Abstract
Correlated observations arise due to repeated measures on the subjects, or in the case of clustered data, due to the hierarchical structure of the design. In addition, the correlation may be realized due to the time-dependent covariate created between the responses at a particular time and the predictors at earlier times. Also, there is feedback between response at present and the covariates at a later time, though this may not always be significant. In any event, these correlations must be taken into consideration when conducting an analysis.
Several researchers have provided models that reflect the direct impact and the delayed impact of covariates on the response. They have utilized valid moment conditions to estimate such regression coefficients. However, in applications, such as in the example of the Philippines health data, one cannot ignore the impact of the responses on future covariates.
The use of a two-stage model to account for feedback while modeling the direct impact, as well as the delayed effect, of the covariates on future responses is demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Diggle, P., Heagerty, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of longitudinal data. Oxford: Oxford University Press.
Harris, K. M., & Udry, J. R. (2016). National longitudinal study of adolescent to adult health (add health), 1994-2008 [public use]. Inter-university Consortium for Political and Social Research (ICPSR) [distributor].
Irimata, K. M., & Wilson, J. R. (2018). Using SAS to Estimate Lagged Coefficients with the %partitionedGMM Macro. SAS Global Forum Paper 2661–2018 pp 1–8.
Irimata, K. M., Broatch, J., & Wilson, J. R. (2019). Partitioned GMM logistic regression models for longitudinal data. Statistics in Medicine, 38(12), 2171–2183.
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.
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.
Lipsitz, S. R., Fitzmaurice, G. M., Ibrahim, J. G., Sinha, D., Parzen, M., & Lipshultz, S. (2009). Joint generalized estimating equations for multivariate longitudinal binary outcomes with missing data: An application to AIDS. Journal of the Royal Statistical Society, Series A (Statistics in Society), 172(1), 3–20.
Martorell, R., & Ho, T. J. (1984). Malnutrition, morbidity, and mortality. Population and Development Review, 10, 49–68.
Zeger, S. L., & Liang, K.-Y. (1992). An overview of methods for the analysis of longitudinal data. Statistics in Medicine, 11(14–15), 1825–1839.
Zeng, Y., Vaupel, J. W., Xiao, Z., Zhang, C., Liu, Y. (2002). Sociodemographic and health profiles of the oldest old in China. Population and Development Review, 28(2), 251–273.
Zhou, Y., Lefante, J., Rice, J., & Chen, S. (2014). Using modified approaches on marginal regression analysis of longitudinal data with time dependent covariates. Statistics in Medicine, 33(19), 3354–3364.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Wilson, J.R., Vazquez-Arreola, E., Chen, (.DG. (2020). A Two-Part GMM Model for Impact and Feedback for Time-Dependent Covariates. 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_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-48904-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-48903-8
Online ISBN: 978-3-030-48904-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)