Discourage the weights= option of lm with summarized data

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Discourage the weights= option of lm with summarized data

Arie ten Cate
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, [hidden email] 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:[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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Re: 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:[hidden email]] On Behalf Of Arie ten Cate
Sent: Sunday, 08 October, 2017 14:55
To: [hidden email]
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, [hidden email] 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:[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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Re: Discourage the weights= option of lm with summarized data

Arie ten Cate
Yes.  Thank you; I should have quoted it.
I suggest to remove this text or to add the word "not" at the beginning.

   Arie

On Sun, Oct 8, 2017 at 4:38 PM, Viechtbauer Wolfgang (SP)
<[hidden email]> wrote:

> 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:[hidden email]] On Behalf Of Arie ten Cate
> Sent: Sunday, 08 October, 2017 14:55
> To: [hidden email]
> 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, [hidden email] 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:[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
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

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Re: Discourage the weights= option of lm with summarized data

Peter Dalgaard-2
AFAIR, it is a little more subtle than that.

If you have replication weights, then the estimates are right, it is "just" that the SE from summary.lm() are wrong. Somehow, the text should reflect this.

It is of some importance when you put glm() into the mix, because you can in fact get correct results from things like

y <- c(0,1)
w <- c(49,51)
glm(y~1, weights=w, family=binomial)

-pd
 


> On 9 Oct 2017, at 07:58 , Arie ten Cate <[hidden email]> wrote:
>
> Yes.  Thank you; I should have quoted it.
> I suggest to remove this text or to add the word "not" at the beginning.
>
>   Arie
>
> On Sun, Oct 8, 2017 at 4:38 PM, Viechtbauer Wolfgang (SP)
> <[hidden email]> wrote:
>> 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:[hidden email]] On Behalf Of Arie ten Cate
>> Sent: Sunday, 08 October, 2017 14:55
>> To: [hidden email]
>> 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, [hidden email] 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:[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
>>
>> ______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: [hidden email]  Priv: [hidden email]

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Re: Discourage the weights= option of lm with summarized data

Arie ten Cate
 OK. We have now three suggestions to repair the text:
 - remove the text
 - add "not" at the beginning of the text
 - add at the end of the text a warning; something like:

  "Note that in this case the standard estimates of the parameters are
in general not correct, and hence also the t values and the p value.
Also the number of degrees of freedom is not correct. (The parameter
values are correct.)"

A remark about the glm example: the Reference manual says: "For a
binomial GLM prior weights are used to give the number of trials when
the response is the proportion of successes ....".  Hence in the
binomial case the weights are frequencies.
With y <- 0.51 and w <- 100 you get the same result.

   Arie

On Mon, Oct 9, 2017 at 5:22 PM, peter dalgaard <[hidden email]> wrote:

> AFAIR, it is a little more subtle than that.
>
> If you have replication weights, then the estimates are right, it is "just" that the SE from summary.lm() are wrong. Somehow, the text should reflect this.
>
> It is of some importance when you put glm() into the mix, because you can in fact get correct results from things like
>
> y <- c(0,1)
> w <- c(49,51)
> glm(y~1, weights=w, family=binomial)
>
> -pd
>
>> On 9 Oct 2017, at 07:58 , Arie ten Cate <[hidden email]> wrote:
>>
>> Yes.  Thank you; I should have quoted it.
>> I suggest to remove this text or to add the word "not" at the beginning.
>>
>>   Arie
>>
>> On Sun, Oct 8, 2017 at 4:38 PM, Viechtbauer Wolfgang (SP)
>> <[hidden email]> wrote:
>>> 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:[hidden email]] On Behalf Of Arie ten Cate
>>> Sent: Sunday, 08 October, 2017 14:55
>>> To: [hidden email]
>>> 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, [hidden email] 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:[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
>>>
>>> ______________________________________________
>>> [hidden email] mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>
>> ______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>
> --
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Office: A 4.23
> Email: [hidden email]  Priv: [hidden email]
>
>
>
>
>
>
>
>
>

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