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Kanuti Ngailo E, Ngaruye I. Asymptotic results for expected probability of misclassifications in linear discriminant analysis with repeated measurements. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2116286] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Edward Kanuti Ngailo
- Department of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, University of Dar es Salaam, Dar es Salaam, Tanzania
| | - Innocent Ngaruye
- Department of Mathematics, College of Science and Technology, University of Rwanda, Kigali, Rwanda
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2
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Jurková V, Žežula I, Klein D, Hutník O. Unbiased estimator of correlation coefficient. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1743314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Veronika Jurková
- Institute of Mathematics, P. J. Šafárik University, Košice, Slovakia
| | - Ivan Žežula
- Institute of Mathematics, P. J. Šafárik University, Košice, Slovakia
| | - Daniel Klein
- Institute of Mathematics, P. J. Šafárik University, Košice, Slovakia
| | - Ondrej Hutník
- Institute of Mathematics, P. J. Šafárik University, Košice, Slovakia
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3
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Jurková V, Žežula I, Klein D. Testing in the growth curve model with intraclass correlation structure. STATISTICS-ABINGDON 2020. [DOI: 10.1080/02331888.2020.1811983] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Veronika Jurková
- Department of Mathematics, University of P. J. Šafárik, Košice, Slovakia
| | - Ivan Žežula
- Department of Mathematics, University of P. J. Šafárik, Košice, Slovakia
| | - Daniel Klein
- Department of Mathematics, University of P. J. Šafárik, Košice, Slovakia
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4
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Hamid JS, Huang WL, von Rosen D. Graphical analysis of residuals in multivariate growth curve models and applications in the analysis of longitudinal data. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1775849] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Jemila S. Hamid
- Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
- McMaster University, Hamilton, Canada
| | | | - Dietrich von Rosen
- Swedish Agricultural University, Uppsala, Sweden
- Linköping University, Linköping, Sweden
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5
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Jana S, Balakrishnan N, Hamid JS. Inference in the Growth Curve Model under Multivariate Skew Normal Distribution. SANKHYA B 2018. [DOI: 10.1007/s13571-018-0174-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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6
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Jana S, Balakrishnan N, Hamid JS. Bayesian growth curve model useful for high-dimensional longitudinal data. J Appl Stat 2018. [DOI: 10.1080/02664763.2018.1517145] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Sayantee Jana
- Department of Mathematics and Statistics, McMaster University, Hamilton, Canada
| | | | - Jemila S. Hamid
- Department of Mathematics and Statistics, McMaster University, Hamilton, Canada
- Li Ka Shing Knowledge Institute, St. Michael's Hospital, Toronto, Canada
- Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Canada
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7
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Estimation of the parameters of the extended growth curve model under multivariate skew normal distribution. J MULTIVARIATE ANAL 2018. [DOI: 10.1016/j.jmva.2018.02.008] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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8
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Xin X, Qiu F. Multiple-response repeated measurement or multivariate growth curve model with distribution-free errors. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2017.1300273] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Xin Xin
- School of Mathematics and Statistics, Henan University, Kaifeng, Henan, P.R. China
| | - Feng Qiu
- Science College, Zhejiang Agriculture and Forestry University, Linan, Zhejiang, P.R. China
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9
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Berger MPF. A Comparison of Efficiencies of Longitudinal, Mixed Longitudinal, and Cross-Sectional Designs. ACTA ACUST UNITED AC 2016. [DOI: 10.3102/10769986011003171] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The choice among a longitudinal, mixed longitudinal, or cross-sectional design is often called for in educational and psychological research. The problem of choosing the most efficient design to estimate polynomial parameters for time-structured data is considered, and the comparison of the efficiencies shows that the assumed degree of the polynomial is crucial for the selection of the most efficient design. When the degree is much smaller than the number of time points and the correlations between adjacent time points are not too large, cross-sectional and mixed longitudinal designs are more efficient than a longitudinal design.
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10
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11
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High dimensional extension of the growth curve model and its application in genetics. STAT METHOD APPL-GER 2016. [DOI: 10.1007/s10260-016-0369-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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12
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Abstract
The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j
in a subset of Rp
and θ is a finite-dimensional parameter. The particular cases of
0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j
} are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient.
Contributions of the paper include: study of the Rp
case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j
} is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.
