Skip to main content
SpringerLink
Log in

A Mixture Partial Credit Model Analysis Using Language-Based Covariates

  • Conference paper
Quantitative Psychology (IMPS 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 196))

Included in the following conference series:

Abstract

A mixture partial credit model (MixPCM) can be used to classify examinees into discrete latent classes based on their performance on items scored in multiple ordered categories. Characterizing the latent classes, however, is not always straightforward, particularly when analyzing text from constructed responses. This is because there may be information in the constructed responses that is not captured by the scores. Latent Dirichlet allocation (LDA) is a statistical model that has been used to detect latent topics in textual data. The topics can be used to characterize documents, such as answers on a constructed-response test, as mixtures of the topics. In this study, we used one of the topics from the LDA as a covariate in a MixPCM to help characterize the different latent classes detected by the MixPCM.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • R. Arun, V. Suresh, C.V. Madhavan, M.N. Murthy, On finding the natural number of topics with latent Dirichlet allocation: some observations, in Advances in Knowledge Discovery and Data Mining: Vol. 21. Topic Modeling/Information Extraction, ed. by M.J. Zaki, J.X. Yu, B. Ravindran, V. Pudi (Springer, Heidelberg, 2010), pp. 391–402

    Chapter  Google Scholar 

  • I. Bíró, D. Siklósi, J. Szabó, A.A. Benczúr, Linked latent Dirichlet allocation in web spam filtering, in Proceedings of the 5th International Workshop on Adversarial Information Retrieval on the Web: Temporal Analysis, ed. by D. Fetterly, Z. Gyöngyi (Association for Computing Machinery, New York, 2009), pp. 37–40

    Google Scholar 

  • D.M. Blei, A.Y. Ng, M.I. Jordan, Latent dirichlet allocation. J. Mach. Learn. Res. 3, 993–1022 (2003)

    MATH  Google Scholar 

  • K.R. Canini, L. Shi, T.L. Griffiths, Online inference of topics with latent Dirichlet allocation, in International Conference on Artificial Intelligence and Statistics: Vol. 5, ed. by D. Dyk, M. Welling (2009), pp. 65–72

    Google Scholar 

  • J. Chang, Not-so-latent Dirichlet allocation: collapsed Gibbs sampling using human judgments, in Proceedings of the North American Chapter of the Association for Computational Linguistics Human Language Technologies 2010 Workshop on Creating Speech and Language Data with Amazon’s Mechanical Turk, ed. by C. Callison-Burch, M. Dredze (Association for Computational Linguistics, Stroudsburg, 2010), pp. 131–138

    Google Scholar 

  • J. Chang, lda: collapsed Gibbs sampling methods for topic models. R package version 1.4.2 (2015)

    Google Scholar 

  • S.J. Cho, A.S. Cohen, S.H. Kim, Markov chain Monte Carlo estimation of a mixture item response theory model. J. Stat. Comput. Simul. 83 (2), 278–306 (2013)

    Article  MathSciNet  Google Scholar 

  • Y.J. Choi, N. Alexeev, A.S. Cohen, Differential item functioning analysis using a mixture 3-parameter logistic model with a covariate on the TIMSS 2007 mathematics test. Int. J. Test. 15 (3), 239–253 (2015)

    Article  Google Scholar 

  • A.S. Cohen, D.M. Bolt, A mixture model analysis of differential item functioning. J. Educ. Meas. 42 (2), 133–148 (2005)

    Article  Google Scholar 

  • C.M. Dayton, G.B. Macready, Concomitant-variable latent-class models. J. Am. Stat. Assoc. 83 (401), 173–178 (1988)

    Article  MathSciNet  Google Scholar 

  • T.L. Griffiths, M. Steyvers, Finding scientific topics. Proc. Natl. Acad. Sci. 101 (suppl 1), 5228–5235 (2004)

    Article  Google Scholar 

  • T.L. Griffiths, M. Steyvers, J.B. Tenenbaum, Topics in semantic representation. Psychol. Rev. 114, 211 (2007)

    Article  Google Scholar 

  • P. Heidelberger, P.D. Welch, A spectral method for confidence interval generation and run length control in simulations. Commun. ACM 24 (4), 233–245 (1981)

    Article  MathSciNet  Google Scholar 

  • G. Heinrich, Parameter estimation for text analysis. University of Leipzig, Technical Report (2009)

    Google Scholar 

  • T.-H. Kang, A.S. Cohen, H.-J. Sung, IRT model selection methods for polytomous items. Appl. Psychol. Meas. 33 (7), 499–518 (2009)

    Article  Google Scholar 

  • F. Li, A.S. Cohen, S.H. Kim, S.J. Cho, Model selection methods for mixture dichotomous IRT models. Appl. Psychol. Meas. 33 (5), 353–373 (2009)

