### The Modification of Dichotomous and Polytomous Item Response Theory to Structural Equation Modeling Analysis

#### Abstract

The objective of the present research was to make modifications to Structural Equation modeling analysis by Dichotomous and Polytomous Item Response Theory (SEDPIRT) which consisted of 4 stages of 1) The development of structural equation modeling analysis, 2) Data simulation for analysis, 3) Verification and comparison of analysis results through the SEDPIRT with Path Analysis by LISREL (PAL) using data simulation and 4) trying-out SEDPIRT analysis with empirical data. The study resulted in a structural equation modeling analysis SEDPIRT in which a person’s true ability and attributes obtained from Item Response Theory (IRT) analysis is used for observable variables. It is assumed that such observable variables are latent with no measurement deviation for use as the data for assessing path coefficients and structural equation modeling analysis. The SEDPIRT measurement is valid and would not deviate because of changes in the tests or test takers. A verification of an analysis of simulation data showed that standard error in the estimation of every paths coefficient (Pij) and the iteration of Pij by SEDPIRT analysis is significantly less than the PAL at the .01 level of significance and the root mean squared residuals of SEDPIRT and PAL are not significantly different, although the SEDPIRT analysis yields a model with greater validity than the PAL at the .01 level of significance. The SEDPIRT analysis model shows a model validation of 97.50 % while the PAL one shows 77.50%, and all path coefficients of the SEDPIRT and PAL are positively correlated at the .01 level of significance. It was found from applying the two techniques to empirical data that standard error in the estimation of all the path coefficients, the root mean square residual of the deviation, the number of iteration and the adjustment count in an attempt to make the two models consistent with empirical data in the SEDPIRT are less than the PAL; the Goodness-of Fit Index (GFI) and the Adjusted Goodness-of Fit Index(AGFI) in the SEDPIRT are more than the PAL; and path coefficients of the SEDPIRT and PAL show a positive correlation at the .01 level of significance with a Pearson-product moment correlation coefficient of .869.

**Key words:** Structural equation modeling analysis by Dichotomous and Polytomous Item Response Theory (SEDPIRT); Path analysis by LISREL (PAL); Grade- Response Model (GRM); Three parameter logistic model

#### Keywords

#### References

Baker, F. B. (1992). *Item Characteristic Curve: Dichotomous Response in Item Response Theory : Parameter Estimation Technique.* New York: Marcel Dekker.

Bollen, K. A. (1989). *Structural Equations with Latent Variable.* New York: John Wiley & Sons.

Boonruangrat, S. (1997). *Multivariate Analysis *(2nd ed.). Bangkok: Tonoor Grammy.

Dodd, B. G., Ayala, R. J., & Koch, W. R. (1995). Computerized Adaptive Testing With Polytomous Item. *Psychological Measurement*, *19*(1), 5-22.

Embretson, S. E., & Reise, S. P. (2000). *Item Response Theory for Psychologists. *New Jersey: Lawrence Erlbaum Associates, Inc.

Fischer, G. H., & Molenaar, I. W. (Eds.) (1995). *Rasch Model: Foundation, Recent developments, and Applications.*** **New York: Springer - Verlag.

Kampoogeo, T. (2010). *The Multi Level Structural Equation Model of the Factors Affecting Mathematics Learning Achievement of Grade 6 Students, Office of Udonthani Education Service Area. *(Unpublished master thesis). Mahasarakham University, Thailand.

Kanjanawasri, S. (2007). *Modern Test Theories* (3rd ed.). Bangkok: The Printing Press of Chulalongkorn University.

Linderman, R. H., Merenda, P. F., & Gold, R. Z. (1980). *Introduction to Bivariate and Multivariate Analysis.*** **Glenview, Illinois: Scott, Foresman and Company.

Prajanban, P. (2006). *Modification of Dichotomous Item Response Theory in Path Analysis for Latent Variables Model.* (Unpublished doctoral dissertation). Naresuan University, Thailand.

Randall, E. S., & Richard, G. L. (1996). *A Beginner’s Guide to Structural Equation Modeling. *New Jersey: Lawrence Erlbaum Associates, Inc.

Shanghai, T. (1991). *A Comparative Study of Efficiency in the Estimation of the Examination of the Taylor Pyramid with the Format and Scoring*,* Different Monte Carlo Methods. *(Unpublished doctoral dissertation).* Srinakharinwirot University*

*, Thailand.*

*Linear Structural Relations (LISREL) Statistical Analysis for This Study Social and Behavioral Sciences*(3rd ed.). Bangkok: The Printing Press of Chulalongkorn University.

DOI: http://dx.doi.org/10.3968/j.css.1923669720120805.1148

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