[Rd] Discourage the weights= option of lm with summarized data
Arie ten Cate
arietencate at gmail.com
Sat Oct 7 09:35:34 CEST 2017
In the Details section of lm (linear models) in the Reference manual,
it is suggested to use the weights= option for summarized data. This
must be discouraged rather than encouraged. The motivation for this is
as follows.
With summarized data the standard errors get smaller with increasing
numbers of observations. However, the standard errors in lm do not get
smaller when for instance all weights are multiplied with the same
constant larger than one, since the inverse weights are merely
proportional to the error variances.
Here is an example of the estimated standard errors being too large
with the weights= option. The p value and the number of degrees of
freedom are also wrong. The parameter estimates are correct.
n <- 10
x <- c(1,2,3,4)
y <- c(1,2,5,4)
w <- c(1,1,1,n)
xb <- c(x,rep(x[4],n-1)) # restore the original data
yb <- c(y,rep(y[4],n-1))
print(summary(lm(yb ~ xb)))
print(summary(lm(y ~ x, weights=w)))
Compare with PROC REG in SAS, with a WEIGHT statement (like R) and a
FREQ statement (for summarized data).
Arie
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