Goodness of Fit Indices for Different Cases

Abstract

Path analysis is used to estimate a system of equations of the observed variables. These models assume perfect measurement of the observed variables. The relationships between observed variables are modeled. These models are used when one or more variables is mediating the relationship between two others. Structural equation modeling is a methodology for representing, estimating, and testing the relationships between measured and latent variables. This paper provides a combination between the path Analysis and the structural equation modeling to analyze three practical data: Hunua, Respiratory and Iris data, using AMOS program. In each case, the numerical results are constructed and compared according to nature of analysis and methods. Regression weights between all variables are estimated using the maximum likelihood estimation, and its tests are constructed for each data. From the regression weights, and the network of relationships, we constructed the structural equation modeling for all data. The estimated errors are indicated for the endogenous variables. Many indices, which indicate the goodness of fit of all models, are presented and compared. The best indices of goodness of fit of the models are Chi-Square, Root Mean Squared Error Approximately, and Normal Fit Index. These indices are consistent together.