Profile Analysis with Random-Effects Covariance Structure

Srivastava, M. S.; Singull, Martin

doi:10.14490/jjss.42.145

Cited by 8 publications

(7 citation statements)

References 11 publications

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“…Remark 1. As we mentioned in Section 1, Srivastava and Singull (2012) suggest using the M-LRT even in the case of testing (1.4) although the M-LRT is derived for testing (1.5). However, the null hypothesis H 0 * considered by Srivastava and Singull (2012) includes H 11 (i.e., H 11 is a part of the null hypothesis H 0 * ).…”

Section: Conservativeness and Powermentioning

confidence: 99%

“…Then, the hypothesis (1.5) is tested by using χ 2 f . Under H 0 Srivastava and Singull (2012) showed that the limiting approximation of the distribution of the M-LRT is better than that of the R-LRT proposed by Yokoyama (1995). Moreover, through numerical experiments, they also showed that the power for the M-LRT is larger than the power for the R-LRT.…”

Section: Introductionmentioning

confidence: 97%

“…On the other hand, Srivastava and Singull (2012) constructed the test based on the likelihood ratio, without the non-negativity of λ 2 in (1.4), for testing the random-effects covariance structure under the parallel profile model. In other words, they considered the following hypothesis: H 0 * : Σ = ρ1 p 1 p + σ 2 I p for some ρ > −σ 2 /p and σ 2 > 0 v.s.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic Expansions of the Null Distribution of the LR Test Statistic for Random-Effects Covariance Structure in a Parallel Profile Model

Inatsu

Wakaki

2016

JJSS

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This paper is concerned with the null distribution of the likelihood ratio test statistic −2 log Λ for testing the adequacy of a random-effects covariance structure in a parallel profile model. It is known that the null distribution of −2 log Λ converges to χ 2 f or 0.5χ 2 f + 0.5χ 2 f +1 when the sample size tends to infinity. In order to extend this result, we derive asymptotic expansions of the null distribution of −2 log Λ. The accuracy of the approximations based on the limiting distribution and an asymptotic expansion are compared through numerical experiments.

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Section: Conservativeness and Powermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic Expansions of the Null Distribution of the LR Test Statistic for Random-Effects Covariance Structure in a Parallel Profile Model

Inatsu

Wakaki

2016

JJSS

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“…This class of model has been considered by many authors and estimation of parameters of interest has been discussed with different choices of C and Z. See for example Nummi (1997); Ip et al (2007); Lange and Laird (1989); Yokoyama and Fujikoshi (1993); Yokoyama (2001); Srivastava and Singull (2012) for more details.…”

Section: Random Effect Growth Curve Modelmentioning

confidence: 99%

Small Area Estimation for Multivariate Repeated Measures Data

Ngaruye

2014

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This thesis considers Small Area Estimation with a main focus on estimation and prediction theory for repeated measures data. The demand for small area statistics is for both cross-sectional and repeated measures data. For instance, small area estimates for repeated measures data may be used by public policy makers for different purposes such as funds allocation, new educational or health programs and in some cases, they might be interested in a given group of population.It has been shown that the multivariate approach for model-based methods in small area estimation may achieve substantial improvement over the usual univariate approach. In this work, we consider repeated surveys including the same subjects at different time points. The population from which a sample has been drawn is partitioned into several subpopulations and within all subpopulations there is the same number of group units. For this setting a multivariate linear regression model is formulated. The aim of the proposed model is to borrow strength across small areas and over time with a particular interest of growth profiles over time. The model accounts for repeated surveys, group individuals and random effects variations.The estimation of model parameters is discussed with a restricted maximum likelihood based approach. The prediction of random effects and the prediction of small area means across time points, per group units and for all time points are derived. The theoretical results have also been supported by a simulation study and finally, suggestions for future research are presented.v Populärvetenskaplig sammanfattning I den här avhandling diskuteras small area estimation (SAE) med fokus pȧ skattningar av parametrarna samt prediktion för slumpvariabler givet en modell för upprepade mät-ningar. Efterfrȧgan pȧ statistisk inferens för undergrupper av en population (small area statistics) har ökat markant. Till exempel kan sȧdan inferens för upprepad mätningar användas av offentliga beslutsfattare vid tilldelning av ekonomiska resurser, planering av nya utbildnings-eller hälsoprogram och i vissa fall kan det vara av intresse att studera en specifik undergrupp av befolkningen.Det har visat sig att den multivariata framställningen för modellbaserade metoder vid SAE kan uppnȧ betydande bättre resultat jämfört med det vanliga endimensionella modellantagandet. I detta arbete betraktar vi upprepade undersökningar pȧ samma individer vid olika tidpunkter. Populationen frȧn vilket ett urval har tagits är uppdelat i flera delpopulationer och inom alla undergrupper finns det samma antal observationer. För dessa förutsättningar, är en multivariat linjär regressionsmodell formulerad. Syftet med den för-slagna modellen är att lȧna egenskaper mellan undergrupperna och över tid. I modellen ingȧr det upprepade undersökningar, grupper av individer samt slumpmässiga effekter.Parametrarna i den föreslagna modellen skattas med hjälp av restricted maximum likelihood metoden. Prediktion av slumpmässiga effekter samt prediktion av de förväntade värdena i u...

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“…This class of models has been considered by many authors and estimation of parameters of interest has been discussed with different choices of A and Z. See for example Nummi (1997); Ip et al (2007); Lange and Laird (1989); Yokoyama and Fujikoshi (1993);Yokoyama (2001); Srivastava and Singull (2012) for more details. In what follows, we consider a particular case where Σ e has simple structure, i.e., Σ e = σ 2 e I p and present the estimation and prediction framework in model (2.11).…”

Section: Random Effects Growth Curve Modelsmentioning

confidence: 99%

Contributions to Small Area Estimation: Using Random Eects Growth Curve Model

Ngaruye¹

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Profile Analysis with Random-Effects Covariance Structure

Cited by 8 publications

References 11 publications

Asymptotic Expansions of the Null Distribution of the LR Test Statistic for Random-Effects Covariance Structure in a Parallel Profile Model

Asymptotic Expansions of the Null Distribution of the LR Test Statistic for Random-Effects Covariance Structure in a Parallel Profile Model

Small Area Estimation for Multivariate Repeated Measures Data

Contributions to Small Area Estimation: Using Random Eects Growth Curve Model

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