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13
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Srivastava MS, Singull M. Test for the mean matrix in a Growth Curve model for high dimensions. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2015.1132328] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | - Martin Singull
- Department of Mathematics, Linköping University, Linköping, Sweden
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14
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Bejar II. Nutritional Intervention. Eval Health Prof 2016. [DOI: 10.1177/016327878100400203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A secondary analysis of a nutrition experi ment in Cali, Colombia was conducted. The theme of the reanalysis was the notion of competing methods of analysts. Specifically, the effect of nutritional supplementa tion on the physical development of malnourished children was analyzed by means of univariate and multivariate methods for the analysis of repeated measures. It was concluded that the nutritional treatment was successful, but to assess the precise nature of the effect, it was necessary to resort to the multivariate approach.
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15
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Song G, Chang H. Equalities of various estimators in the general growth curve model and the restricted growth curve model. J Stat Plan Inference 2016. [DOI: 10.1016/j.jspi.2015.09.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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16
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Browne MW, Shapiro A. Comment on the asymptotics of a distribution-free goodness of fit test statistic. PSYCHOMETRIKA 2015; 80:196-199. [PMID: 24306556 DOI: 10.1007/s11336-013-9383-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Indexed: 06/02/2023]
Abstract
In a recent article Jennrich and Satorra (Psychometrika 78: 545-552, 2013) showed that a proof by Browne (British Journal of Mathematical and Statistical Psychology 37: 62-83, 1984) of the asymptotic distribution of a goodness of fit test statistic is incomplete because it fails to prove that the orthogonal component function employed is continuous. Jennrich and Satorra (Psychometrika 78: 545-552, 2013) showed how Browne's proof can be completed satisfactorily but this required the development of an extensive and mathematically sophisticated framework for continuous orthogonal component functions. This short note provides a simple proof of the asymptotic distribution of Browne's (British Journal of Mathematical and Statistical Psychology 37: 62-83, 1984) test statistic by using an equivalent form of the statistic that does not involve orthogonal component functions and consequently avoids all complicating issues associated with them.
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Affiliation(s)
- Michael W Browne
- Department of Psychology, The Ohio State University, 1835 Neil Avenue, Columbus, OH, 43210-1222, USA,
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17
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Ricker M, Peña Ramírez VM, von Rosen D. A new method to compare statistical tree growth curves: the PL-GMANOVA model and its application with dendrochronological data. PLoS One 2014; 9:e112396. [PMID: 25402427 PMCID: PMC4234403 DOI: 10.1371/journal.pone.0112396] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2014] [Accepted: 10/14/2014] [Indexed: 11/18/2022] Open
Abstract
Growth curves are monotonically increasing functions that measure repeatedly the same subjects over time. The classical growth curve model in the statistical literature is the Generalized Multivariate Analysis of Variance (GMANOVA) model. In order to model the tree trunk radius (r) over time (t) of trees on different sites, GMANOVA is combined here with the adapted PL regression model Q = A · T+E, where for b ≠ 0 : Q = Ei[-b · r]-Ei[-b · r1] and for b = 0 : Q = Ln[r/r1], A = initial relative growth to be estimated, T = t-t1, and E is an error term for each tree and time point. Furthermore, Ei[-b · r] = ∫(Exp[-b · r]/r)dr, b = -1/TPR, with TPR being the turning point radius in a sigmoid curve, and r1 at t1 is an estimated calibrating time-radius point. Advantages of the approach are that growth rates can be compared among growth curves with different turning point radiuses and different starting points, hidden outliers are easily detectable, the method is statistically robust, and heteroscedasticity of the residuals among time points is allowed. The model was implemented with dendrochronological data of 235 Pinus montezumae trees on ten Mexican volcano sites to calculate comparison intervals for the estimated initial relative growth A. One site (at the Popocatépetl volcano) stood out, with A being 3.9 times the value of the site with the slowest-growing trees. Calculating variance components for the initial relative growth, 34% of the growth variation was found among sites, 31% among trees, and 35% over time. Without the Popocatépetl site, the numbers changed to 7%, 42%, and 51%. Further explanation of differences in growth would need to focus on factors that vary within sites and over time.
