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

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

##### Date

2012-07-25

##### Authors

Eideh, Abdulhakeem A. H.

##### Journal Title

##### Journal ISSN

##### Volume Title

##### Publisher

Taylor & Francis

##### 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.

##### Description

##### Keywords

Fixed effects model,
Informative sampling,
Maximum likelihood estimation,
Pseudo maximum likelihood,
Sample distribution,
Variance components model

##### 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