A model that extends the Rasch model and the Partial Credit Model to account for subject-specific uncertainty when responding to items is proposed. It is demonstrated that ignoring the subject-specific uncertainty may yield biased estimates of model parameters. In the extended version of the model, uncertainty and the underlying trait are linked to explanatory variables. The parameterization allows to identify subgroups that differ in uncertainty and the underlying trait. The modeling approach is illustrated using data on the confidence of citizens in public institutions.
AllisonP. D. (1999). Comparing logit and probit coefficients across groups. Sociological Methods & Research, 28(2), 186–208.
2.
BaumgartnerH.SteenkampJ.-B. E. (2001). Response styles in marketing research: A cross-national investigation. Journal of Marketing Research, 38(2), 143–156.
BöckenholtU.MeiserT. (2017). Response style analysis with threshold and multi-process IRT models: A review and tutorial. British Journal of Mathematical and Statistical Psychology, 70(1), 159–181.
5.
BoltD. M.JohnsonT. R. (2009). Addressing score bias and differential item functioning due to individual differences in response style. Applied Psychological Measurement, 33(5), 335–352.
6.
BoltD. M.NewtonJ. R. (2011). Multiscale measurement of extreme response style. Educational and Psychological Measurement, 71(5), 814–833.
7.
BreenR.HolmA.KarlsonK. B. (2014). Correlations and nonlinear probability models. Sociological Methods & Research, 43(4), 571–605.
8.
ConijnJ. M.EmonsW. H.van AssenM. A.SijtsmaK. (2011). On the usefulness of a multilevel logistic regression approach to person-fit analysis. Multivariate Behavioral Research, 46(2), 365–388.
9.
EidM.RauberM. (2000). Detecting measurement invariance in organizational surveys. European Journal of Psychological Assessment, 16(1), 20–30.
10.
FalkC. F.CaiL. (2016). A flexible full-information approach to the modeling of response styles. Psychological Methods, 21(3), 328–347.
11.
FerrandoP. J. (2009). A graded response model for measuring person reliability. British Journal of Mathematical and Statistical Psychology, 62(3), 641–662.
12.
FerrandoP. J. (2014). A factor-analytic model for assessing individual differences in response scale usage. Multivariate Behavioral Research, 49(4), 390–405.
13.
FerrandoP. J. (2016). An IRT modeling approach for assessing item and person discrimination in binary personality responses. Applied Psychological Measurement, 40(3), 218–232.
14.
GollwitzerM.EidM.JürgensenR. (2005). Response styles in the assessment of anger expression. Psychological Assessment, 17(1), 56–69.
15.
GottardA.IannarioM.PiccoloD. (2016). Varying uncertainty in CUB. Advances in Data Analysis and Classification, 10(2), 225–244.
16.
IannarioM.PiccoloD. (2016). A comprehensive framework of regression models for ordinal data. Metron, 74(2), 233–252.
17.
JinK.-Y.WangW.-C. (2014). Generalized IRT models for extreme response style. Educational and Psychological Measurement, 74(1), 116–138.
18.
JohnsonT. R. (2003). On the use of heterogeneous thresholds ordinal regression models to account for individual differences in response style. Psychometrika, 68(4), 563–583.
19.
JohnsonT. R.BoltD. M. (2010). On the use of factor-analytic multinomial logit item response models to account for individual differences in response style. Journal of Educational and Behavioral Statistics, 35(1), 92–114.
20.
KarlsonK. B.HolmA.BreenR. (2012). Comparing regression coefficients between same-sample nested models using logit and probit: A new method. Sociological Methodology, 42(1), 286–313.
21.
Maij-de MeijA. M.KeldermanH.van der FlierH. (2008). Fitting a mixture item response theory model to personality questionnaire data: Characterizing latent classes and investigating possibilities for improving prediction. Applied Psychological Measurement, 32(8), 611–631.
22.
MastersG. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.
23.
MastersG. N.WrightB. (1984). The essential process in a family of measurement models. Psychometrika, 49(4), 529–544.
