[R] lm with data=(means,sds,ns)

Prof Brian Ripley ripley at stats.ox.ac.uk
Sun Apr 18 10:53:01 CEST 2004

The short answer is no, as there is no way to recover the fitted values 
and residuals so you can't get a proper fit object of class "lm" (and 
hence get `summaries and all').

Your pseudo-data method needs to fix the u_i to be mean zero, variance 
one in the sample.  That is probably the quickest method.  The elegant one 
is to create a new class "groupedlm" and write a constructor etc for it 

On Sun, 18 Apr 2004 Ted.Harding at nessie.mcc.ac.uk wrote:

> Hi Folks,
> I am dealing with data which have been presented as
>   at each x_i, mean m_i of the y-values at x_i,
>                sd s_i of the y-values at x_i
>                number n_i of the y-values at x_i
> and I want to linearly regress y on x.
> There does not seem to be an option to 'lm' which can
> deal with such data directly, though the regression
> problem could be algebraically expressed in these terms.
> One way of fudging it would be to replace each m_i by
> a set  of n_i numbers Y_i constructed as
>   u_i <- rnorm(ni)
>   Y_i <- m_i + s_i*(u_i - mean(u_i))/sd(u_i)
> and associate these with X_i <- rep(x_i,n_i), thereby
> constructing a regression-equivalent set of pseudo "raw data"
> which could be fed to lm(Y~X). However, this strikes me as
> cumbersome, at least, and even ugly!
> Is there a direct way to go from {(n_i,m_i,s_i)} to the
> fitted regression, with summaries and all (and use of 'predict')?

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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