 Hi Colin,

The GAMLSS package allows modelling of the response variable distribution
using either Exponential family or non-Exponential family distributions.
It also allows modelling of the scale parameter
(and hence the dispersion parameter for Exponential family distributions)
using explanatory variables.
This can be important for selecting mean model terms
and is particularly important when interest lies in the variance and/or
quantiles
of the response variable.

Robert Rigby


On 06/11/13 21:46, Collin Lynch wrote:
> Greetings, My question is more algorithmic than prectical.  What I am
> trying to determine is, are the GAM algorithms used in the mgcv package
> affected by nonnormally-distributed residuals?
>
> As I understand the theory of linear models the Gauss-Markov theorem
> guarantees that least-squares regression is optimal over all unbiased
> estimators iff the data meet the conditions linearity, homoscedasticity,
> independence, and normally-distributed residuals.  Absent the last
> requirement it is optimal but only over unbiased linear estimators.
>
> What I am trying to determine is whether or not it is necessary to check
> for normally-distributed errors in a GAM from mgcv.  I know that the
> unsmoothed terms, if any, will be fitted by ordinary least-squares but I
> am unsure whether the default Penalized Iteratively Reweighted Least
> Squares method used in the package is also based upon this assumption or
> falls under any analogue to the Gauss-Markov Theorem.
>
> Thank you in advance for any help.
>
>       Sincrely,
>       Collin Lynch

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