81
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Understanding Ability and Reliability Differences Measured with Count Items: The Distributional Regression Test Model and the Count Latent Regression Model

ORCID Icon, ORCID Icon & ORCID Icon

References

  • Andersson, B., & Xin, T. (2021). Estimation of latent regression item response theory models using a second-order Laplace approximation. Journal of Educational and Behavioral Statistics, 46(2), 244–265. https://doi.org/10.3102/1076998620945199
  • Baker, F. B., & Kim, S.-H. (2004). Item response theory: Parameter estimation techniques. CRC Press.
  • Beisemann, M. (2022). A flexible approach to modeling over-, under-and equidispersed count data in IRT: The two-parameter Conway-Maxwell-Poisson model. The British Journal of Mathematical and Statistical Psychology, 75(3), 411–443. https://doi.org/10.1111/bmsp.12273
  • Beisemann, M., Wartlick, O., & Doebler, P. (2020). Comparison of recent acceleration techniques for the EM algorithm in one-and two-parameter logistic IRT models. Psych, 2(4), 209–252. https://doi.org/10.3390/psych2040018
  • Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46(4), 443–459. https://doi.org/10.1007/BF02293801
  • Casals, M., Langohr, K., Carrasco, J. L., & Rönnegård, L. (2015). Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles: A simulation study. SORT: Statistics and Operations Research Transactions, 39(2), 0281–0308.
  • Chalmers, R. P. (2018). Numerical approximation of the observed information matrix with Oakes’ identity. The British Journal of Mathematical and Statistical Psychology, 71(3), 415–436. https://doi.org/10.1111/bmsp.12127
  • De Boeck, P., & Wilson, M. (Eds.). (2004). Explanatory item response models: A generalized linear and nonlinear approach. Springer.
  • Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
  • Doebler, A., Doebler, P., & Holling, H. (2014). A latent ability model for count data and application to processing speed. Applied Psychological Measurement, 38(8), 587–598. https://doi.org/10.1177/0146621614543513
  • Doebler, A., & Holling, H. (2016). A processing speed test based on rule-based item generation: An analysis with the Rasch Poisson counts model. Learning and Individual Differences, 52, 121–128. https://doi.org/10.1016/j.lindif.2015.01.013
  • Eckes, T. (2011). Item banking for C-tests: A polytomous Rasch modeling approach. Psychological Test and Assessment Modeling, 53(4), 414.
  • Eckes, T., & Baghaei, P. (2015). Using testlet response theory to examine local dependence in C-tests. Applied Measurement in Education, 28(2), 85–98. https://doi.org/10.1080/08957347.2014.1002919
  • Eddelbuettel, D., & Francois, R. (2011). Rcpp: Seamless R and C++ Integration. Journal of Statistical Software, 40(8), 1–18. https://doi.org/10.18637/jss.v040.i08
  • Fischer, G. H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 37(6), 359–374. https://doi.org/10.1016/0001-6918(73)90003-6
  • Forthmann, B., Çelik, P., Holling, H., Storme, M., & Lubart, T. (2018). Item response modeling of divergent-thinking tasks: A comparison of Rasch’s Poisson model with a two-dimensional model extension. The International Journal of Creativity & Problem Solving, 28(2), 83–95.
  • Forthmann, B., & Doebler, P. (2021). Reliability of researcher capacity estimates and count data dispersion: A comparison of Poisson, negative binomial, and Conway-Maxwell-Poisson models. Scientometrics, 126(4), 3337–3354. https://doi.org/10.1007/s11192-021-03864-8
  • Forthmann, B., Gerwig, A., Holling, H., Çelik, P., Storme, M., & Lubart, T. (2016). The be-creative effect in divergent thinking: The interplay of instruction and object frequency. Intelligence, 57, 25–32. https://doi.org/10.1016/j.intell.2016.03.005
  • Forthmann, B., Grotjahn, R., Doebler, P., & Baghaei, P. (2020). A comparison of different item response theory models for scaling speeded C-tests. Journal of Psychoeducational Assessment, 38(6), 692–705. https://doi.org/10.1177/0734282919889262
  • Forthmann, B., Gühne, D., & Doebler, P. (2020). Revisiting dispersion in count data item response theory models: The Conway–Maxwell–Poisson counts model. The British Journal of Mathematical and Statistical Psychology, 73 (S1), 32–50. https://doi.org/10.1111/bmsp.12184
  • Forthmann, B., Holling, H., Çelik, P., Storme, M., & Lubart, T. (2017). Typing speed as a confounding variable and the measurement of quality in divergent thinking. Creativity Research Journal, 29(3), 257–269. https://doi.org/10.1080/10400419.2017.1360059
  • Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Alken, P., … Rossi, F. (2010). Gnu scientific library reference manual (3rd ed.) [Computer software manual]. http://www.gnu.org/software/gsl
  • Graßhoff, U., Holling, H., & Schwabe, R. (2013). Optimal design for count data with binary predictors in item response theory. In D. Ucinski, A. C. Atkinson, M. Patan (Eds.), Moda 10–advances in model-oriented design and analysis (pp. 117–124). Springer.
  • Graßhoff, U., Holling, H., & Schwabe, R. (2020). D-optimal design for the Rasch counts model with multiple binary predictors. The British Journal of Mathematical and Statistical Psychology, 73(3), 541–555. https://doi.org/10.1111/bmsp.12204
