## Fitting Variance Components Model and Fixed Effects Model for One-Way Analysis of Variance to Complex Survey Data

 dc.contributor.author Eideh, Abdulhakeem A. H. dc.date.accessioned 2018-08-26T09:59:02Z dc.date.available 2018-08-26T09:59:02Z dc.date.issued 2012-07-25 dc.description.abstract Under complex survey sampling, in particular when selection probabilities depend on the response variable (informative sampling), the sample and population distributions are different, possibly resulting in selection bias. This article is concerned with this problem by fitting two statistical models, namely: the variance components model (a two-stage model) and the fixed effects model (a single-stage model) for one-way analysis of variance, under complex survey design, for example, two-stage sampling, stratification, and unequal probability of selection, etc. Classical theory underlying the use of the two-stage model involves simple random sampling for each of the two stages. In such cases the model in the sample, after sample selection, is the same as model for the population; before sample selection. When the selection probabilities are related to the values of the response variable, standard estimates of the population model parameters may be severely biased, leading possibly to false inference. The idea behind the approach is to extract the model holding for the sample data as a function of the model in the population and of the first order inclusion probabilities. And then fit the sample model, using analysis of variance, maximum likelihood, and pseudo maximum likelihood methods of estimation. The main feature of the proposed techniques is related to their behavior in terms of the informativeness parameter. We also show that the use of the population model that ignores the informative sampling design, yields biased model fitting. en_US dc.description.sponsorship The author is grateful to Gad Nathan, to the Associate Editor and to the referees for constructive comments and suggestions that helped improving the quality of the article. en_US dc.identifier.citation Abdulhakeem A. H. Eideh (2012): Fitting Variance Components Model and Fixed Effects Model for One- Way Analysis of Variance to Complex Survey Data, Communications in Statistics - Theory and Methods, 41:16-17, 3278-3300 en_US dc.identifier.issn 1532-415X dc.identifier.uri https://dspace.alquds.edu/handle/20.500.12213/784 dc.language.iso en_US en_US dc.publisher Taylor & Francis en_US dc.subject Fixed effects model en_US dc.subject Informative sampling en_US dc.subject Maximum likelihood estimation en_US dc.subject Pseudo maximum likelihood en_US dc.subject Sample distribution en_US dc.subject Variance components model en_US dc.title Fitting Variance Components Model and Fixed Effects Model for One-Way Analysis of Variance to Complex Survey Data en_US dc.type Article en_US
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