Robust diagnostics and monitoring for Linear Mixed Models

L. Grossi

{}^{1}

A. Corbellini

{}^{2}

F. Laurini

{}^{3}

Abstract

The resilience of linear mixed models (LMM) with random effects is investigated with the use of the forward search (FS). The constraints imposed by the model and its estimations provide new computing challenges when extending the FS to the LMM. The method is illustrated by looking at coffee shipments to the European Union using real data and looking for anomalies that could point to fraud.

Robust estimators may be utilised to monitor the detrimental effects of outliers and important data on the parameter estimations of these models. Certain current diagnostics suffer from ”masking” when the real number of outliers is more than $k$ . Most other diagnostic methods rely on the leave- $k$ -out method.

Despite its relatively high processing costs, the forward search (FS) strategy is an alternative ”monitoring” technique that has shown to be particularly effective in dealing with the masking effect in numerous multivariate situations due to its high degree of flexibility, speed, and resilience.

${}^{1}$

Ro.S.A. and Department of Engineering and Architecture, University of Parma, Italy, [luigi.grossi@unipr.it]
${}^{2}$

Ro.S.A. and Department of Economics, University of Parma, Italy, [aldo.corbellini@unipr.it]
${}^{3}$

Ro.S.A. and Department of Economics, University of Parma, Italy, [fabrizio.laurini@unipr.it]

Keywords: Informative plotting – Linear mixed models – Outlier detection – Robust estimators