  • Grotjahn, R. (2016). The electronic C-test bibliography: Version 2016. http://www.c-test.de
  • Grotjahn, R., Schlak, T., & Aguado, K. (2010). S-C-Tests: Messung automatisierter sprachlicher Kompetenzen anhand von C-Tests mit massiver textspezifischer Zeitlimitierung. In R. Grotjahn (Ed.), S-C-Tests: Measurement of automated linguistic competences using C-Tests with massive text-specific time limitation (pp. 297–319). Lang.
  • Guilford, J. P. (1967). The nature of human intelligence. McGraw-Hill.
  • Heine, S. (2017). Foreign and second language success and its explanation through acquisition age, cognitive, affective-motivational, and sociocultural variables: An empirical study. Kassel University Press GmbH.
  • Holling, H., Böhning, W., & Böhning, D. (2015). The covariate-adjusted frequency plot for the Rasch Poisson counts model. Thailand Statistician, 13(1), 67–78.
  • Huang, A. (2017). Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts. Statistical Modelling, 17(6), 359–380. https://doi.org/10.1177/1471082X17697749
  • Hung, L.-F. (2012). A negative binomial regression model for accuracy tests. Applied Psychological Measurement, 36(2), 88–103. https://doi.org/10.1177/0146621611429548
  • Jansen, M. G. (1994). Parameters of the latent distribution in Rasch’s Poisson counts model. In G. Fischer & D. Laming (Eds.), Contributions to mathematical psychology, psychometrics, and methodology. (pp. 319–326). Springer.
  • Jansen, M. G., & van Duijn, M. A. (1992). Extensions of Rasch’s multiplicative Poisson model. Psychometrika, 57(3), 405–414. https://doi.org/10.1007/BF02295428
  • Jendryczko, D., Berkemeyer, L., & Holling, H. (2020). Introducing a computerized figural memory test based on automatic item generation: An analysis with the Rasch Poisson Counts Model. Frontiers in Psychology, 11, 945. https://doi.org/10.3389/fpsyg.2020.00945
  • Magnus, B. E., & Thissen, D. (2017). Item response modeling of multivariate count data with zero inflation, maximum inflation, and heaping. Journal of Educational and Behavioral Statistics, 42(5), 531–558. https://doi.org/10.3102/1076998617694878
  • McLachlan, G. J., & Krishnan, T. (2007). The EM algorithm and extensions (Vol. 382). John Wiley & Sons.
  • Mutz, R., & Daniel, H.-D. (2018). The bibliometric quotient (BQ), or how to measure a researcher’s performance capacity: A Bayesian Poisson Rasch model. Journal of Informetrics, 12(4), 1282–1295. https://doi.org/10.1016/j.joi.2018.10.006
  • Myszkowski, N., & Storme, M. (2021). Accounting for variable task discrimination in divergent thinking fluency measurement: An example of the benefits of a 2-Parameter Poisson Counts Model and its bifactor extension over the Rasch Poisson Counts Model. The Journal of Creative Behavior, 55(3), 800–818. https://doi.org/10.1002/jocb.490
  • Oakes, D. (1999). Direct calculation of the information matrix via the EM. Journal of the Royal Statistical Society Series B: Statistical Methodology, 61(2), 479–482. https://doi.org/10.1111/1467-9868.00188
  • Ogasawara, H. (1996). Rasch’s multiplicative Poisson model with covariates. Psychometrika, 61(1), 73–92. https://doi.org/10.1007/BF02296959
  • Pritikin, J. N. (2017). A comparison of parameter covariance estimation methods for item response models in an expectation-maximization framework. Cogent Psychology, 4(1), 1279435. https://doi.org/10.1080/23311908.2017.1279435
  • R Core Team. (2021). R: A language and environment for statistical computing [Computer software manual]. https://www.R-project.org/
  • Raatz, U., & Klein-Braley, C. (1981). The C-test–A modification of the cloze procedure. In T. Culhane, C. Klein-Barley, & D. Stevenson (Eds.), Practice and problems in language testing (pp. 113–148). University of Essex Occasional Paper.
  • Rasch, G. (1960). Studies in mathematical psychology: I. probabilistic models for some intelligence and attainment tests. Nielsen & Lydiche.
  • Rigby, R. A., & Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society Series C: Applied Statistics, 54(3), 507–554. https://doi.org/10.1111/j.1467-9876.2005.00510.x
  • Runco, M. A., & Acar, S. (2012). Divergent thinking as an indicator of creative potential. Creativity Research Journal, 24(1), 66–75. https://doi.org/10.1080/10400419.2012.652929
  • Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. CRC.
  • Verhelst, N. D., & Kamphuis, F. H. (2009). A Poisson-Gamma model for speed tests (Cito Measurement and Research Department Reports No. Technical Report 2009-2). Cito.
  • Wallach, M. A., & Kogan, N. (1965). Modes of thinking in young children. Holt, Rinehart & Winston.
  • Wedel, M., Böckenholt, U., & Kamakura, W. A. (2003). Factor models for multivariate count data. Journal of Multivariate Analysis, 87(2), 356–369. https://doi.org/10.1016/S0047-259X(03)00020-4
  • Zwinderman, A. H. (1991). A generalized Rasch model for manifest predictors. Psychometrika, 56(4), 589–600. https://doi.org/10.1007/BF02294492

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.