Using 'weights' is not meant to indicate that the same observation is repeated 'n' times. It is meant to indicate different variances (or to be precise, that the variance of the last observation in 'x' is sigma^2 / n, while the first three observations have variance sigma^2).

Best,

Wolfgang

-----Original Message-----

From: R-devel [mailto:

[hidden email]] On Behalf Of Arie ten Cate

Sent: Saturday, 07 October, 2017 9:36

To:

[hidden email]
Subject: [Rd] Discourage the weights= option of lm with summarized data

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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