Constructing indicators of unobservable variables from parallel measurements


Abstract


The social and economic research often focuses on the construction of composite indicators for unobservable (or latent) variables using data from a questionnaire with Likert-type scales. Within the variety of procedures, we focus on the data analysis technique of Principal Components Analysis, in its Linear and NonLinear versions. This paper shows that when the variables are parallel measurements of the same latent unobservable variable, Linear and NonLinear Principal Components Analyses practically lead to the same composite indicators.

DOI Code: 10.1285/i20705948v5n3p320

Keywords: Principal Components Analysis; ordinal variables; nonlinearity; latent variables; Probabilistic gauge; Monte Carlo gauge

References


.Brentari, E., Golia, S., Manisera, M. (2007). Models for categorical data: a comparison between the Rasch model and Nonlinear Principal Component Analysis. Statistica & Applicazioni, 5, 53-77.

.Carpita, M., Manisera, M. (2011). On the nonlinearity of homogeneous ordinal variables. In New Perspectives in Statistical Modeling and Data Analysis, eds. S. Ingrassia, R. Rocci, M. Vichi, Heidelberg: Springer, 489-496.

.Ferrari, P.A., Barbiero, A. (2012). Nonlinear principal component analysis, in Modern Analysis of Customer Surveys: with applications using R, eds. R.S. Kennett and S. Salini, Chichester: John Wiley, 333-356.

.Ferrari, P.A., Annoni, P., Salini, S. (2005). A comparison between alternative models for environmental ordinal data: Nonlinear PCA vs Rasch Analysis, in Statistical Solutions to Modern Problems: Proceedings of the 20th international Workshop on Statistical Modelling, eds. A.R. Francis, K.M. Matawie, A. Oshlack and G.K. Smyth, Sydney: University of Western Sydney, 173-177.

.Gifi, A. (1990). Nonlinear multivariate analysis. Chichester: John Wiley.

.Heiser, W.J., Meulman, J.J. (1994). Homogeneity analysis: exploring the distribution of variables and their nonlinear relationships, in Correspondence analysis in the social sciences, eds. M. Greenacre and M. Blasius, New York: Academic Press, 179-209.

.Jolliffe, I.T. (2002). Principal component analysis, 2nd Ed. New York: Springer.

.Linting, M., Meulman, J.J., Groenen, P.J.F., Van der Kooij, A. (2007). Stability of Nonlinear Principal Components Analysis: An empirical study using the balanced bootstrap. Psychological Methods, 12, 359-379.

.van Rijckevorsel, J., Bettonvil, B., de Leeuw, J. (1985). Recovery and stability in nonlinear PCA, Dept. Data Theory, Leiden Univ, RR-85-21.


Full Text: PDF
کاغذ a4

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.