Iteratively Reweighted Generalized Least Squares for Estimation and Testing With Correlated Data: An Inference Function Framework

Loader, Catherine; Pilla, Ramani S.

doi:10.1198/106186007x238828

Cited by 12 publications

(9 citation statements)

References 12 publications

(22 reference statements)

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“…Can also be turned into linear type of the new variable 5 1 , , Z Z : ε β β β β β β (10) Such transformations can be adopted by the independent variables into a linear type of regression problems; can be seen as the promotion of the linear model.…”

Section: Generalized Linear Regressionmentioning

confidence: 99%

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Notice of Retraction: Study of vehicle braking model and simulation

Zhan-qing

Shi-yong

2010

2010 International Conference on Computer Application and System Modeling (ICCASM 2010)

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In order to accurate calculation vehicle pre-braking speed by the regression analysis data of vehicle braking speed, comparing and analyzing with LS estimation algorithm, instrumental variable estimation algorithm, generalized least squares estimation algorithm and Cor-LS algorithm, LS estimation algorithms is used to study on parameter estimation of the vehicle braking model, introducing multiple linear regression theory, building the pre-brake speed regression model. By using the simulation data, to calculate the braking system dynamic growth factor, to gain pre-braking speed regression model. Solved the problem of calculating vehicle brake speed. In the end, through the high-precision vehicle dynamics simulation model (veDYNA) platform to simulation, comparing the speed model and original model to verify the model speed validity and accuracy, the simulation results show good results

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Section: Generalized Linear Regressionmentioning

confidence: 99%

“…As the vehicle pre-braking speed estimate is subject to many factors, in order to pre-braking speed model can more accurately calculate the pre-braking speed, thus the introduction of multiple linear regression theory [10,11] .…”

Section: A Velocity Pre-braking Speed Modelmentioning

confidence: 99%

Notice of Retraction: Study of vehicle braking model and simulation

Zhan-qing

Shi-yong

2010

2010 International Conference on Computer Application and System Modeling (ICCASM 2010)

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“…In practice, estimated regression parameters,

\overset{bold-italicβ}{true}

, are used inside the empirical covariance weighting matrix,

C_{N} (\overset{bold-italicβ}{true})

, where

\overset{bold-italicβ}{true}

represents the current estimate for β inside QIF's estimating equations at any given point of the iterative estimation procedure that eventually produces the final estimate,

\overset{bold-italicβ}{true}

. Furthermore, initial consistent parameter estimates for the QIF estimation procedure can be found by using GEE with a working independence correlation structure . The use of estimated, rather than true, empirical covariances leads to two sources of negative bias in QIF's SE estimates.…”

Section: A Bias‐corrected Covariance Estimatementioning

confidence: 99%

A bias‐corrected covariance estimate for improved inference with quadratic inference functions

Westgate

2012

Statistics in Medicine

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The method of quadratic inference functions (QIF) is an increasingly popular method for the analysis of correlated data because of its multiple advantages over generalized estimating equations (GEE). One advantage is that it is more efficient for parameter estimation when the working covariance structure for the data is misspecified. In the QIF literature, the asymptotic covariance formula is used to obtain standard errors. We show that in small to moderately sized samples, these standard error estimates can be severely biased downward, therefore inflating test size and decreasing coverage probability. We propose adjustments to the asymptotic covariance formula that eliminate finite-sample biases and, as shown via simulation, lead to substantial improvements in standard error estimates, inference, and coverage. The proposed method is illustrated in application to a cluster randomized trial and a longitudinal study. Furthermore, QIF and GEE are contrasted via simulation and these applications.

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“…is the QIF for the ith group. The form of Q i,n i .γ i / is exactly the same as that derived by Pilla and Loader (2005) provided that we omit the group index i from γ and replace the number of subjects n i with N. The estimatorγ i is found by minimizing Q i,n i .γ i / via the iteratively reweighted generalized least squares (IRGLS) algorithm (Loader and Pilla, 2005a).…”

Section: Large Sample Properties Of the Quadratic Inference Function mentioning

confidence: 99%

“…The QIF estimatorsγ,γ andγ are found by using the IRGLS algorithm (Pilla and Loader, 2005;Loader and Pilla, 2005a). The IRGLS algorithm has the following advantages:…”

Section: Algorithm To Find the Quadratic Inference Function Estimatorsmentioning

confidence: 99%

Testing for Order-Restricted Hypotheses in Longitudinal Data

Pilla

Loader

2006

Journal of the Royal Statistical Society Series B: Statistical Methodology

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In many biomedical studies, we are interested in comparing treatment effects with an inherent ordering. We propose a "quadratic score test" (QST) based on a quadratic inference function for detecting an order in treatment effects for correlated data. The quadratic inference function is similar to the negative of a log-likelihood, and it provides test statistics in the spirit of a "χ"-super-2-test for testing nested hypotheses as well as for assessing the goodness of fit of model assumptions. Under the null hypothesis of no order restriction, it is shown that the QST statistic has a Wald-type asymptotic representation and that the asymptotic distribution of the QST statistic is a weighted "χ"-super-2-distribution. Furthermore, an asymptotic distribution of the QST statistic under an arbitrary convex cone alternative is provided. The performance of the QST is investigated through Monte Carlo simulation experiments. Analysis of the polyposis data demonstrates that the QST outperforms the Wald test when data are highly correlated with a small sample size and there is a significant amount of missing data with a small number of clusters. The proposed test statistic accommodates both time-dependent and time-independent covariates in a model. Copyright 2006 Royal Statistical Society.

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Iteratively Reweighted Generalized Least Squares for Estimation and Testing With Correlated Data: An Inference Function Framework

Cited by 12 publications

References 12 publications

Notice of Retraction: Study of vehicle braking model and simulation

Notice of Retraction: Study of vehicle braking model and simulation

A bias‐corrected covariance estimate for improved inference with quadratic inference functions

Testing for Order-Restricted Hypotheses in Longitudinal Data

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