IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v81y2016i3d10.1007_s11336-015-9489-2.html
   My bibliography  Save this article

An autoregressive growth model for longitudinal item analysis

Author

Listed:
  • Minjeong Jeon

    (Ohio State University)

  • Sophia Rabe-Hesketh

    (University of California, Berkeley)

Abstract

A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students’ self-esteem.

Suggested Citation

  • Minjeong Jeon & Sophia Rabe-Hesketh, 2016. "An autoregressive growth model for longitudinal item analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 830-850, September.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-015-9489-2
    DOI: 10.1007/s11336-015-9489-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-015-9489-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-015-9489-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Erling Andersen, 1985. "Estimating latent correlations between repeated testings," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 3-16, March.
    2. Li Cai, 2010. "A Two-Tier Full-Information Item Factor Analysis Model with Applications," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 581-612, December.
    3. Francesco Bartolucci & Valentina Nigro, 2010. "A Dynamic Model for Binary Panel Data With Unobserved Heterogeneity Admitting a √n-Consistent Conditional Estimator," Econometrica, Econometric Society, vol. 78(2), pages 719-733, March.
    4. Jeffrey M. Wooldridge, 2005. "Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 39-54, January.
    5. Anders Skrondal & Sophia Rabe-Hesketh, 2014. "Handling initial conditions and endogenous covariates in dynamic/transition models for binary data with unobserved heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(2), pages 211-237, February.
    6. Mark Wilson & Raymond Adams, 1995. "Rasch models for item bundles," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 181-198, June.
    7. Dunson, David B., 2003. "Dynamic Latent Trait Models for Multidimensional Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 555-563, January.
    8. N. Verhelst & C. Glas, 1993. "A dynamic generalization of the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 395-415, September.
    9. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
    10. De Boeck, Paul & Bakker, Marjan & Zwitser, Robert & Nivard, Michel & Hofman, Abe & Tuerlinckx, Francis & Partchev, Ivailo, 2011. "The Estimation of Item Response Models with the lmer Function from the lme4 Package in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i12).
    11. Vassilis Vasdekis & Silvia Cagnone & Irini Moustaki, 2012. "A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 425-441, July.
    12. Robert Gibbons & Donald Hedeker, 1992. "Full-information item bi-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 423-436, September.
    13. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
    14. Albert Satorra & Willem Saris, 1985. "Power of the likelihood ratio test in covariance structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 83-90, March.
    15. James Robins & Andrea Rotnitzky & Stijn Vansteelandt, 2007. "Discussions," Biometrics, The International Biometric Society, vol. 63(3), pages 650-653, September.
    16. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    17. Minjeong Jeon & Sophia Rabe-Hesketh, 2012. "Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures," Journal of Educational and Behavioral Statistics, , vol. 37(4), pages 518-542, August.
    18. Johan Braeken, 2011. "A Boundary Mixture Approach to Violations of Conditional Independence," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 57-76, January.
    19. Wiji Arulampalam & Mark B. Stewart, 2009. "Simplified Implementation of the Heckman Estimator of the Dynamic Probit Model and a Comparison with Alternative Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 659-681, October.
    20. Kenneth A. Bollen & Robert A. Stine, 1992. "Bootstrapping Goodness-of-Fit Measures in Structural Equation Models," Sociological Methods & Research, , vol. 21(2), pages 205-229, November.
    21. Johan Braeken & Francis Tuerlinckx & Paul Boeck, 2007. "Copula Functions for Residual Dependency," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 393-411, September.
    22. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2013. "Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model," Journal of Educational and Behavioral Statistics, , vol. 38(1), pages 32-60, February.
    23. Susan Embretson, 1991. "A multidimensional latent trait model for measuring learning and change," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 495-515, September.
