Abstract
In meta-analysis, generalized linear mixed models (GLMMs) are usually used when heterogeneity is present and individual patient data (IPD) are available, while accepting binary, discrete as well as continuous response variables. In the present paper some measures of influence diagnostics based on log-likelihood are suggested and discussed. A known measure is approximated to get a simpler form, for which the information matrix is no more necessary. The performance of the proposed measure is assessed through a diagnostic analysis on simulated data reproducing a possible meta-analytical context of IPD with influential outliers. The proposed measure is showed to work well and to have a form similar to the gradient statistic, recently introduced.
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
Cook, R. D. (1977). Detection of influential observations in linear regression. Technometrics, 19, 15–18.
Cook, R. D. (1986). Assessment of local influence. Journal of the Royal Statistical Society Series B Methodology, 4(2), 133–169.
Cook, R. D., & Weisberg, S. (1982). Residuals and influence in regression. New York: Chapman and Hall.
Everitt, B. S. (2002). The Cambridge dictionary of statistics (2nd ed.). New York: Cambridge University Press.
Lesaffre, E., & Verbeke, G. (1998). Local influence in linear mixed models. Biometrics, 54(2), 570–582.
Ouwens, M. J. N. M., Tan, F. E. S., & Berger, M. P. F. (2001). Local influence to detect influential data structures for generalized linear mixed models. Biometrics, 57(42), 1166–1172.
R Core Team. (2012). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. http://www.R-project.org/. ISBN 3-900051-07-0
Riley, R. D., & Steyerberg, E. W. (2010). Meta-analysis of a binary outcome using individual patient data and aggregate data. Research Synthesis Methods, 1, 2–19.
Terrell, G. R. (2002). The gradient statistic. Computing Science and Statistics, 34, 206–215.
Tukey, J. W. (1977). Exploratory data analysis. Reading: Addison-Wesley.
Viechtbauer, W., & Cheung, M. W.-L. (2010). Outlier and influence diagnostics for meta-analysis. Research Synthesis Methods, 1(2), 112–125.
Xu, L., Lee, S., & Poon, W. (2006). Deletion measures for generalized linear mixed models. Computational Statistics & Data Analysis, 51, 1131–1146.
Zhu, H., Lee, S., Wei, B., & Zhou, J. (2001). Case-deletion measures for models with incomplete data. Biometrika, 88(3), 727–737.
Acknowledgements
We are grateful to dr. V. Muggeo for having brought to our attention the gradient statistic.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Enea, M., Plaia, A. (2014). Influence Diagnostics for Meta-Analysis of Individual Patient Data Using Generalized Linear Mixed Models. In: Vicari, D., Okada, A., Ragozini, G., Weihs, C. (eds) Analysis and Modeling of Complex Data in Behavioral and Social Sciences. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-06692-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-06692-9_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06691-2
Online ISBN: 978-3-319-06692-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)