This note is concerned with evaluation of location parameters for polytomous items in multiple-component measuring instruments. A point and interval estimation procedure for these parameters is outlined that is developed within the framework of latent variable modeling. The method permits educational, behavioral, biomedical, and marketing researchers to quantify important aspects of the functioning of items with ordered multiple response options, which follow the popular graded response model. The procedure is routinely and readily applicable in empirical studies using widely circulated software and is illustrated with empirical data.
duToitM. (Ed.). (2003). IRT from SSI. Scientific International.
5.
EmbretsonS. E.ReiseS. P. (2000). Item response theory for psychologists. Taylor & Francis.
6.
MuthénB. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 87–117.
7.
NeringM. L.OstiniR. (2010). Handbook of polytomous item response theory models. Taylor & Francis.
8.
RaykovT.CalantoneR. J. (2014). The utility of item response modeling in marketing research. Journal of the Academy of Marketing Science, 42, 337–360.
9.
RaykovT.DimitrovD. M.MarcoulidesG. A.HarrisonM. (2019). On the connections between item response theory and classical test theory: A note on true score evaluation with polytomous items via item response modeling. Educational and Psychological Measurement, 79, 1198–1209.
10.
RaykovT.MarcoulidesG. A. (2004). Using the delta method for approximate interval estimation of parametric functions in covariance structure models. Structural Equation Modeling, 11, 659–675.
11.
RaykovT.MarcoulidesG. A. (2018). A course in item response theory and modeling with Stata. Stata Press.
12.
RaykovT.MarcoulidesG. A.ChangC. (2016). Studying population heterogeneity in finite mixture settings using latent variable modeling. Structural Equation Modeling, 23, 726–730.
13.
ReckaseM. D. (2009). Multidimensional item response theory. Springer.
14.
SamejimaF. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, no. 18.
15.
SamejimaF. (2016). Graded response models. In van der LindenW. J. (Ed.), Handbook of item response theory (Vol. 1, pp. 95–108). CRC Press.
16.
Stata Base Reference Manual. (2019). Stata Press.
17.
Stata Item Response Theory Reference Manual Release 1. 7. (2021). Stata Press.
18.
ThissenD.SteinbergL. (1988). Data analysis using item response theory. Psychological Bulletin, 104, 385–395.
19.
van der LindenW. J. (2016). Unidimensional logistic response models. In van der LindenW. J. (Ed.), Handbook of item response theory (Vol. 1, pp. 13–30). CRC Press.
20.
ZhangS.PetersenJ. H. (2018). Quantifying rater variation for ordinal data using a rating scale model. Statistics in Medicine, 37, 2223–2237.
