Scoring ordinal variables for constructing composite indicators
AbstractIn order to provide composite indicators of latent variables, for example of customer satisfaction, it is opportune to identify the structure of the latent variable, in terms of the assignment of items to the subscales defining the latent variable. Adopting the reflective model, the impact of four different methods of scoring ordinal variables on the identification of the true structure of latent variables is investigated. A simulation study composed of 5 steps is conducted: (1) simulation of population data with continuous variables measuring a two-dimensional latent variable with known structure; (2) draw of a number of random samples; (3) discretization of the continuous variables according to different distributional forms; (4) quantification of the ordinal variables obtained in step (3) according to different methods; (5) construction of composite indicators and verification of the correct assignment of variables to subscales by the multiple group method and the factor analysis. Results show that the considered scoring methods have similar performances in assigning items to subscales, and that, when the latent variable is multinormal, the distributional form of the observed ordinal variables is not determinant in suggesting the best scoring method to use.
I.H. BERNSTEIN, (1988), Applied multivariate analysis, Springer, New York.
K.A. BOLLEN, (2002), Latent variables in psychology and the social sciences, “Annual Review of Psychology”, 53, pp. 605-634.
K.A. BOLLEN, R. LENNOX, (1991), Conventional wisdom on measurement: a structural equation perspective, “Psychological Bulletin”, 110, pp. 305-314.
E. BRENTARI, S. GOLIA, M. MANISERA, (2007), Models for categorical data: a comparison between the Rasch model and Nonlinear Principal Component Analysis, “Statistica & Applicazioni”, V, 1, pp. 53-77.
M. CARPITA, M. MANISERA, (2006), Un’analisi delle relazioni tra equità, motivazione e soddisfazione per il lavoro. In M. Carpita, L. D’Ambra, M. Vichi, G. Vittadini (Eds.), Valutare la qualità. I servizi di pubblica utilità alla persona. Guerini editore, Milano, pp. 311-360.
J.R. EDWARDS, R.P. BAGOZZI, (2000), On the nature and direction of relationships between constructs and measures, “Psychological Methods”, 5, pp. 155-174.
A. GIFI, (1990), Nonlinear multivariate analysis, Wiley, Chichester.
K.J. HOLZINGER, (1944), A simple method of factor analysis, “Psychometrika”, 9, pp. 257-262.
K.G. JÖRESKOG, (1969), A general approach to confirmatory maximum likelihood factor analysis, “Psychometrika”, 34, pp. 183-202.
S.P. LIN, R.C. BENDEL, (1985), Algorithm AS213: Generation of population correlation on matrices with specified eigenvalues, “Applied Statistics”, 34, pp. 193-198.
G. MARBACH, (1974), Sulla presunta equidistanza degli intervalli nelle scale di valutazione, “Metron”, XXXII, n. 1-4.
J.J. MEULMAN, (1982), Homogeneity analysis of incomplete data, DSWO Press, Leiden.
G. PORTOSO, (2003), L’esponenziale e la normale nella quantificazione determinata indiretta; un indicatore d’uso, “Rivista Italiana di Economia Demografia e Statistica”, LVII, pp. 135-139.
I. STUIVE, H.A.L. KIERS, M.E. TIMMERMAN, J.M.F. TEN BERGE, (2007), A comparison of methods for empirical verification of assignment of items to subtests, University of Groningen, Submitted for publication.
G.H. THOMSON, (1951), The factorial analysis of human ability, London University Press, London.
W.S. TORGERSON, (1958), Theory and methods of scaling, Wiley, New York.
J. VAN RIJCKEVORSEL, B. BETTONVIL, J. DE LEEUW, (1985), Recovery and stability in nonlinear PCA, Dept. of Data Theory, Univ. of Leiden, RR-85-21.
H. WAINER, (1976), Estimating coefficients in linear models: it don’t make no nevermind, “Psychological Bulletin”, 83, pp. 213-217.
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