Partial possibilistic regression path modeling: handling uncertainty in path modeling
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Partial possibilistic regression path modeling: handling uncertainty in path modeling Rosaria Romano1
· Francesco Palumbo2
Received: 10 July 2019 / Accepted: 14 August 2020 © The Author(s) 2020
Abstract The paper presents a new insight of a recently proposed method named partial possibilistic regression path modeling. This method combines the principles of path modeling with those of possibilistic regression to model the net of relations among blocks of variables, where a weighted composite summarizes each block. It assumes that randomness can refer back as the measurement error, which is the error in modeling the relations between the observed variables and the corresponding composite, and the vagueness to the structural error, which is the uncertainty in modeling the relations among the composites behind each block of variables. The comparison of the proposed method with a classical composite-based path model is based on a simulation study. A case study on the use of Wikipedia in higher education illustrates a fruitful usability context of the proposed method. Keywords Interval data · Randomness–vagueness · Structural equation modeling · Least absolute values
1 Introduction Socio-economic and natural systems can be defined as having complex relationships between sets (or blocks) of variables. Regression analysis is likely the statistical method most widely used to study the dependencies between two sets of variables. However, when the phenomenon increases in complexity, a single equation model becomes inadequate for analyzing and describing the data dependence structures. Complex as the mathematical model may be, it is approximate and can account for a
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Rosaria Romano [email protected] Francesco Palumbo [email protected]
1
Department of Economics and Statistics, University of Naples Federico II, Naples, Italy
2
Department of Political Sciences, University of Naples Federico II, Naples, Italy
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R. Romano, F. Palumbo
simplified abstraction of the reality. Therefore, classical statistical models are developed under the following paradigm (Judd et al. 2011): D AT A = M O D E L + E R R O R. Regression analysis can model only direct relationships between independent and dependent variable(s). It strongly limits the variables in that they cannot have any indirect effects on each other. The path analysis approach (Tukey 1964; Alwin and Hauser 1975) offers a way to overcome such a limitation by allowing to model a set of relationships between observed variables. In other words, path analysis is constructed through a system of simultaneous simple or multiple regressions. Several approaches exist to path models; the most known is structural equation modeling (SEM) (Bollen 1989; Kaplan 2008). SEM combines the ideas behind path analysis with the basic principles of confirmatory factor analysis (Thurstone 1931), which presumes that fewer factors than the number of observed variables are responsible for the shared variancecovariance matrix. Through this analysis, SEM carries the idea that different subsets or b
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