Simplifying General Least Squares

Hayes, Kevin J.; Haslett, John

doi:10.2307/2686060

Cited by 5 publications

(9 citation statements)

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“…hence, for example,β = BY andγ j = τ j Z j QY estimate β and predict γ j . (There are, however, errors in Table 1 in Hayes and Haslett (1999); see Appendix B). The matrix Q is of central importance; it is often shown in the literature as Haslett and Hayes, 1998) is…”

Section: The Conditional Residual and Some Related Identitiesmentioning

confidence: 99%

“…For example, with U = β, we have C = 0 and A = I; with U = γ j , C = τ j Z j and A = 0. Then, following Hayes and Haslett (1999), the matrices Λ, Λ .a/ and L .a/ satisfy…”

Section: Proof Of Identitymentioning

confidence: 99%

“…This completes the proof. Hayes and Haslett (1999) showed that most useful matrices that are needed in generalized least squares derive from writing…”

Section: Proof Of Identitymentioning

confidence: 99%

“…There are errors in Table 1 in Hayes and Haslett (1999). In their notation, at expression (2) should be the pair .X T 0 , 0/ and at expression (4) should be the pair .WGW T 0 , 0/.…”

Section: Appendix B: Errata In Hayes and Haslett (1999)mentioning

confidence: 99%

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Application of ‘Delete = Replace’ to Deletion Diagnostics for Variance Component Estimation in the Linear Mixed Model

Haslett

Dillane²

2003

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary. ‘Delete = replace’ is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by‐product of the fitting process. We illustrate the effect of the deletion of individual observations, of ‘subjects’ and of arbitrary subsets. Central to the identity and its application is the conditional residual.

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Section: The Conditional Residual and Some Related Identitiesmentioning

confidence: 99%

“…For example, with U = β, we have C = 0 and A = I; with U = γ j , C = τ j Z j and A = 0. Then, following Hayes and Haslett (1999), the matrices Λ, Λ .a/ and L .a/ satisfy…”

Section: Proof Of Identitymentioning

confidence: 99%

“…This completes the proof. Hayes and Haslett (1999) showed that most useful matrices that are needed in generalized least squares derive from writing…”

Section: Proof Of Identitymentioning

confidence: 99%

“…There are errors in Table 1 in Hayes and Haslett (1999). In their notation, at expression (2) should be the pair .X T 0 , 0/ and at expression (4) should be the pair .WGW T 0 , 0/.…”

Section: Appendix B: Errata In Hayes and Haslett (1999)mentioning

confidence: 99%

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Application of ‘Delete = Replace’ to Deletion Diagnostics for Variance Component Estimation in the Linear Mixed Model

Haslett

Dillane²

2003

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…A first set of deleted estimates can be obtained by application of the results of Haslett and Hayes, and Hayes and Haslett [17,35], viz. :̂(…”

Section: Deletion Estimatesmentioning

confidence: 99%

Deletion diagnostics for the generalised linear mixed model with independent random effects

Ganguli

Roy

Naskar

et al. 2015

Statistics in Medicine

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The Generalised Linear Mixed Model (GLMM) is widely used for modelling environmental data. However, such data are prone to influential observations which can distort the estimated exposure-response curve particularly in regions of high exposure. Deletion diagnostics for iterative estimation schemes commonly derive the deleted estimates based on a single iteration of the full system holding certain pivotal quantities such as the information matrix to be constant. In this paper, we present an approximate formula for the deleted estimates and Cook’s distance for the GLMM which does not assume that the estimates of variance parameters are unaffected by deletion. The procedure allows the user to calculate standardised DFBETAs for mean as well as variance parameters. In certain cases, such as when using the GLMM as a device for smoothing, such residuals for the variance parameters are interesting in their own right. In general, the procedure leads to deleted estimates of mean parameters which are corrected for the effect of deletion on variance components as estimation of the two sets of parameters is interdependent. The probabilistic behaviour of these residuals is investigated and a simulation based procedure suggested for their standardisation. The method is used to identify influential individuals in an occupational cohort exposed to silica. The results show that failure to conduct post model fitting diagnostics for variance components can lead to erroneous conclusions about the fitted curve and unstable confidence intervals.

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Deletion, replacement and mean-shift for diagnostics in linear mixed models

Shi

Chen

2012

Computational Statistics & Data Analysis

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Simplifying General Least Squares

Cited by 5 publications

References 0 publications

Application of ‘Delete = Replace’ to Deletion Diagnostics for Variance Component Estimation in the Linear Mixed Model

Application of ‘Delete = Replace’ to Deletion Diagnostics for Variance Component Estimation in the Linear Mixed Model

Deletion diagnostics for the generalised linear mixed model with independent random effects

Deletion, replacement and mean-shift for diagnostics in linear mixed models

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