Methods for linking item response theory (IRT) parameters are developed for attitude questionnaire responses calibrated with the generalized graded unfolding model (GGUM). One class of IRT linking methods derives the linking coefficients by comparing characteristic curves, and three of these methods—test characteristic curve (TCC), item characteristic curve (ICC), and operating characteristic curve (OCC)—are extended for use with the GGUM. Alternate versions of these methods are developed to produce both symmetric and asymmetric solutions. The adequacy of these methods for use with the GGUM is evaluated in a simulation that varied the distributions of θ in the groups to be linked and the number of individuals and anchor items used for linking. All methods performed well under the conditions studied. Statistically significant effects were found for sample size and number of anchor items. It is recommended that choice of linking method should consider the context and intent of the linking.
Andrich, D. (1996). A hyperbolic cosine latent trait model for unfolding polytomous responses: Reconciling Thurstone and Likert methodologies. British Journal of Mathematical and Statistical Psychology, 49, 347-365.
2.
Baker, F.B. (1993). Equating tests under the nominal response model . Applied Psychological Measurement, 17, 239-251.
3.
Baker, F.B., & Al-Karni, A. (1991). A comparison of two procedures for computing IRT equating coefficients. Journal of Educational Measurement , 28, 147-162.
4.
Cohen, A.S., & Kim, S. (1993, April). A comparison of equating methods under the graded response model. Paper presented at the annual meeting of the National Council on Measurement in Education, Atlanta, GA.
5.
Cohen, A.S., & Kim, S. (1998). An investigation of linking methods under the graded response model. Applied Psychological Measurement, 22, 116-130.
6.
Davison, M., Robbins, A., & Swanson, D. (1978). Stage structure in objective moral judgments. Developmental Psychology, 14, 137-146.
7.
Dorans, N.J., & Schmitt, A.P. (1989, March). The methods for dimensionality assessment and DIF detection. Paper presented at the annual meeting of the National Council on Measurement in Education, San Francisco, CA.
8.
Green, B.F., Crone, C.R., & Folk, V.G. (1989). A method for studying differential distractor functioning. Journal of Educational Measurement, 26, 147-160.
9.
Haebara, T. (1980). Equating logistic ability scales by a weighted least squares method. Japanese Psychological Research, 22, 144-149.
10.
Harris, D.J. (1993, April). Practical issues in equating. Paper presented at the annual meeting of the American Educational Research Association, Atlanta, GA.
11.
Huynh, H., & Feldt. L.S. (1976). Estimation of the Box correction for degrees of freedom from sample data in the randomized block and split plot designs. Journal of Educational Statistics, 1, 69-82.
12.
Kim, S., & Cohen, A.S. (1995). A minimum chisquared method for equating tests under the graded response model. Applied Psychological Measurement , 19, 167-176.
13.
Kim, S., & Cohen, A.S. (1997, March). A comparison of linking and concurrent calibration under the graded response model. Paper presented at the annual meeting of the American Educational Research Association , Chicago, IL.
14.
Koenig, J. (2003). Comparison of characteristic curve methods for linking parameters estimated with the generalized graded unfolding model. Dissertation Abstracts International, 64(11), 4023A. (UMI No. 3112572)
15.
Kolen, M.J. (2003, April). Equating. Paper presented at the American Educational Research Association, Chicago, IL.
16.
Li, Y.H., Griffith, W.D., & Tam, H.P. (1997, July). Equating multiple tests via an IRT linking design: Utilizing a single set of anchor items with fixed common item parameters during the calibration process. Paper presented at the Psychometric Society Meeting, Knoxville, TN.
17.
Loyd, G.H., & Hoover, H.D. (1980). Vertical equating using the Rasch model. Journal of Educational Measurement, 17, 179-193.
18.
Noël, Y. (1999). Recovering unimodal latent patterns of change by unfolding analysis: Application to smoking cessation. Psychological Methods, 4, 173-191.
19.
Potenza, M.T., & Dorans, N.J. (1995). DIF assessment for polytomously scored items: A framework for classification and evaluation. Applied Psychological Measurement, 19, 23-37.
20.
Roberts, J.S. (2001a, April). Equating parameter estimates from the generalized graded unfolding model. Paper presented at the annual meeting of the American Educational Research Association, Seattle, WA.
21.
Roberts, J.S. (2001b). GGUM2000: Software to estimate parameters in the generalized graded unfolding model. Applied Psychological Measurement, 25, 38.
22.
Roberts, J.S., Bao, H., Huang, C.W., & Gagne, P. (2003, April). Exploring alternative characteristic curve approaches to linking parameter estimates from the generalized partial credit model. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
23.
Roberts, J.S., Donoghue, J.R., & Laughlin, J.E. (2000). A general item response theory model for unfolding unidimensional polytomous responses. Applied Psychological Measurement, 24, 3-32.
24.
Roberts, J.S., Donoghue, J.R., & Laughlin, J.E. (2002). Characteristics of MML/EAP parameter estimates in the generalized graded unfolding model. Applied Psychological Measurement, 26, 192-207.
25.
Roberts, J.S., & Laughlin, J.E. (1996). A unidimensional item response model for unfolding responses from a graded disagree-agree response scale . Applied Psychological Measurement, 20, 231-255.
26.
Sherif, C.W., Sherif, M., & Nebergall, R.E. (1965). Attitude and attitude change: The social judgment-involvement approach. Philadelphia : W. B. Saunders.
27.
Skaggs, G., & Lissitz, R.W. (1986). IRT test equating: Relevant issues and a review of recent research. Review of Educational Research, 56, 495-529.
28.
Skaggs, G., & Lissitz, R.W. (1988). Effect of examinee ability on test equating invariance . Applied Psychological Measurement, 12, 69-82.
29.
Stocking, M.L., & Lord, F.M. (1983). Developing a common metric in item response theory . Applied Psychological Measurement, 7, 201-210.
30.
Thissen, D., Steinberg, L., & Wainer, H. (1993). Detection of differential item functioning using the parameters of item response models. In P. W. Holland & H. Wainer (Eds.), Differential Item Functioning (pp. 67-113). Hillsdale, NJ: Lawrence Erlbaum.
31.
Way, W.D., & Tang, K.L. (1991, April). A comparison of four logistic model equating methods. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
32.
Wingersky, M.S., Cook, L.L., & Eignor, D.R. (1986, April). Specifying the characteristics of linking items used for item response theory item calibration. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.
33.
Yang, W. (1997, March).The effects of content mix and equating method on the accuracy of test equating using anchor-item design. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