24.
MoodC. (2010). Logistic regression: Why we cannot do what we think we can do, and what we can do about it. European Sociological Review, 26(1), 67–82.
25.
MoorsG. (2010). Ranking the ratings: A latent-class regression model to control for overall agreement in opinion research. International Journal of Public Opinion Research, 22(1), 93–119.
26.
MurakiE. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159–176.
27.
MurakiE. (1997). A generalized partial credit model. In van der LindenW. J.HambletonR. K. (Eds.), Handbook of modern item response theory (pp. 153–164). Springer.
28.
PiccoloD. (2003). On the moments of a mixture of uniform and shifted binomial random variables. Quaderni di Statistica, 5, 85–104.
29.
PiccoloD.SimoneR. (2019). The class of CUB models: Statistical foundations, inferential issues and empirical evidence. Statistical Methods & Applications, 28(3), 389–435.
30.
PlieningerH. (2016). Mountain or molehill? A simulation study on the impact of response styles. Educational and Psychological Measurement, 77(1), 32–53.
31.
R Core Team. (2019). R: A language and environment for statistical computing [Computer software manual].
32.
ReiseS. P. (2000). Using multilevel logistic regression to evaluate person-fit in IRT models. Multivariate Behavioral Research, 35(4), 543–568.
33.
RostJ.CarstensenC.von DavierM. (1996). Applying the mixed Rasch model to personality questionnaires. In RostJ.LangeheineR. (Eds.), Applications of latent trait and latent class models in the social sciences (pp. 324–332). Waxmann.
34.
SamejimaF. (1997). Graded response model. In van der LindenW. J.HambletonR. K. (Eds.), Handbook of modern item response theory (pp. 85–100). Springer.
35.
SimoneR.TutzG. (2018). Modelling uncertainty and response styles in ordinal data. Statistica Neerlandica, 72(3), 224–245.
36.
TutzG. (1989). Sequential item response models with an ordered response. British Journal of Statistical and Mathematical Psychology, 43(1), 39–55.
37.
TutzG. (2018). Binary response models with underlying heterogeneity: Identification and interpretation of effects. European Sociological Review, 34(2), 211–221.
38.
TutzG.SchaubergerG.BergerM. (2018). Response styles in the partial credit model. Applied Psychological Measurement, 42(6), 407–427.
39.
TutzG.SchneiderM.IannarioM.PiccoloD. (2017). Mixture models for ordinal responses to account for uncertainty of choice. Advances in Data Analysis and Classification, 11(2), 281–305.
40.
Van RosmalenJ.Van HerkH.GroenenP. (2010). Identifying response styles: A latent-class bilinear multinomial logit model. Journal of Marketing Research, 47(1), 157–172.
41.
Van VaerenberghY.ThomasT. D. (2013). Response styles in survey research: A literature review of antecedents, consequences, and remedies. International Journal of Public Opinion Research, 25(2), 195–217.
42.
VerhelstN. D.GlasC. A. W.de VriesH. H. (1997). A steps model to analyze partial credit. In van der LindenW. J.HambletonR. K. (Eds.), Handbook of modern item response theory (pp. 123–138). Springer.
43.
von DavierM.RostJ. (2016). Logistic mixture-distribution response models. In Van der LindenW. J. (Ed.), Handbook of item response theory: Volume 1 (pp. 421–434). Chapman & Hall/CRC.
44.
von DavierM.YamamotoK. (2007). Mixture-distribution and hybrid Rasch models. In von DavierM.CarstensenC. H. (Eds.), Multivariate and mixture distribution Rasch models (pp. 99–115). Springer.
45.
WetzelE.CarstensenC. H. (2017). Multidimensional modeling of traits and response styles. European Journal of Psychological Assessment, 33, 352–364.
46.
WilliamsR. (2009). Using heterogeneous choice models to compare logit and probit coefficients across groups. Sociological Methods & Research, 37(4), 531–559.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
