Abstract
This paper presents a robust procedure for the detection of atypical observations and for the analysis of their effect on model inference in random effects models. Given that the observations can be outlying at different levels of the analysis, we focus on the evaluation of the effect of both first and second level outliers and, in particular, on their effect on the higher level variance which is statistically evaluated with the Likelihood-Ratio Test. A cut-off point separating the outliers from the other observations is identified through a graphical analysis of the information collected at each step of the Forward Search procedure; the Robust Forward LRT is the value of the classical LRT statistic at the cut-off point.
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
Atkinson, A. C., & Riani, M. (2000). Robust diagnostic regression analysis. New York: Springer.
Barnett, V., & Lewis, T. (1993). Outliers in statistical data (3rd ed.). New York: Wiley.
Bertaccini, B., & Varriale, R. (2007). Robust ANalysis Of VAriance: An approach based on the Forward Search. Computational Statistics and Data Analysis, 51, 5172–5183.
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust statistics: The approach based on influence functions. New York: Wiley.
Heritier, S., Cantoni, E., Copt, S., & Victoria-Feser, M. (2009). Robust methods in biostatistics. Chichester: Wiley.
Searle, S. R., Casella, G., & McCulloch, C. E. (1992). Variance components. New York: Wiley.
Self, S. G., & Liang, K. Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the Acoustical Society of America, 82, 605–610.
Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal and structural equation models. Boca Raton: Chapman & Hall/CRC.
Staudte, R. G., & Sheather, S. J. (1990). Robust estimation and testing. New York: Wiley.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bertaccini, B., Varriale, R. (2013). Robust Random Effects Models: A Diagnostic Approach Based on the Forward Search. In: Giusti, A., Ritter, G., Vichi, M. (eds) Classification and Data Mining. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28894-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-28894-4_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28893-7
Online ISBN: 978-3-642-28894-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)