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Affiliation(s)
- Martin Ricker
- Departamento de Botánica, Instituto de Biología, Universidad Nacional Autónoma de México (UNAM), México D.F., Mexico
- * E-mail:
| | - Víctor M. Peña Ramírez
- Posgrado en Ciencias Biológicas, Universidad Nacional Autónoma de México (UNAM), México D.F., Mexico
| | - Dietrich von Rosen
- Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden
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18
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Jöreskog KG, van Thillo M, Gruvaeus GT. ACOVSM: A GENERAL COMPUTER PROGRAM FOR ANALYSIS OF COVARIANCE STRUCTURES INCLUDING GENERALIZED MANOVA1. ACTA ACUST UNITED AC 2014. [DOI: 10.1002/j.2333-8504.1971.tb00180.x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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19
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Hu J, Xin X, You J. Model determination and estimation for the growth curve model via group SCAD penalty. J MULTIVARIATE ANAL 2014. [DOI: 10.1016/j.jmva.2013.11.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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20
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Friedrich T, Knapp G. Generalised interval estimation in the random effects meta regression model. Comput Stat Data Anal 2013. [DOI: 10.1016/j.csda.2013.03.011] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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21
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Jing Song G, Wen Wang Q. On the weighted least-squares, the ordinary least-squares and the best linear unbiased estimators under a restricted growth curve model. Stat Pap (Berl) 2012. [DOI: 10.1007/s00362-012-0483-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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22
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Wu J, Bentler PM. Limited Information Estimation in Binary Factor Analysis: A Review and Extension. Comput Stat Data Anal 2012; 57:392-403. [PMID: 22904587 DOI: 10.1016/j.csda.2012.06.022] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
Based on the Bayes modal estimate of factor scores in binary latent variable models, this paper proposes two new limited information estimators for the factor analysis model with a logistic link function for binary data based on Bernoulli distributions up to the second and the third order with maximum likelihood estimation and Laplace approximations to required integrals. These estimators and two existing limited information weighted least squares estimators are studied empirically. The limited information estimators compare favorably to full information estimators based on marginal maximum likelihood, MCMC, and multinomial distribution with a Laplace approximation methodology. Among the various estimators, Maydeu-Olivares and Joe's (2005) weighted least squares limited information estimators implemented with Laplace approximations for probabilities are shown in a simulation to have the best root mean square errors.
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23
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Hu J, Liu F, You J. Estimation of parameters in a generalized GMANOVA model based on an outer product analogy and least squares. J Stat Plan Inference 2012. [DOI: 10.1016/j.jspi.2012.01.022] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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24
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Estimation of parameters in the growth curve model via an outer product least squares approach for covariance. J MULTIVARIATE ANAL 2012. [DOI: 10.1016/j.jmva.2012.02.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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25
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Stanek EJ, Koch GG. The Equivalence of Parameter Estimates from Growth Curve Models and Seemingly Unrelated Regression Models. AM STAT 2012. [DOI: 10.1080/00031305.1985.10479417] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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26
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Zhang G, Ferrari S, Cai C. A comparison of information functions and search strategies for sensor planning in target classification. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS. PART B, CYBERNETICS : A PUBLICATION OF THE IEEE SYSTEMS, MAN, AND CYBERNETICS SOCIETY 2011; 42:2-16. [PMID: 22057064 DOI: 10.1109/tsmcb.2011.2165336] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
This paper investigates the comparative performance of several information-driven search strategies and decision rules using a canonical target classification problem. Five sensor models are considered: one obtained from classical estimation theory and four obtained from Bernoulli, Poisson, binomial, and mixture-of-binomial distributions. A systematic approach is presented for deriving information functions that represent the expected utility of future sensor measurements from mutual information, Rènyi divergence, Kullback-Leibler divergence, information potential, quadratic entropy, and the Cauchy-Schwarz distance. The resulting information-driven strategies are compared to direct-search, alert-confirm, task-driven (TS), and log-likelihood-ratio (LLR) search strategies. Extensive numerical simulations show that quadratic entropy typically leads to the most effective search strategy with respect to correct-classification rates. In the presence of prior information, the quadratic-entropy-driven strategy also displays the lowest rate of false alarms. However, when prior information is absent or very noisy, TS and LLR strategies achieve the lowest false-alarm rates for the Bernoulli, mixture-of-binomial, and classical sensor models.
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Affiliation(s)
- Guoxian Zhang
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA.
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27
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Hu J, Yan G, You J. Estimation for an additive growth curve model with orthogonal design matrices. BERNOULLI 2011. [DOI: 10.3150/10-bej315] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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28
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29
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Hamid JS, Beyene J, von Rosen D. A novel trace test for the mean parameters in a multivariate growth curve model. J MULTIVARIATE ANAL 2011. [DOI: 10.1016/j.jmva.2010.09.001] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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30
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Asmussen S, Rydén T. A Note on Skewness in Regenerative Simulation. COMMUN STAT-SIMUL C 2010. [DOI: 10.1080/03610918.2010.526740] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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31
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Abstract
We extend the standard multivariate mixed model by incorporating a smooth time effect and relaxing distributional assumptions. We propose a semiparametric Bayesian approach to multivariate longitudinal data using a mixture of Polya trees prior distribution. Usually, the distribution of random effects in a longitudinal data model is assumed to be Gaussian. However, the normality assumption may be suspect, particularly if the estimated longitudinal trajectory parameters exhibit multimodality and skewness. In this paper we propose a mixture of Polya trees prior density to address the limitations of the parametric random effects distribution. We illustrate the methodology by analyzing data from a recent HIV-AIDS study.
