Hello

I'd really appreciate any advice or references anyone may have about 
the following problem.

I'm investigating a multi-stage cluster design sampling problem.  I've 
estimated variance components (using REML as the data is unbalanced) 
which when examining the residuals showed the data was skewed.  So 
after log transforming the data, for which the residuals are constant, 
the variance components when used in the multi-stage formulae give 
unrealistic answers.

I know its to do with arithmetic versus geometric but I am unsure as to 
the appropriate transfromation which needs to be applied to the 
variance components of the log transformed data.

I've just ordered the papers

Wilson BG, Adams BJ and Karney BJ (1990).  Bias in log-transformed 
frequency distributions.  J. Hydrol. Amst., 118, 19-37

Lyles RH and Kupper LL. (1998).   UMVU estimators for the population 
mean and variance based on random effects models for lognormal data.  
Comm. in Stats. - Theory and Methods, 27, 4, 795-818

Attfield MD and Hewett P (1992).  Exact expressions for the bias and 
variance of estimators of the mean of a lognormal distribution. Amer. 
Ind. Hyg. Assoc. J., 53, 7, 432-435  (This paper deals with balanced 
data)

which will hopefully shed some light on the problem.

Many thanks in advance.

Michelle.


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Michelle Allen

Biometrics Division
Department of Agriculture for Northern Ireland (DANI)
Newforge Lane
Belfast BT9 5PX

E-mail:  [log in to unmask]

Tel No:  44 +1232 255235     Fax No:  44 +1232 681216

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