Abstract
This paper introduces structural equation modeling for imprecise data, which enables evaluations with different types of uncertainty. Coming under the framework of variance-based analysis, the proposed method called Partial Possibilistic Regression Path Modeling (PPRPM) combines the principles of PLS path modeling to model the network of relations among the latent concepts, and the principles of possibilistic regression to model the vagueness of the human perception. Possibilistic regression defines the relation between variables through possibilistic linear functions and considers the error due to the vagueness of human perception as reflected in the model via interval-valued parameters. PPRPM transforms the modeling process into minimizing components of uncertainty, namely randomness and vagueness. A case study on the motivational and emotional aspects of teaching is used to illustrate the method.
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References
Billard, L., Diday, E.: Regression analysis for interval-valued data. In: Kiers, H.A.L., Rasson, J.P., Groenen, P.J.F., Schader, M. (eds.) Data Analysis, Classification and Related Methods, Proceedings of 7th Conference IFCS, Namur, pp. 369–374 (2000)
Blanco-Fernndez, A., Corral, N., González-RodrÃguez, G.: Estimation of a flexible simple linear model for interval data based on set arithmetic. Comput. Stat. Data Anal. 55, 2568–2578 (2011)
Bollen, K.A.: Structural Equations with Latent Variables. Wiley, New York (1989)
Chin, W.W.: The partial least squares approach for structural equation modeling. In: Macoulides, G.A. (ed.) Modern Methods for Business Research, pp. 295–336. Lawrence Erlbaum Associates, Mahwah (1998)
Coppi, R.: Management of uncertainty in statistical reasoning: the case of regression analysis. Int. J. Approx. Reason. 47, 284–305 (2008)
Coppi, R., D’Urso, P., Giordani, P., Santoro, A.: Least squares estimation of a linear regression model with LR fuzzy. Comput. Stat. Data Anal. 51, 267–286 (2006)
Davino, C., Furno, M., Vistocco, D.: Quantile Regression: Theory and Applications. Wiley, Chichester (2013)
Diamond, P.: Fuzzy least squares. Inf. Sci. 46, 141–157 (1988)
Diamond, P.: Least squares fitting of compact set-valued data. J. Math. Anal. Appl. 147, 531–544 (1990)
Jöreskog, K.G.: A general method for analysis of covariance structures. Biometrika 57, 239–251 (1970)
Judd, C.M., McClelland, G.H.: Data Analysis: A Model Comparison Approach. Routledge, New York (2009)
Kim, K.J., Moskowitz, H., Koksalan, D.: Fuzzy versus statistical linear regression. Eur. J. Oper. Res. 92, 417–434 (1996)
Koenker, R., Basset, G.W.: Regression quantiles. Econometrica 46, 33–50 (1978)
Lima Neto, E.A., de Carvalho, F.A.T.: Constrained linear regression models for symbolic interval-valued variables. Comput. Stat. Data Anal. 54, 333–347 (2010)
Marino, M., Palumbo, F.: Interval arithmetic for the evaluation of imprecise data effects in least squares linear regression. Ital. J. Appl. Stat. 14, 277–291 (2002)
Moè, A., Pazzaglia, F., Friso, G.: MESI, Motivazioni, Emozioni, Strategie e Insegnamento. Questionari metacognitivi per insegnanti. Erickson, Trento (2010)
Palumbo, F., Romano, R.: Possibilistic PLS path modeling: a new approach to the multigroup comparison. In: Brito, P. (ed.) Compstat 2008, pp. 303–314. Physica-Verlag, Heidelberg (2008)
Palumbo, F., Romano, R., Esposito Vinzi, V.: Fuzzy PLS path modeling: a new tool for handling sensory data. In: Preisach, C., Burkhardt, H., Schmidt-Thieme, L., Decker, R. (eds.) Data Analysis, Machine Learning and Applications, pp. 689–696. Springer, Berlin/Heidelberg (2008)
Palumbo, F., Strollo, M.R., Melchiorre, F.: Stress and burnout in the school teachers: a study on the motivations to teach in the Neapolitan district. (in Italian). In: Strollo, M.R. (ed.) La motivazione nel contesto scolastico. pp. 3–47. Franco Angeli, Milan (2014)
Romano, R., Palumbo, F.: Partial possibilistic regression path modeling for subjective measurement. QdS – J Methodol. Appl. Stat. 15, 177–190 (2013)
Tanaka, H.: Fuzzy data analysis by possibilistic linear models. Fuzzy Sets Syst. 24, 363–375 (1987)
Tanaka, H., Guo, P.: Possibilistic Data Analysis for Operations Research. Physica-Verlag, Wurzburg (1999)
Tanaka, H., Uejima, S., Asai, K.: Linear regression analysis with fuzzy model. IEEE Trans. Syst. Man Cyber. 12, 903–907 (1982)
Tenenhaus, M., Esposito Vinzi, V., Chatelin, Y.-M., Lauro, C.: PLS path modeling. Comput. Stat. Data Anal. 48, 159–205 (2005)
Wang, H.F., Tsaur, R.C.: Insight of a fuzzy regression model. Fuzzy Sets Syst. 112, 355–369 (2000)
Wold, H.: Modelling in complex situations with soft information. In: Third World Congress of Econometric Society, Toronto (1975)
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 1, 28–44 (1973)
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Romano, R., Palumbo, F. (2016). Partial Possibilistic Regression Path Modeling. In: Abdi, H., Esposito Vinzi, V., Russolillo, G., Saporta, G., Trinchera, L. (eds) The Multiple Facets of Partial Least Squares and Related Methods. PLS 2014. Springer Proceedings in Mathematics & Statistics, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-40643-5_12
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