[Rd] Discourage the weights= option of lm with summarized data

[Viechtbauer Wolfgang (SP)]

Ah, I think you are referring to this part from ?lm:

"(including the case that there are w_i observations equal to y_i and the data have been summarized)"

I see; indeed, I don't think this is what 'weights' should be used for (the other part before that is correct). Sorry, I misunderstood the point you were trying to make.

Best,
Wolfgang

-----Original Message-----
From: R-devel [mailto:r-devel-bounces at r-project.org] On Behalf Of Arie ten Cate
Sent: Sunday, 08 October, 2017 14:55
To: r-devel at r-project.org
Subject: [Rd] Discourage the weights= option of lm with summarized data

Indeed: Using 'weights' is not meant to indicate that the same
observation is repeated 'n' times.  As I showed, this gives erroneous
results. Hence I suggested that it is discouraged rather than
encouraged in the Details section of lm in the Reference manual.

   Arie

---Original Message-----
On Sat, 7 Oct 2017, wolfgang.viechtbauer at maastrichtuniversity.nl wrote:

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:r-devel-bounces at r-project.org] On Behalf Of Arie ten Cate
Sent: Saturday, 07 October, 2017 9:36
To: r-devel at r-project.org
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