IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v87y2022i3d10.1007_s11336-021-09816-8.html
   My bibliography  Save this article

The Role of Conditional Likelihoods in Latent Variable Modeling

Author

Listed:
  • Anders Skrondal

    (Norwegian Institute of Public Health
    University of Oslo
    University of California, Berkeley)

  • Sophia Rabe-Hesketh

    (University of California, Berkeley)

Abstract

In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, “cluster” refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and “unit” refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

Suggested Citation

  • Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    • Handle: RePEc:spr:psycho:v:87:y:2022:i:3:d:10.1007_s11336-021-09816-8
    DOI: 10.1007/s11336-021-09816-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-021-09816-8
    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/s11336-021-09816-8?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. Wooldridge, Jeffrey M., 1999. "Distribution-free estimation of some nonlinear panel data models," Journal of Econometrics, Elsevier, vol. 90(1), pages 77-97, May.
    2. 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.
    3. Henk Kelderman & Carl Rijkes, 1994. "Loglinear multidimensional IRT models for polytomously scored items," Psychometrika, Springer;The Psychometric Society, vol. 59(2), pages 149-176, June.
    4. Fran�ois Laisney & Michael Lechner, 2003. "Almost Consistent Estimation of Panel Probit Models with "Small" Fixed Effects," Econometric Reviews, Taylor & Francis Journals, vol. 22(1), pages 1-28, February.
    5. Hausman, Jerry A & Taylor, William E, 1981. "Panel Data and Unobservable Individual Effects," Econometrica, Econometric Society, vol. 49(6), pages 1377-1398, November.
    6. Jay Teachman & Greg J. Duncan & W. Jean Yeung & Dan Levy, 2001. "Covariance Structure Models for Fixed and Random Effects," Sociological Methods & Research, , vol. 30(2), pages 271-288, November.
    7. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    8. Zhang, Daowen & Davidian, Marie, 2004. "Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 90-106, October.
    9. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    10. Little, Roderick J A, 1985. "A Note about Models for Selectivity Bias," Econometrica, Econometric Society, vol. 53(6), pages 1469-1474, November.
    11. P. Diggle & M. G. Kenward, 1994. "Informative Drop‐Out in Longitudinal Data Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 49-73, March.
    12. John M. Neuhaus & Charles E. McCulloch, 2006. "Separating between‐ and within‐cluster covariate effects by using conditional and partitioning methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 859-872, November.
    13. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    14. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    15. E. Maris, 1998. "On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation," Psychometrika, Springer;The Psychometric Society, vol. 63(1), pages 65-71, March.
    16. Griliches, Zvi & Hausman, Jerry A., 1986. "Errors in variables in panel data," Journal of Econometrics, Elsevier, vol. 31(1), pages 93-118, February.
    17. Laszlo Matyas (ed.), 2017. "The Econometrics of Multi-dimensional Panels," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-319-60783-2, July-Dece.
    18. Peter Ebbes & Ulf Böckenholt & Michel Wedel, 2004. "Regressor and random‐effects dependencies in multilevel models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 161-178, May.
    19. Barry E. Storer & Sholom Wacholder & Norman E. Breslow, 1983. "Maximum Likelihood Fitting of General Risk Models to Stratified Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 172-181, June.
    20. Michael E. Sobel, 2012. "Does Marriage Boost Men’s Wages?: Identification of Treatment Effects in Fixed Effects Regression Models for Panel Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 521-529, June.
    21. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    22. Paul Holland, 1990. "On the sampling theory roundations of item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 577-601, December.
    23. 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.
    24. Ridder, Geert & Tunali, Insan, 1999. "Stratified partial likelihood estimation," Journal of Econometrics, Elsevier, vol. 92(2), pages 193-232, October.
    25. Bound, John & Solon, Gary, 1999. "Double trouble: on the value of twins-based estimation of the return to schooling," Economics of Education Review, Elsevier, vol. 18(2), pages 169-182, April.