    Article  MathSciNet  Google Scholar 

  • K. Lu, D. Wolfram, Measuring author research relatedness: a comparison of word-based, topic-based, and author co-citation approaches. J. Am. Soc. Inf. Sci. Technol. 63, 1973–1986 (2012)

    Article  Google Scholar 

  • D.J. Lunn, A. Thomas, N. Best, D. Spiegelhalter, WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Stat. Comput. 10 (4), 325–337 (2000)

    Article  Google Scholar 

  • G.N. Masters, A Rasch model for partial credit scoring. Psychometrika 47 (2), 149–174 (1982)

    Article  Google Scholar 

  • R.J. Mislevy, N. Verhelst, Modeling item responses when different subjects employ different solution strategies. Psychometrika 55 (2), 195–215 (1990)

    Article  Google Scholar 

  • I.V.S. Mullis, M.O. Martin, G.J. Ruddock, C.Y. O’Sullivan, A. Arora, E. Erberber, TIMSS 2007 Assessment Frameworks (Boston College, Chestnut Hill, 2005)

    Google Scholar 

  • M.J. Paul, M. Dredze, You are what you Tweet: analyzing Twitter for public health, in Proceedings of the 5th International AAAI Conference on Weblogs and Social Media (2011), pp. 265–272

    Google Scholar 

  • X.H. Phan, L.M. Nguyen, S. Horiguchi, Learning to classify short and sparse text & web with hidden topics from large-scale data collections, in Proceedings of the 17th International Conference on World Wide Web (ACM, New York, 2008), pp. 91–100

    Google Scholar 

  • M. Plummer, N. Best, K. Cowles, K. Vines, CODA: convergence diagnosis and output analysis for MCMC. R News 6 (1), 7–11 (2006)

    Google Scholar 

  • I. Porteous, D. Newman, A. Ihler, A. Asuncion, P. Smyth, M. Welling, Fast collapsed Gibbs sampling for latent Dirichlet allocation, in Proceedings of the 14th Association for Computing Machinery SIG-Knowledge Discovery and Data Mining International Conference on Knowledge Discovery and Data mining: Vol. 1. Research Papers, ed. by Y. Li, B. Liu, S. Sarawagi (Association for Computing Machinery, New York, 2008), pp. 569–577

    Google Scholar 

  • M. Rosen-Zvi, C. Chemudugunta, T. Griffiths, P. Smyth, M. Steyvers, Learning author-topic models from text corpora. Assoc. Comput. Mach. Trans. Inf. Syst. 28, 4 (2010)

    Google Scholar 

  • J. Rost, Rasch models in latent classes: an integration of two approaches to item analysis. Appl. Psychol. Meas. 14 (3), 271–282 (1990)

    Article  Google Scholar 

  • J. Rost, A logistic mixture distribution model for polychotomous item responses. Br. J. Math. Stat. Psychol. 44 (1), 75–92 (1991)

    Article  Google Scholar 

  • A. Smit, H. Kelderman, H. van der Flier, Collateral information and mixed Rasch models. Methods Psychol. Res. Online 4 (3), 19–32 (1999)

    Google Scholar 

  • S.W. Thomas, B. Adams, A.E. Hassan, D. Blostein, Studying software evolution using topic models. Sci. Comput. Program. 80, 457–479 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Georgia, 125P Aderhold Hall, 110 Carlton street, Athens, GA, 30602, USA

    Seohyun Kim

  2. The University of Georgia, 126C Aderhold Hall, 110 Carlton street, Athens, GA, 30602, USA

    Minho Kwak

  3. The University of Georgia, 125M Aderhold Hall, 110 Carlton street, Athens, GA, 30602, USA

    Allan S. Cohen

Authors
  1. Seohyun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Minho Kwak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Allan S. Cohen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seohyun Kim .

Editor information

Editors and Affiliations

  1. Research Institute for Child Development and Education, University of Amsterdam, Amsterdam, The Netherlands

    L. Andries van der Ark

  2. Department of Statistics, USBE, Umeå University, Umeå, Sweden

    Marie Wiberg

  3. Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, Illinois, USA

    Steven A. Culpepper  & Jeffrey A. Douglas  & 

  4. Department of Psychology, The Educational University of Hong Kong, Hong Kong, China

    Wen-Chung Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Kim, S., Kwak, M., Cohen, A.S. (2017). A Mixture Partial Credit Model Analysis Using Language-Based Covariates. In: van der Ark, L.A., Wiberg, M., Culpepper, S.A., Douglas, J.A., Wang, WC. (eds) Quantitative Psychology. IMPS 2016. Springer Proceedings in Mathematics & Statistics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-319-56294-0_28

Download citation

Publish with us

Policies and ethics

Search

Navigation