Skip to main content
SpringerLink
Log in

Partitioned GMM for Correlated Data with Bayesian Intervals

  • Chapter
  • First Online:
Marginal Models in Analysis of Correlated Binary Data with Time Dependent Covariates

Part of the book series: Emerging Topics in Statistics and Biostatistics ((ETSB))

  • 422 Accesses

Abstract

A Partitioned GMM logistic regression model with Bayes intervals for marginal means with time-dependent covariates is presented. The model is flexible and attainable in obtaining credible intervals of the regression coefficients for time-dependent covariates. It converges in cases where the frequentist model does not.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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

  • Anchen, C. H. (2001). Why lagged dependent variables can suppress the explanatory power of other independent variables. In Annual Meeting of the Political Methodology Science Association, Los Angeles, CA.

    Google Scholar 

  • Azzalini, A. (1994). Logistic regression for autocorrelated data with application to repeated measures. Biometrika, 81(4), 767–775.

    Article  MathSciNet  MATH  Google Scholar 

  • Caragea, P. C., Smith, R. L. (2007). Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models. J Multivar Anal. 98(7):1417–1440.

    Google Scholar 

  • Chandler, R. E., Bate, S. (2007). Inference for clustered data using the independence loglikelihood. Biometrika, 94(1), 167–183.

    Google Scholar 

  • Cox, D. R., Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities. Biometrika, 91(3), 729–737.

    Google Scholar 

  • Diggle, P., Heagerty, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of longitudinal data. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Efron, B. (2015). Frequentist accuracy of Bayesian estimates. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 77(3), 617–649.

    Article  MathSciNet  MATH  Google Scholar 

  • Givens, G. H., & Hoeting, J. A. (2013). Computational statistics (2nd ed.). Chichester, UK: Wiley.

    MATH  Google Scholar 

  • Hall, A. R. (2005). Generalized method of moments. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029–1054.

    Article  MathSciNet  MATH  Google Scholar 

  • Hansen, L. P., Heaton, J., & Yaron, A. (1996). Finite-sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics, 14(3), 262–280.

    Google Scholar 

  • Heagerty, P. J. (2002). Marginalized transition models and likelihood inference for longitudinal categorical data. Biometrics, 58(2), 342–351.

    Article  MathSciNet  MATH  Google Scholar 

  • Heagerty, P. J., & Comstock, B. A. (2013). Exploration of lagged associations using longitudinal data. Biometrics, 69(1), 197–205.

    Article  MathSciNet  MATH  Google Scholar 

  • Heagerty, P. J., & Zeger, S. L. (2000). Marginalized multilevel models and likelihood inference. Statistical Science, 15(1), 1–26.

    MathSciNet  Google Scholar 

  • Hoff, P. D. (2009). A first course in Bayesian statistical methods. New York: Springer.

    Book  MATH  Google Scholar 

  • Hong, I., Coker-Bolt, P., Anderson, K. R., Lee, D., & Velozo, C. A. (2016). Relationship between physical activity and overweight and obesity in children: Findings from the 2012 National Health and Nutrition Examination Survey National Youth Fitness Survey. The American Journal of Occupational Therapy, 70(5), 7005180060p1–7005180060p8.

    Article  Google Scholar 

  • Irimata, K. M., Broatch, J., & Wilson, J. R. (2019). Partitioned GMM logistic regression models for longitudinal data. Statistics in Medicine, 38(12), 2171–2183.

    Article  MathSciNet  Google Scholar 

  • Keele, L., & Kelly, N. J. (2006). Dynamic models for dynamic theories: The ins and outs of lagged dependent variables. Political Analysis, 14(2), 186–205.

    Article  Google Scholar 

  • Lai, T. L., & Small, D. (2007). Marginal regression analysis of longitudinal data with time-dependent covariates: A generalised method of moments approach. Journal of the Royal Statistical Society, Series B, 69(1), 79–99.

    Article  MathSciNet  Google Scholar 

  • Lalonde, T. L., Wilson, J. R., & Yin, J. (2014). GMM logistic regression models for longitudinal data with time-dependent covariates. Statistics in Medicine, 33(27), 4756–4769.

