences. , 1974 .

[5]  Stan Lipovetsky,et al.  Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models , 2005, Technometrics.

[6]  Esfandiar Maasoumi,et al.  Multivariate Measures of Well-Being and an Analysis of Inequality in the Michigan Data , 1988 .

[7]  Ingrid Robeyns,et al.  Sen's Capability Approach to Welfare Economics , 2004 .

[8]  M. Browne.  Asymptotically distribution-free methods for the analysis of covariance structures. , 1984, The British journal of mathematical and statistical psychology.

[9]  Christine Eiser,et al.  Measuring quality of life , 1997, Archives of disease in childhood.

[10]  M. Kirchman.  Measuring the Quality of Life , 1986 .

[11]  D. Slottje.  MEASURING THE QUALITY OF LIFE OF ACROSS COUNTRIES , 1991 .

[12]  Jaya Krishnakumar,et al.  Going Beyond Functionings to Capabilities: An Econometric Model to Explain and Estimate Capabilities , 2007 .

[13]  K. Jöreskog,et al.  Structural Equation Modeling with Ordinal Variables using LISREL , 2004 .

[14]  Wiebke Kuklys.  Amartya Sen's Capability Approach: Theoretical Insights and Empirical Applications , 2005 .

[15]  R. Sugden.  Commodities and Capabilities , 1986 .

[16]  Mark McGillivray,et al.  Measuring Non-Economic Well-Being Achievement , 2005 .

[17]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .

[18]  K. Jöreskog.  A General Method for Estimating a Linear Structural Equation System. , 1970 .

[19]  Maria Laura Di Tommaso,et al.  Measuring the well being of children using a capability approach An application to Indian data , 2006 .

[20]  S. Klasen,et al.  Measuring Poverty And Deprivation In South Africa , 2000 .

[21]  Alessandro Balestrino,et al.  Should we use functionings instead of income to measure well-being? Theory, and some evidence from Italy , 2001 .

[22]  Sara Lelli,et al.  Factor Analysis vs. Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen's Functioning Approach , 2001 .

[23]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[24]  Rati Ram,et al.  Composite indices of physical quality of life, basic needs fulfilment, and income: A ‘principal component’ representation , 1982 .

[25]  B. Muthén.  BEYOND SEM: GENERAL LATENT VARIABLE MODELING , 2002 .

[26]  Tauhidur Rahman,et al.  Measuring the Quality of Life across Countries , 2005 .

[27]  C. Gouriéroux,et al.  PSEUDO MAXIMUM LIKELIHOOD METHODS: THEORY , 1984 .

[28]  F. Caliendo,et al.  A Multivariate Analysis of the Human Development Index , 2002 .

[29]  Stan Lipovetsky,et al.  Latent Variable Models and Factor Analysis , 2001, Technometrics.

[30]  A. Goldberger,et al.  Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable , 1975 .

[31]  R. Mittelhammer,et al.  Measuring the quality of life across countries: A sensitivity analysis of well-being indices , 2005 .

[32]  L. Corrado.  Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models , 2005 .

[33]  Paola Ballon,et al.  Estimating Basic Capabilities: A Structural Equation Model Applied to Bolivia , 2008 .

[34]  M. Turshen.  Development as Freedom , 2001 .

[35]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[36]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[37]  Udaya Wagle,et al.  Please Scroll down for Article Journal of Human Development Multidimensional Poverty Measurement with Economic Well-being, Capability, and Social Inclusion: a Case from Kathmandu, Nepal Multidimensional Poverty Measurement with Economic Well-being, Capability, and Social Inclusion: a Case from Kathm , 2022 .

[38]  A. L. Nagar,et al.  Weighting Socioeconomic Indicators of Human Development: A Latent Variable Approach , 2002 .

[39]  G. Arminger,et al.  Specification and Estimation of Mean- and Covariance-Structure Models , 1995 .

[40]  M. D. Morris,et al.  Measuring the Condition of the World's Poor: The Physical Quality of Life Index , 1979 .