[R] how to verify gauss-markov hypothesis for linear model validity?

[Charles C. Berry]

On Tue, 16 Jun 2009, jose romero wrote:

> Hello list:
>
> (This is probably a stupid question). Is there a "quick and easy" way to 
> confirm the gauss-markov conditions of a linear multiple regression 
> model?

Well, those 'conditions' are  _assumptions_, and as often happens they 
can be hard to verify. 

> That the mean of the residuals is 0 can easily be tested for.

Wrong. In general, it cannot. The residuals at issue here are not the 
deviations of the data from the fitted values, which are set to have mean 
zero. Rather they are the unobserved differences between what is observed 
and what would have been predicted given the true values of the regression 
coefficients.

> The 
> normality of the residuals as well (shapiro-wilk?). But what about 
> homoscedasticity?

Well, if you have a good candidate for departures from homoscedasticity, 
you are in business. But you have to 'know something' about your setup 
to be this lucky. Or, if you have replicate observations for some values 
of the regressors - as in designed experiments with replication - it is 
possible. If neither if these applies, it will usually be difficult.


> And independence of residuals with respect to the 
> model variables?

This can be tough. If there is a variable that is omitted and that is 
related to (e.g. correlated with) your regressors, then the assumption 
fails. But you cannot test for this in most circumstances.

Also, certain kinds of measurement error will cause the assumption 
to fail.

HTH,

Chuck

>
> Thanks in advance
>
>
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>
>

Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901