Handling Uncertainty in Structural Equation Modeling
This paper attempts to propose an overview of a recent method named partial possibilistic regression path modeling (PPRPM), which is a particular structural equation model that combines the principles of path modeling with those of possibilistic regressio
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Abstract This paper attempts to propose an overview of a recent method named partial possibilistic regression path modeling (PPRPM), which is a particular structural equation model that combines the principles of path modeling with those of possibilistic regression to model the net of relations among variables. PPRPM assumes that the randomness can be referred to the measurement error, that is the error in modeling the relations among the observed variables, and the vagueness to the structural error, that is the uncertainty in modeling the relations among the latent variables behind each block. PPRPM gives rise to possibilistic regressions that account for the imprecise nature or vagueness in our understanding phenomena, which is manifested by yielding interval path coefficients of the structural model. However, possibilistic regression is known to be a model sensitive to extreme values. That is way recent developments of PPRPM are focused on robust procedures for the detection of extreme values to omit or lessen their effect on the modeling. A case study on the motivational and emotional aspects of teaching is used to illustrate the procedure. Keywords Interval-valued data · Possibilistic regression · SEM · Extreme values
1 Introduction Path Analysis (PA) represents a widely used tool in exploratory and confirmatory statistical analysis to describe direct dependencies among set of variables [10]. A special class of PA is represented by Structural Equation Models (SEM) [4], which aim to estimate a network of causal relationships among latent variables (LVs) defined by blocks of manifest variables (MVs). The relations among the LVs define the structural model, whereas the relations between each LV and its own block of MVs R. Romano (B) University of Calabria, Cosenza, Italy e-mail: [email protected] F. Palumbo University of Naples Federico II, Naples, Italy e-mail: [email protected] © Springer International Publishing Switzerland 2017 M.B. Ferraro et al. (eds.), Soft Methods for Data Science, Advances in Intelligent Systems and Computing 456, DOI 10.1007/978-3-319-42972-4_53
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define the measurement model. The common features of PA and SEM are that: (i) two or more sets of variables are involved; (ii) at least one of these variables is latent. SEM are generally divided into two categories, according to the estimation procedure [21]: covariance based SEM (CBSEM) and variance based SEM (VBSEM). CBSEM estimates the model parameters through a unique estimation of the Variance-Covariance matrix. Under the usual assumptions, estimation is achieved via Maximum Likelihood (ML) approach. VBSEM estimation is a two-step procedure. Partial Least Squares Path Modeling (PLSPM) is the most largely used approach for VBSEM that partially estimates the outer model parameters and the inner model parameters alternatively [22]. Each block is estimated independently and the procedure stops when the convergence is reached. Albeit the original proposal is based on ordinary least squares estimatio
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