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The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models

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  • Bhat, Chandra R.

Abstract

This monograph presents the basics of the composite marginal likelihood (CML) inference approach, discussing the asymptotic properties of the CML estimator and the advantages and limitations of the approach. The composite marginal likelihood (CML) inference approach is a relatively simple approach that can be used when the full likelihood function is practically infeasible to evaluate due to underlying complex dependencies. The history of the approach may be traced back to the pseudo-likelihood approach of Besag (1974) for modeling spatial data, and has found traction in a variety of fields since, including genetics, spatial statistics, longitudinal analyses, and multivariate modeling. However, the CML method has found little coverage in the econometrics field, especially in discrete choice modeling. This monograph fills this gap by identifying the value and potential applications of the method in discrete dependent variable modeling as well as mixed discrete and continuous dependent variable model systems. In particular, it develops a blueprint (complete with matrix notation) to apply the CML estimation technique to a wide variety of discrete and mixed dependent variable models.

Suggested Citation

  • Bhat, Chandra R., 2014. "The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models," Foundations and Trends(R) in Econometrics, now publishers, vol. 7(1), pages 1-117, July.
    • Handle: RePEc:now:fnteco:0800000022
    DOI: 10.1561/0800000022
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    Cited by:

    1. Dubey, Subodh & Bansal, Prateek & Daziano, Ricardo A. & Guerra, Erick, 2020. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 114-141.
    2. Bhat, Chandra R. & Astroza, Sebastian & Hamdi, Amin S., 2017. "A spatial generalized ordered-response model with skew normal kernel error terms with an application to bicycling frequency," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 126-148.
    3. Kamargianni, Maria & Dubey, Subodh & Polydoropoulou, Amalia & Bhat, Chandra, 2015. "Investigating the subjective and objective factors influencing teenagers’ school travel mode choice – An integrated choice and latent variable model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 78(C), pages 473-488.
    4. Dannemiller, Katherine A. & Mondal, Aupal & Asmussen, Katherine E. & Bhat, Chandra R., 2021. "Investigating autonomous vehicle impacts on individual activity-travel behavior," Transportation Research Part A: Policy and Practice, Elsevier, vol. 148(C), pages 402-422.
    5. Bhat, Chandra R. & Mondal, Aupal, 2022. "A New Flexible Generalized Heterogeneous Data Model (GHDM) with an Application to Examine the Effect of High Density Neighborhood Living on Bicycling Frequency," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 244-266.
    6. Mozharovskyi, Pavlo & Vogler, Jan, 2016. "Composite marginal likelihood estimation of spatial autoregressive probit models feasible in very large samples," Economics Letters, Elsevier, vol. 148(C), pages 87-90.
    7. Mondal, Aupal & Bhat, Chandra R., 2022. "A spatial rank-ordered probit model with an application to travel mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 374-393.
    8. Dubey, Subodh & Sharma, Ishant & Mishra, Sabyasachee & Cats, Oded & Bansal, Prateek, 2022. "A General Framework to Forecast the Adoption of Novel Products: A Case of Autonomous Vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 63-95.
    9. Bhat, Chandra R. & Pinjari, Abdul R. & Dubey, Subodh K. & Hamdi, Amin S., 2016. "On accommodating spatial interactions in a Generalized Heterogeneous Data Model (GHDM) of mixed types of dependent variables," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 240-263.
    10. Chandra R. Bhat & Subodh K. Dubey & Mohammad Jobair Bin Alam & Waleed H. Khushefati, 2015. "A New Spatial Multiple Discrete-Continuous Modeling Approach To Land Use Change Analysis," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 801-841, November.
    11. Asmussen, Katherine E. & Mondal, Aupal & Bhat, Chandra R., 2022. "Adoption of partially automated vehicle technology features and impacts on vehicle miles of travel (VMT)," Transportation Research Part A: Policy and Practice, Elsevier, vol. 158(C), pages 156-179.
    12. Bhat, Chandra R., 2015. "A new generalized heterogeneous data model (GHDM) to jointly model mixed types of dependent variables," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 50-77.
    13. Chandra R. Bhat & Patrícia S. Lavieri, 2018. "A new mixed MNP model accommodating a variety of dependent non-normal coefficient distributions," Theory and Decision, Springer, vol. 84(2), pages 239-275, March.
    14. Dubey, Subodh & Cats, Oded & Hoogendoorn, Serge & Bansal, Prateek, 2022. "A multinomial probit model with Choquet integral and attribute cut-offs," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 140-163.
    15. Subodh Dubey & Ishant Sharma & Sabyasachee Mishra & Oded Cats & Prateek Bansal, 2021. "A General Framework to Forecast the Adoption of Novel Products: A Case of Autonomous Vehicles," Papers 2109.06169, arXiv.org.
    16. Patil, Priyadarshan N. & Dubey, Subodh K. & Pinjari, Abdul R. & Cherchi, Elisabetta & Daziano, Ricardo & Bhat, Chandra R., 2017. "Simulation evaluation of emerging estimation techniques for multinomial probit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 9-20.
    17. Büscher, Sebastian & Bauer, Dietmar, 2024. "Weighting strategies for pairwise composite marginal likelihood estimation in case of unbalanced panels and unaccounted autoregressive structure of the errors," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    18. Bhat, Chandra R. & Dubey, Subodh K., 2014. "A new estimation approach to integrate latent psychological constructs in choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 68-85.
    19. Chandra Bhat, 2015. "A new spatial (social) interaction discrete choice model accommodating for unobserved effects due to endogenous network formation," Transportation, Springer, vol. 42(5), pages 879-914, September.
    20. Bhat, Chandra R. & Dubey, Subodh K. & Nagel, Kai, 2015. "Introducing non-normality of latent psychological constructs in choice modeling with an application to bicyclist route choice," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 341-363.
    21. Subodh Dubey & Prateek Bansal & Ricardo A. Daziano & Erick Guerra, 2019. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Papers 1904.08332, arXiv.org, revised Jan 2020.

    More about this item

    Keywords

    Composite marginal likelihood; Statistical inference; Discrete choice models; Joint mixed model systems;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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