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.
| Published in | American Journal of Mathematical and Computer Modelling (Volume 6, Issue 4) |
| DOI | 10.11648/j.ajmcm.20210604.12 |
| Page(s) | 63-75 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
Path Analysis, Structural Equation Modeling, Comparative Fit Index, Root Mean Squared Error Approximately, Normal Fit Index, Measured Variables, Latent Variables, AMOS Program
| [1] | Anderson, E. (1935). The irises of the Gaspe Peninsula, Bulletin of the American Iris Society, 59, pp. 2–5. |
| [2] | Chou, C. P. & Bentler, P. M. (1995). Estimates and tests in structural equation modeling. In Structural equation modeling: Concepts, issues, and applications, R. H. Hoyle (editor). Thousand Oaks, CA: Sage Publications, Inc. |
| [3] | Curran, P. J., Stice, E., and Chassin, L. (1997). The relation between adolescent alcohol use and peer alcohol use: A longitudinal random coefficients model. Journal of Consulting and Clinical Psychology, 68 (1), pp. 130-140. |
| [4] | Davis, C. S. (1991). Semi-parametric and non-parametric methods for the analysis of repeated measurements with applications to clinical trials. Statistics in Medicine, 10, pp. 1959–1980. |
| [5] | Duncan, T. E., Duncan, S. C., Alpert, A., Hops, H., Stoolmiller, M., and Muthen, B. (1997). Latent variable modeling of longitudinal and multilevel substance use data. Multivariate Behavioral Research, 32 (3), pp. 275-318. |
| [6] | Duncan, T. E., Duncan, S. C., Strycker, L. A., Li, F., & Alpert, A. (1999). An introduction to latent variable modeling: Concepts, issues, and applications. Mahwah, NJ: Lawrence Erlbaum Associates, Publishers. |
| [7] | Duncan, T. E., and McAuley, E. (1993). Social support and efficacy cognitions in exercise adherence: A latent growth curve analysis. Journal of Behavioral Medicine, 16 (2), pp. 199-218. |
| [8] | Duncan, T. E., Oman, R., and Duncan, S. C. (1994). Modeling incomplete data in exercise behavior research using structural equation methodology. Journal of Sport and Exercise Psychology, 16, pp. 187-203. |
| [9] | Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, Part II, pp. 179–188. |
| [10] | Hoyle, R. H. (1995). The structural equation modeling approach: Basic concepts and fundamental issues. In Structural equation modeling: Concepts, issues, and applications, R. H. Hoyle (editor). Thousand Oaks, CA: Sage Publications, Inc., pp. 1-15. |
| [11] | Hu, L. and Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6 (1), pp. 1-55. |
| [12] | Kline, R. B. (1998). Principles and Practice of Structural Equation Modeling. New York: The Guilford Press. |
| [13] | MacCallum, R. C. and Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual Review of Psychology, 51, pp. 201-226. |
| [14] | Rigdon, E. E. (1998). Structural equation modeling. In Modern methods for business research, G. A. Marcoulides (editor). |
| [15] | Schumacker, R. E. & Lomax, R. G. (1996). A Beginner’s Guide to Structural Equation Modeling. Mahwah, New Jersey: Lawrence Erlbaum Associates, Publishers. |
APA Style
Ahmed Mohamed Mohamed Elsayed, Nevein Nagy Aneis. (2021). Goodness of Fit Indices for Different Cases. American Journal of Mathematical and Computer Modelling, 6(4), 63-75. https://doi.org/10.11648/j.ajmcm.20210604.12
ACS Style
Ahmed Mohamed Mohamed Elsayed; Nevein Nagy Aneis. Goodness of Fit Indices for Different Cases. Am. J. Math. Comput. Model. 2021, 6(4), 63-75. doi: 10.11648/j.ajmcm.20210604.12
AMA Style
Ahmed Mohamed Mohamed Elsayed, Nevein Nagy Aneis. Goodness of Fit Indices for Different Cases. Am J Math Comput Model. 2021;6(4):63-75. doi: 10.11648/j.ajmcm.20210604.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajmcm.20210604.12,
author = {Ahmed Mohamed Mohamed Elsayed and Nevein Nagy Aneis},
title = {Goodness of Fit Indices for Different Cases},
journal = {American Journal of Mathematical and Computer Modelling},
volume = {6},
number = {4},
pages = {63-75},
doi = {10.11648/j.ajmcm.20210604.12},
url = {https://doi.org/10.11648/j.ajmcm.20210604.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20210604.12},
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.},
year = {2021}
}
TY - JOUR T1 - Goodness of Fit Indices for Different Cases AU - Ahmed Mohamed Mohamed Elsayed AU - Nevein Nagy Aneis Y1 - 2021/11/25 PY - 2021 N1 - https://doi.org/10.11648/j.ajmcm.20210604.12 DO - 10.11648/j.ajmcm.20210604.12 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 63 EP - 75 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20210604.12 AB - 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. VL - 6 IS - 4 ER -
Information
Email: