R help - Dec 2009 - Statistical question and implementation

Dear R/Statistics-gurus!

I tried to find answer to my hypothetical question and in vain. Sorry, I
don't have a dataset that fits into this hypothetical question and pardon me
if my explanations/use of statistical terms are not accurate.

It does sound a weird question, but I want to rule out that line of thought.
Is it possible to develop a model (or a simulation) such that the upper
variability is different from lower variability? e.g, the upper variability
in the data above a model predicted value may be less than the variability
in the data below a model predicted value. I guess mixture model is not
applicable here

Around a population estimate (say, mean or maximum likelihood) one of the
following may apply:
total standard deviation (SD) = SD(lower) + SD(upper)
total variance (var) = var(lower) + var(upper);

If it is possible, how do I assign variability in parameters and residual
(additive + proportional) errors?
To fit the observed,
Y = F + (a^2 +b^2/F^2)
F = f(x,Ai, var(Ai)); where Ai = a matrix of parameters; x = a vector
independent variables; var(Ai) = variability in the parameter (Ai)

Regards,
Santosh

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On Dec 10, 2009, at 10:59 AM, Santosh wrote:
> Dear R/Statistics-gurus!
>
> I tried to find answer to my hypothetical question and in vain.  
> Sorry, I
> don't have a dataset that fits into this hypothetical question and  
> pardon me
> if my explanations/use of statistical terms are not accurate.
>
> It does sound a weird question, but I want to rule out that line of  
> thought.
> Is it possible to develop a model (or a simulation) such that the  
> upper
> variability is different from lower variability? e.g, the upper  
> variability
> in the data above a model predicted value may be less than the  
> variability
> in the data below a model predicted value. I guess mixture model is  
> not
> applicable here
Wouldn't any model with Poisson- (and by extension gamma-) distributed  
errors satisfy this requirement? (Not to mention models with even  
heavier right tails)
>
> Around a population estimate (say, mean or maximum likelihood) one  
> of the
> following may apply:
> total standard deviation (SD) = SD(lower) + SD(upper)
> total variance (var) = var(lower) + var(upper);
>
> If it is possible, how do I assign variability in parameters and  
> residual
> (additive + proportional) errors?
> To fit the observed,
> Y = F + (a^2 +b^2/F^2)
> F = f(x,Ai, var(Ai)); where Ai = a matrix of parameters; x = a vector
> independent variables; var(Ai) = variability in the parameter (Ai)
>
> Regards,
> Santosh


David Winsemius, MD
Heritage Laboratories
West Hartford, CT