Advances and Applications in Statistics
Volume 4, Issue 3, Pages 253 - 264
(December 2004)
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EXTRA-VARIATION AND BAYESIAN BINOMIAL REGRESSION MODELS FOR ESTIMATING EARNINGS PROBABILITIES USING A THREE-WAY LAYOUT INCOME DATA
Ibrahim M. Abdalla (U. A. E.)
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Abstract: This paper
attempts to obtain improved estimates of
probabilities in a three-way
cross-classification of categorical variables;
namely, education level, labor market sector
and workers’ nationality. Analysis is based
on data made available from Abu-Dhabi Emirate
Family Expenditure Survey, 1997, to estimate
probability of low earnings. The sample
proportion, the maximum likelihood estimate,
is the classical estimator for this parameter.
However, the estimate may possess undesirable
features, particularly, when the data are
sparse. Alternatively, a main effects model
could be fitted to the data, seeking
relationships between the proportion at each
combination and certain levels of the
categorical variables involved. This could
produce smaller standard errors, but does not
take into account uncertainty associated with
model parameters and may not account for extra
sampling variance in the data. An expanded
model that accounts for over-dispersion in the
data could improve the fit. However, a random
effect model through Bayesian estimation,
based on Markov Chain Monte Carlo (MCMC)
simulation implemented using WinBUGS software,
provides better estimates that compromise
between the two classical and main effects
approaches. |
Keywords and phrases: logistic regression, extra-variation, earnings probabilities, Bayesian methods. |
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