Can the Generalized Graded Unfolding Model Fit Dominance Responses?

Abstract

Theoretically, the generalized graded unfolding model (GGUM) is more flexible than the generalized partial credit model (GPCM), a dominance model. For item responses generated by the GPCM, the GGUM estimations can generate overlapping item response curves with those from the GPCM over a range of latent trait scores covering almost all of the population. The discrimination and category threshold estimates from the two models are approximately equal. It is necessary to use an informative prior around an extreme location (e.g., 4 for a positive GPCM item) or fix the extreme locations in the GGUM estimation of GPCM items to achieve the desired estimation. The simulation study and the applications on two real datasets support the theoretical claims. Various practical implications are discussed, and suggestions for future research are provided.

Keywords

Likert scale generalized graded unfolding model generalized partial credit model extreme item

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References

Andrich

(1996). A hyperbolic cosine latent trait model for unfolding polytomous responses: Reconciling thurstone and likert methodologies. British Journal of Mathematical and Statistical Psychology, 49(2), 347–365. https://doi.org/10.1111/j.2044-8317.1996.tb01093.x

Baker

F. B.

Kim

S. H.

(2004). Item response theory: Parameter estimation techniques (2nd ed.). CRC Press. https://doi.org/10.1201/9781482276725

Birnbaum

(1968). Some latent trait models and their use in inferring an examinee’s ability. In Lord

F. M.

Novick

M. R.

(Eds.), Statistical theories of mental test scores (pp. 397–479). Addison-Wesley.

Brown

(2016). Item response models for forced-choice questionnaires: A common framework. Psychometrika, 81(4), 135–160. https://doi.org/10.1007/s11336-014-9434-9

Carter

N. T.

Dalal

D. K.

(2010). An ideal point account of the JDI work satisfaction scale. Personality and Individual Differences, 49(7), 743–748. https://doi.org/10.1016/j.paid.2010.06.019

Chalmers

R. P.

(2012). Mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1–29. https://doi.org/10.18637/jss.v048.i06

Drasgow

Chernyshenko

O. S.

Stark

(2010). 75 years after likert: Thurstone was right. Industrial and Organizational Psychology, 3(4), 465–476. https://doi.org/10.1111/j.1754-9434.2010.01273.x

Engelhard

(2023). Functional approaches for modeling unfolding data. Educational and Psychological Measurement, 83(6), 1139–1159. https://doi.org/10.1177/00131644221143474

Engelhard

Yuan

(2022). A historical perspective on unfolding models. Journal of Applied Measurement, 23(1/2), 1–18.

10.

Likert

(1932). A technique for the measurement of attitudes. Archives of Psychology, 22 140, 55.

11.

Luo

(2001). A class of probabilistic unfolding models for polytomous responses. Journal of Mathematical Psychology, 45(2), 224–248. https://doi.org/10.1006/jmps.2000.1310

12.

Muraki

(1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159–176. https://doi.org/10.1177/014662169201600206

13.

Orlando

Thissen

(2000). Likelihood-based item-fit indices for dichotomous item response theory models. Applied Psychological Measurement, 24(1), 50–65. https://doi.org/10.1177/01466216000241003

14.

Orlando

Thissen

(2003). Further investigation of the performance of s-x squared: An item fit index for use with dichotomous item response theory models. Applied Psychological Measurement, 27(4), 289–298. https://doi.org/10.1177/0146621603027004004

15.

R Core Team . (2023). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/

16.

Roberts

J. S.

(1995). Item response theory approaches to attitude measurement [unpublished doctoral dissertation]. University of South Carolina.

17.

Roberts

J. S.

(2008). Modified likelihood-based item fit statistics for the generalized graded unfolding model. Applied Psychological Measurement, 32(5), 407–423. https://doi.org/10.1177/0146621607301278

18.

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(1), 3–32. https://doi.org/10.1177/01466216000241001

19.

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(3), 231–255. https://doi.org/10.1177/014662169602000305

20.

Roberts

J. S.

Laughlin

J. E.

Wedell

D. H.

(1999). Validity issues in the likert and thurstone approaches to attitude measurement. Educational and Psychological Measurement, 59(2), 211–233. https://doi.org/10.1177/00131649921969811

21.

Roberts

J. S.

Thompson

V. M.

(2011). Marginal maximum a posteriori item parameter estimation for the generalized graded unfolding model. Applied Psychological Measurement, 35(4), 259–279. https://doi.org/10.1177/0146621610392565

22.

Samejima

(1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika, 34(4, Pt. 2), 100–114. https://doi.org/10.1007/bf03372160

23.

Schwarz

G. E.

(1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. https://doi.org/10.1214/aos/1176344136.MR468014

24.

Spector

P. E.

Van Katwyk

P. T.

Brannick

M. T.

Chen

P. Y.

(1997). When two factors don’t reflect two constructs: How item characteristics can produce artifactual factors. Journal of Management, 23(5), 659–677. https://doi.org/10.1016/S0149-2063(97)90020-9

25.

Tay

Ali

U. S.

Drasgow

Williams

(2011). Fitting IRT models to dichotomous and polytomous data: Assessing the relative model–data fit of ideal point and dominance models. Applied Psychological Measurement, 35(4), 280–295. https://doi.org/10.1177/0146621610390674

26.

van Schuur

W. H.

Kiers

H. A. L.

(1994). Why factor analysis often is the incorrect model for analyzing bipolar concepts and what model to use instead. Applied Psychological Measurement, 18(2), 97–110. https://doi.org/10.1177/014662169401800201

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