High-Breakdown Inference for Mixed Linear Models

Copt, Samuel; Victoria‐Feser, Maria‐Pia

doi:10.1198/016214505000000772

Cited by 43 publications

(93 citation statements)

References 88 publications

(113 reference statements)

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“…In addition, once a high breakdown estimate of the covariance matrix has been obtained via a S-estimator, M M-estimators follow as later suggested by Copt and Heritier (2007); see Heritier et al (2009) and the book website and also Koller (2016) for R code. More recently, Chervoneva and Vishnyakov (2014) extended the theory developed in Copt and Victoria-Feser (2006) by relaxing the assumption of the same number of observations per cluster. Their general S-estimator shares similar properties to the ones proposed earlier but can accommodate unbalanced clustered data.…”

Section: Mixed Linear Modelsmentioning

confidence: 99%

“…In this situation, the clusters are independent and a multivariate normal formulation is available at the cluster level. Copt and Victoria-Feser (2006) exploited this equivalence and proposed S-estimators in the balanced case, i.e. all clusters have the same dimension p. The difference with the multivariate model considered by Cerioli et al (2018) is that (i) μ i , the mean of the outcome y i for cluster i can be written as a linear combination of covariates, i.e.…”

Section: Mixed Linear Modelsmentioning

confidence: 99%

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Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini

Héritier

Victoria‐Feser

2017

Stat Methods Appl

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This paper discusses the contribution of Cerioli et al. (Stat Methods Appl, 2018), where robust monitoring based on high breakdown point estimators is proposed for multivariate data. The results follow years of development in robust diagnostic techniques. We discuss the issues of extending data monitoring to other models with complex structure, e.g. factor analysis, mixed linear models for which S and M Mestimators exist or deviating data cells. We emphasise the importance of robust testing that is often overlooked despite robust tests being readily available once S and M Mestimators have been defined. We mention open questions like out-of-sample inference or big data issues that would benefit from monitoring.

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Section: Mixed Linear Modelsmentioning

confidence: 99%

Section: Mixed Linear Modelsmentioning

confidence: 99%

Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini

Héritier

Victoria‐Feser

2017

Stat Methods Appl

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“…In the FA model, the elements of Σ are not linear combinations of the model's parameters γ j and ψ 2 j . Therefore it is not possible (at least not in an easy manner), to use the algorithm proposed by Copt and Victoria-Feser (2006) to find estimates for γ j and ψ 2 j from σ 2 j . In Appendix A, we derive estimating equations for the FA parameters directly from the objective function of the S-estimator, using the Lagrangian of the minimization of |Σ| subject to (2.1) given by…”

Section: Direct Estimatormentioning

confidence: 99%

“…For this type of problems, one can use the results of Copt and Victoria-Feser (2006) who have developed such an estimator for mixed linear models. The trick is to be able to write the covariance matrix Σ as…”

Section: Direct Estimatormentioning

confidence: 99%

“…In this paper, we also propose to estimate the parameter of the FA model directly in a robust fashion. For that, we use a constrained biweight S-estimator (CBS) in the same spirit as the constrained translated biweight S-estimator proposed by Copt and Victoria-Feser (2006) for mixed linear models. We develop an iterative algorithm to compute it in the framework of confirmatory FA.…”

Section: Q < P · K)mentioning

confidence: 99%

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Robust estimation of constrained covariance matrices for confirmatory factor analysis

Lozeron

Victoria‐Feser

2010

Computational Statistics & Data Analysis

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Confirmatory factor analysis (CFA) is a data anylsis procedure that is widely used in social and behavioral sciences in general and other applied sciences that deal with large quantities of data (variables).The underlying model links a set latent factors, that are supposed to correspond to latent concepts, to a larger set of observed (manifest) variables through linear regression equations. With CFA, it is not necessary that all manifest variables are linked to all latent factors, and is particularly useful for the construction of so-called measurement scales like depression scales in psychology. The classical estimator (and inference) procedures are based either on the maximum likelihood (ML) or generalized least squares (GLS) approaches. Unfortunately these methods are known to be non robust to model misspecification, which in the case of factor analysis in general, and in CFA in particular, is misspecification with respect to the multivariate normal model. A natural robust estimator is obtained by first estimating the (mean and) covariance matrix of the manifest variables and then "plug-in" this statistic into the ML or GLS estimating equations. This two-stage method however doesn't fully take into account the covariance structure implied by the CFA model. In this paper, we propose an S-estimator for 1 the parameters of the CFA model that is computed directly from the data. We derive the estimating equations and an iterative procedure.The two estimators have different asymptotic properties, in that their asymptotic covariance matrix is not the same, and they both depend on the model and the parameters values. We perform a simulation study to compare the finite sample properties of both estimators and find that the direct estimator we propose is more stable (smaller MSE) than the two-stage estimator.2

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2018

Robust Statistics

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High-Breakdown Inference for Mixed Linear Models

Cited by 43 publications

References 88 publications

Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini

Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini

Robust estimation of constrained covariance matrices for confirmatory factor analysis

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