    26. William Greene, 2004. "The behaviour of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 98-119, June.
    27. Richard J. Cook & Vernon T. Farewell, 1999. "The Utility of Mixed-Form Likelihoods," Biometrics, The International Biometric Society, vol. 55(1), pages 284-288, March.
    28. Anders Skrondal & Sophia Rabe‐Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687, June.
    29. Charles E. McCulloch & John M. Neuhaus, 2011. "Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification," Biometrics, The International Biometric Society, vol. 67(1), pages 270-279, March.
    30. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    31. Brumback, Babette A. & Dailey, Amy B. & Brumback, Lyndia C. & Livingston, Melvin D. & He, Zhulin, 2010. "Adjusting for confounding by cluster using generalized linear mixed models," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1650-1654, November.
    32. Karyne B. Charbonneau, 2017. "Multiple fixed effects in binary response panel data models," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 1-13, October.
    33. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    34. Arthur Goldberger, 1971. "Econometrics and psychometrics: A survey of communalities," Psychometrika, Springer;The Psychometric Society, vol. 36(2), pages 83-107, June.
    35. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    36. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    37. Hausman, Jerry A & Wise, David A, 1979. "Attrition Bias in Experimental and Panel Data: The Gary Income Maintenance Experiment," Econometrica, Econometric Society, vol. 47(2), pages 455-473, March.
    38. Robert Zwitser & Gunter Maris, 2015. "Conditional Statistical Inference with Multistage Testing Designs," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 65-84, March.
    39. Sylvie Goetgeluk & Stijn Vansteelandt, 2008. "Conditional Generalized Estimating Equations for the Analysis of Clustered and Longitudinal Data," Biometrics, The International Biometric Society, vol. 64(3), pages 772-780, September.
    40. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    41. Hua Yun Chen, 2007. "A Semiparametric Odds Ratio Model for Measuring Association," Biometrics, The International Biometric Society, vol. 63(2), pages 413-421, June.
    42. Maddala, G S, 1971. "The Use of Variance Components Models in Pooling Cross Section and Time Series Data," Econometrica, Econometric Society, vol. 39(2), pages 341-358, March.
    43. Alban Thomas, 2006. "Consistent estimation of binary-choice panel data models with heterogeneous linear trends," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 177-195, July.
    44. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    45. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    46. Verbeke G. & Spiessens B. & Lesaffre E., 2001. "Conditional Linear Mixed Models," The American Statistician, American Statistical Association, vol. 55, pages 25-34, February.
    47. Erling Andersen & Mette Madsen, 1977. "Estimating the parameters of the latent population distribution," Psychometrika, Springer;The Psychometric Society, vol. 42(3), pages 357-374, September.
    48. Gerhard Arminger & Ronald Schoenberg, 1989. "Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 409-425, September.
    49. Patrick J. Heagerty, 1999. "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data," Biometrics, The International Biometric Society, vol. 55(3), pages 688-698, September.
    50. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    51. A. Skrondal & S. Rabe-Hesketh, 2014. "Protective estimation of mixed-effects logistic regression when data are not missing at random," Biometrika, Biometrika Trust, vol. 101(1), pages 175-188.
    52. D’Haultfœuille, Xavier & Iaria, Alessandro, 2016. "A convenient method for the estimation of the multinomial logit model with fixed effects," Economics Letters, Elsevier, vol. 141(C), pages 77-79.
    53. John M. Neuhaus & Charles E. McCulloch, 2011. "Estimation of covariate effects in generalized linear mixed models with informative cluster sizes," Biometrika, Biometrika Trust, vol. 98(1), pages 147-162.
    54. Katherine E. Castellano & Sophia Rabe-Hesketh & Anders Skrondal, 2014. "Composition, Context, and Endogeneity in School and Teacher Comparisons," Journal of Educational and Behavioral Statistics, , vol. 39(5), pages 333-367, October.
    55. Bo E. Honoré & Ekaterini Kyriazidou, 2000. "Panel Data Discrete Choice Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 68(4), pages 839-874, July.
    56. Kosuke Imai & In Song Kim, 2019. "When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data?," American Journal of Political Science, John Wiley & Sons, vol. 63(2), pages 467-490, April.
