{"title":"Maximum likelihood estimators for extended growth curve model with orthogonal between-individual design matrices","authors":"Daniel Klein, Ivan Žežula","doi":"10.1016/j.stamet.2014.09.005","DOIUrl":null,"url":null,"abstract":"<div><p><span>The extended growth curve model is discussed in this paper. There are two versions of the model studied in the literature, which differ in the way how the column spaces of the design matrices<span> are nested. The nesting is applied either to the between-individual or to the within-individual design matrices. Although both versions are equivalent via reparametrization, the properties of estimators cannot be transferred directly because of non-linearity of estimators. Since in many applications the between-individual matrices are one-way ANOVA matrices, it is reasonable to assume </span></span>orthogonality<span> of the column spaces of between-individual design matrices along with nestedness of the column spaces of within-individual design matrices. We present the maximum likelihood estimators and their basic moments for the model with such orthogonality condition.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"23 ","pages":"Pages 59-72"},"PeriodicalIF":0.0000,"publicationDate":"2015-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.09.005","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312714000732","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 5
Abstract
The extended growth curve model is discussed in this paper. There are two versions of the model studied in the literature, which differ in the way how the column spaces of the design matrices are nested. The nesting is applied either to the between-individual or to the within-individual design matrices. Although both versions are equivalent via reparametrization, the properties of estimators cannot be transferred directly because of non-linearity of estimators. Since in many applications the between-individual matrices are one-way ANOVA matrices, it is reasonable to assume orthogonality of the column spaces of between-individual design matrices along with nestedness of the column spaces of within-individual design matrices. We present the maximum likelihood estimators and their basic moments for the model with such orthogonality condition.
期刊介绍：
Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.
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