    24. William Meredith & Roger Millsap, 1992. "On the misuse of manifest variables in the detection of measurement bias," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 289-311, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sun-Joo Cho & Sarah Brown-Schmidt & Paul De Boeck & Jianhong Shen, 2020. "Modeling Intensive Polytomous Time-Series Eye-Tracking Data: A Dynamic Tree-Based Item Response Model," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 154-184, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vassilis Vasdekis & Silvia Cagnone & Irini Moustaki, 2012. "A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 425-441, July.
    2. Chun Wang & Steven W. Nydick, 2020. "On Longitudinal Item Response Theory Models: A Didactic," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 339-368, June.
    3. Riccardo (Jack) Lucchetti & Claudia Pigini, 2020. "Choice of solutions to the initial-conditions problem in dynamic panel probit models," Working Papers 2020:27, Department of Economics, University of Venice "Ca' Foscari".
    4. Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2018. "Robust Measurement via A Fused Latent and Graphical Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 538-562, September.
    5. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2013. "Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model," Journal of Educational and Behavioral Statistics, , vol. 38(1), pages 32-60, February.
    6. Frank Rijmen & Minjeong Jeon & Matthias von Davier & Sophia Rabe-Hesketh, 2014. "A Third-Order Item Response Theory Model for Modeling the Effects of Domains and Subdomains in Large-Scale Educational Assessment Surveys," Journal of Educational and Behavioral Statistics, , vol. 39(4), pages 235-256, August.
    7. Riccardo Lucchetti & Claudia Pigini, 2018. "Dynamic panel probit: finite-sample performance of alternative random-effects estimators," Working Papers 426, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    8. Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2018. "Robust measurement via a fused latent and graphical item response theory model," LSE Research Online Documents on Economics 103181, London School of Economics and Political Science, LSE Library.
    9. Lionel WILNER, 2019. "The Dynamics of Individual Happiness," Working Papers 2019-18, Center for Research in Economics and Statistics.
    10. Rabe-Hesketh, Sophia & Skrondal, Anders, 2013. "Avoiding biased versions of Wooldridge’s simple solution to the initial conditions problem," Economics Letters, Elsevier, vol. 120(2), pages 346-349.
    11. Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    12. Sebastian Königs, 2013. "The Dynamics of Social Assistance Benefit Receipt in Germany: State Dependence Before and After the Hartz Reforms," OECD Social, Employment and Migration Working Papers 136, OECD Publishing.
    13. Georgios Marios Chrysanthou, 2021. "A Multiple Cohort Study of the Gender Gradient of Life Satisfaction during Adolescence: Longitudinal Evidence from Great Britain," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(6), pages 1341-1376, December.
    14. Manudeep Bhuller & Christian N. Brinch & Sebastian Königs, 2017. "Time Aggregation and State Dependence in Welfare Receipt," Economic Journal, Royal Economic Society, vol. 127(604), pages 1833-1873, September.
    15. Michela Gnaldi & Silvia Bacci & Thiemo Kunze & Samuel Greiff, 2020. "Students’ Complex Problem Solving Profiles," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 469-501, June.
    16. Peida Zhan & Hong Jiao & Dandan Liao & Feiming Li, 2019. "A Longitudinal Higher-Order Diagnostic Classification Model," Journal of Educational and Behavioral Statistics, , vol. 44(3), pages 251-281, June.
    17. Chrysanthou, Georgios Marios & Vasilakis, Chrysovalantis, 2018. "The Dynamics and Determinants of Bullying Victimisation," IZA Discussion Papers 11902, Institute of Labor Economics (IZA).
    18. Vesterberg, Mattias, 2018. "The effect of price on electricity contract choice," Energy Economics, Elsevier, vol. 69(C), pages 59-70.
    19. Minjeong Jeon & Sophia Rabe-Hesketh, 2012. "Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures," Journal of Educational and Behavioral Statistics, , vol. 37(4), pages 518-542, August.
    20. Bartolucci, Francesco & Pigini, Claudia, 2017. "cquad: An R and Stata Package for Conditional Maximum Likelihood Estimation of Dynamic Binary Panel Data Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 78(i07).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-015-9489-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.