    57. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
    58. Breusch, Trevor S., 1987. "Maximum likelihood estimation of random effects models," Journal of Econometrics, Elsevier, vol. 36(3), pages 383-389, November.
    59. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
    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. Sophia Rabe-Hesketh & Anders Skrondal, 2023. "Ignoring Non-ignorable Missingness," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 31-50, 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. Manuel Arellano & Olympia Bover, 1990. "La econometría de datos de panel," Investigaciones Economicas, Fundación SEPI, vol. 14(1), pages 3-45, January.
    2. Seonho Shin, 2021. "Were they a shock or an opportunity?: The heterogeneous impacts of the 9/11 attacks on refugees as job seekers—a nonlinear multi-level approach," Empirical Economics, Springer, vol. 61(5), pages 2827-2864, November.
    3. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    4. Francesco Bartolucci & Francesco Valentini & Claudia Pigini, 2023. "Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 529-557, February.
    5. Bartolucci, Francesco & Belotti, Federico & Peracchi, Franco, 2015. "Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data," Journal of Econometrics, Elsevier, vol. 184(1), pages 111-123.
    6. Francesco Bartolucci & Claudia Pigini & Francesco Valentini, 2023. "Conditional inference and bias reduction for partial effects estimation of fixed-effects logit models," Empirical Economics, Springer, vol. 64(5), pages 2257-2290, May.
    7. Katherine E. Castellano & Sophia Rabe-Hesketh & Anders Skrondal, 2014. "Composition, Context, and Endogeneity in School and Teacher Comparisons," Journal of Educational and Behavioral Statistics, , vol. 39(5), pages 333-367, October.
    8. Aleksey Oshchepkov & Anna Shirokanova, 2020. "Multilevel Modeling For Economists: Why, When And How," HSE Working papers WP BRP 233/EC/2020, National Research University Higher School of Economics.
    9. Bartolucci, Francesco & Bacci, Silvia & Pigini, Claudia, 2017. "Misspecification test for random effects in generalized linear finite-mixture models for clustered binary and ordered data," Econometrics and Statistics, Elsevier, vol. 3(C), pages 112-131.
    10. Czarnitzki, Dirk & Doherr, Thorsten & Hussinger, Katrin & Schliessler, Paula & Toole, Andrew A., 2016. "Knowledge Creates Markets: The influence of entrepreneurial support and patent rights on academic entrepreneurship," European Economic Review, Elsevier, vol. 86(C), pages 131-146.
    11. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    12. Lionel WILNER, 2019. "The Dynamics of Individual Happiness," Working Papers 2019-18, Center for Research in Economics and Statistics.
    13. repec:hal:spmain:info:hdl:2441/75dbbb2hc596np6q8flqf6i79k is not listed on IDEAS
    14. Koen Jochmans, 2017. "Two-Way Models for Gravity," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 478-485, July.
    15. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    16. repec:hal:wpspec:info:hdl:2441/75dbbb2hc596np6q8flqf6i79k is not listed on IDEAS
    17. Francesco Bartolucci & Claudia Pigini, 2017. "Granger causality in dynamic binary short panel data models," Working Papers 421, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    18. Wladimir Raymond & Pierre Mohnen & Franz Palm & Sybrand Schim van der Loeff, 2007. "The Behavior of the Maximum Likelihood Estimator of Dynamic Panel Data Sample Selection Models," CIRANO Working Papers 2007s-06, CIRANO.
    19. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    20. Lucchetti, Riccardo & Pigini, Claudia, 2017. "DPB: Dynamic Panel Binary Data Models in gretl," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i08).
    21. Andrew Bell & Malcolm Fairbrother & Kelvyn Jones, 2019. "Fixed and random effects models: making an informed choice," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(2), pages 1051-1074, March.
    22. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2018. "Modelling And Estimating Individual And Firm Effects With Count Panel Data," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1049-1078, September.
    23. Victor Aguirregabiria & Jesus Carro, 2021. "Identification of Average Marginal Effects in Fixed Effects Dynamic Discrete Choice Models," Working Papers tecipa-701, University of Toronto, Department of Economics.

    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:87:y:2022:i:3:d:10.1007_s11336-021-09816-8. 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.