    Article  MathSciNet  Google Scholar 

  • Liang, G., Yu, B. (2003). Maximum pseudo likelihood estimation in network tomography. IEEE Trans Signal Process, 51(8), 2043–2053.

    Google Scholar 

  • Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13–22.

    Article  MathSciNet  MATH  Google Scholar 

  • Lincoln, K. D., Abdou, C. M., & Lloyd, D. (2014). Race and socioeconomic differences in obesity and depression among Black and non-Hispanic White Americans. Journal of Health Care for the Poor and Underserved, 25(1), 257–275.

    Article  Google Scholar 

  • Luppino, F. S., de Wit, L. M., Bouvy, P. F., Stijnen, T., Cuijpers, P., Penninx, B. W., & Zitman, F. G. (2010). Overweight, obesity, and depression: A systematic review and meta-analysis of longitudinal studies. Archives of General Psychiatry, 67(3), 220–229.

    Article  Google Scholar 

  • McFadden, D. (1989). A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica, 57(5), 995–1026.

    Article  MathSciNet  MATH  Google Scholar 

  • Murphy, S., & Li, B. (1995). Projected partial likelihood and its application to longitudinal data. Biometrika, 82(2), 399–406.

    Article  MathSciNet  MATH  Google Scholar 

  • Obermeier, V., Scheipl, F., Heumann, C., Wassermann, J., & Küchenhoff, H. (2015). Flexible distributed lags for modelling earthquake data. Journal of the Royal Statistical Society Series C (Applied Statistics), 64(2), 395–412.

    Article  MathSciNet  Google Scholar 

  • Schildcrout, J. S., & Heagerty, P. J. (2005). Regression analysis of longitudinal binary data with time-dependent environmental covariates: Bias and efficiency. Biostatistics, 6(4), 633–652.

    Article  MATH  Google Scholar 

  • Singh, G. K., Siahpush, M., & Kogan, M. D. (2010). Rising social inequalities in US childhood obesity, 2003-2007. Annals of Epidemiology, 20(1), 40–52.

    Article  Google Scholar 

  • Tanaka, M. (2020). Adaptive MCMC for Generalized Method of Moments with many moment conditions. ArXiv. 1–10.

    Google Scholar 

  • Traversy, G., & Chaput, J. P. (2015). Alcohol consumption and obesity: An update. Current Obesity Reports, 4(1), 122–130.

    Article  Google Scholar 

  • Varin, C. (2008). On composite marginal likelihoods. AStA Adv Stat Anal. 92:1–28.

    Google Scholar 

  • Varin, C., Reid, N., & Firth, D. (2011). An overview of composite likelihood methods. Stat Sin. 21(1):5–42.

    Google Scholar 

  • Vazquez Arreola, E., & Wilson, J. R. (2020). Partitioned MVM marginal model with Bayes estimates for correlated data and time-dependent covariates. submitted.

    Google Scholar 

  • Yin, G. (2009). Bayesian generalized method of moments. Bayesian Analysis, 4(2), 191–207.

    Article  MathSciNet  MATH  Google Scholar 

  • Yin, G., Ma, Y., Liang, F., & Yuan, Y. (2011). Stochastic generalized method of moments. Journal of Computational and Graphical Statistics, 20(3), 714–727.

    Article  MathSciNet  Google Scholar 

  • Zeger, S. L., & Liang, K.-Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42(1), 121–130.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, W. P. Carey School of Business, Arizona State University, Chandler, AZ, USA

    Jeffrey R. Wilson

  2. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA

    Elsa Vazquez-Arreola

  3. School of Social Work & Department of Biostatistics, University of North Carolina, Chapel Hill, NC, USA

    (Din) Ding-Geng Chen

  4. Department of Statistics, University of Pretoria, Pretoria, South Africa

    (Din) Ding-Geng Chen

Authors
  1. Jeffrey R. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elsa Vazquez-Arreola
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. (Din) Ding-Geng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Wilson, J.R., Vazquez-Arreola, E., Chen, (.DG. (2020). Partitioned GMM for Correlated Data with Bayesian Intervals. In: Marginal Models in Analysis of Correlated Binary Data with Time Dependent Covariates. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-030-48904-5_6

Download citation

Publish with us

Policies and ethics

Search

Navigation