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Affiliation(s)
- Pulak Ghosh
- Department of Quantitative Methods & Information Systems, Indian Institute of Management, Bangalore, India
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32
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Ohlson M, von Rosen D. Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices. J MULTIVARIATE ANAL 2010. [DOI: 10.1016/j.jmva.2009.12.023] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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33
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Hassani H, Zokaei M, von Rosen D, Amiri S, Ghodsi M. Does noise reduction matter for curve fitting in growth curve models? COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2009; 96:173-181. [PMID: 19573946 DOI: 10.1016/j.cmpb.2009.04.014] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2008] [Revised: 03/17/2009] [Accepted: 04/20/2009] [Indexed: 05/28/2023]
Abstract
In this paper, we discuss the efficiency of noise reduction for curve fitting in nonlinear growth curve models. We use singular spectrum analysis as a nonlinear-nonparametric denoising method. A set of longitudinal measurements is used in considering the performance of the method. We also use artificially generated data sets with and without noise for the purpose of validation of the results obtained in this study. The results show that noise reduction is important for curve fitting in growth curve models and also, that the singular spectrum analysis technique can be used as a powerful tool for noise reduction in longitudinal measurements.
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Affiliation(s)
- Hossein Hassani
- Centre for Optimisation and Its Applications, Cardiff University, United Kingdom
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34
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Takane Y, Jung S. Tests of ignoring and eliminating in nonsymmetric correspondence analysis. ADV DATA ANAL CLASSI 2009. [DOI: 10.1007/s11634-009-0054-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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35
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Tian Y, Takane Y. On consistency, natural restrictions and estimability under classical and extended growth curve models. J Stat Plan Inference 2009. [DOI: 10.1016/j.jspi.2008.11.017] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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36
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Jammalamadaka SR, Siddiqi MA, Ghosh K. Analysis of microtubule dynamics using growth curve models. J Appl Stat 2009. [DOI: 10.1080/02664760802479131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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37
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Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions. J MULTIVARIATE ANAL 2009. [DOI: 10.1016/j.jmva.2008.06.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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38
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Kabe DG. Generalized manova double linear hypothesis with double linear restrictions. CAN J STAT 2008. [DOI: 10.2307/3315097] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- D. G. Kabe
- St. Mary's University and Dalhousie University
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39
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Vasdekis VGS. A Comparison of REML and Covariance Adjustment Method in the Estimation of Growth Curve Models. COMMUN STAT-THEOR M 2008. [DOI: 10.1080/03610920802162649] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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40
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Albert JM, Kshirsagar AM. THE REDUCED-RANK GROWTH CURVE MODEL FOR DISCRIMINANT ANALYSIS OF LONGITUDINAL DATA. ACTA ACUST UNITED AC 2008. [DOI: 10.1111/j.1467-842x.1993.tb01342.x] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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41
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42
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Isotalo J, Puntanen S, Styan GPH. A Useful Matrix Decomposition and Its Statistical Applications in Linear Regression. COMMUN STAT-THEOR M 2008. [DOI: 10.1080/03610920701666328] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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43
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Boik RJ. An implicit function approach to constrained optimization with applications to asymptotic expansions. J MULTIVARIATE ANAL 2008. [DOI: 10.1016/j.jmva.2007.01.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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44
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Generalized constrained co-inertia analysis. ADV DATA ANAL CLASSI 2008. [DOI: 10.1007/s11634-008-0017-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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45
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46
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KOLLO TÕNU, ROOS ANU, VON ROSEN DIETRICH. Approximation of the Distribution of the Location Parameter in the Growth Curve Model. Scand Stat Theory Appl 2007. [DOI: 10.1111/j.1467-9469.2006.00546.x] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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47
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48
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Woolson RF, Leeper JD. Growth curve analysis of complete and incomplete longitudinal data. COMMUN STAT-THEOR M 2007. [DOI: 10.1080/03610928008827977] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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49
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50
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Reinsel GC. Effects of the estimation of covariance matrix parameters in the generalized multivariate linear model. COMMUN STAT-THEOR M 2007. [DOI: 10.1080/03610928408828707] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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