Profile Analysis for a Growth Curve Model

Ohlson, Martin; Srivastava, M. S.

doi:10.14490/jjss.40.001

Cited by 9 publications

(4 citation statements)

References 9 publications

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“…The estimation, testing and model diagnostic problems for GC model and its extensions have been investigated by several authors, see for example, Potthoff and Roy (1964); von Rosen (1989); Khatri (1973); Rao (1958); Nzabanita et al (2012); Ohlson and Srivastava (2010). Theorem 2.2 gives the MLEs for a classical GC model.…”

Section: 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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Section: Growth Curve Modelmentioning

confidence: 99%

Small Area Estimation for Multivariate Repeated Measures Data

Ngaruye

2014

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“…Illuminating chapters on profile analysis can be found in the books by Srivastava and Carter [19] and Srivastava [18]. A more sophisticated approach was suggested by Ohlson and Srivastava [13] who considered profile analysis of several groups, where the groups of subjects only partly had a common profile. In von Rosen [22] an overview of classical profile analysis has been given.…”

Section: Introductionmentioning

confidence: 99%

Profile Analysis in High Dimensions

Cengiz

Rosen

Singull

2020

J Stat Theory Pract

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“…Srivastava (1987) considered the following three hypotheses: (i) The first hypothesis is given by Srivastava (1987) have been extended by Ohlson and Srivastava (2010) where subvectors of the mean vectors are equal, that is, the profile analysis in a growth curve model is discussed. Some other aspects of profile analysis have recently been considered by many authors, such as Okamoto et al (2006) and Maruyama (2007).…”

Section: Introductionmentioning

confidence: 99%

Profile Analysis with Random-Effects Covariance Structure

Srivastava

Singull

2012

JJSS

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In this paper, we consider a parallel profile model for several groups. Given the parallel profile model we construct tests based on the likelihood ratio, without any restrictions on the parameter space, for testing the covariance matrix for random-effects structure or sphericity. Furthermore, given both the parallel profile and random-effects covariance structure the level hypothesis is tested. The attained significance levels and the empirical powers for the given tests in this paper are compared with the tests given by Yokoyama and Fujikoshi (1993) and Yokoyama (1995).

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Profile Analysis for a Growth Curve Model

Cited by 9 publications

References 9 publications

Small Area Estimation for Multivariate Repeated Measures Data

Small Area Estimation for Multivariate Repeated Measures Data

Profile Analysis in High Dimensions

Profile Analysis with Random-Effects Covariance Structure

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