---------- Forwarded message ----------
From: Douglas Bonett <[email protected]>
Date: Mon, May 5, 2014 at 10:31 PM
Subject: Re: asymptotic standard error of lambda
To: John Darrington <[email protected]>
For lambda C|R, its variance can be expressed as
(N – A)(A + B – 2C)/(N – B)^3
where N is the total sample size, B is the largest column total, A is the
sum across rows of the largest frequencies within each row. The C term is
the hardest to explain in words – it is the summation of the largest
frequency in each row for *only* those rows where the largest row frequency
is in the same column as the largest column total. It is easier to show it
in an example.
Here is a 2x3 table from Bishop, Fienberg & Holland (page 388):
c1 c2 c3
r1 *225* 53 206
r2 3 1 *12*
*228 * 54 218
A = 225 + 12 = 237
B = 228
C = 225 (since 225 is the only row maximum that occurs in the first column)
VAR[lambda(R|C)] = (500 – 237)(237 + 228 – 2*225)/(500 – 228)^3 = .000196
ASE1 = sqrt(.000196) = .014
SPSS also gives ASE1 = .014
On Mon, May 5, 2014 at 1:24 PM, John Darrington <
[email protected]> wrote:
> On Mon, May 05, 2014 at 11:27:40AM -0700, Ben Pfaff wrote:
> On Mon, May 5, 2014 at 10:51 AM, John Darrington
> <[email protected]> wrote:
> > On Mon, May 05, 2014 at 08:09:16AM -0700, Ben Pfaff wrote:
> > I'm sure there is an error in our implementation. NaN is
> coming from
> > the square root of a negative number, as you said.
> >
> > I made another mistake below. PSPP actually calculates ASE0
> correctly
> > for asymmetric lambda (lambda divided by ASE0 is what's
> displayed as
> > "Approx. T", which matches that calculated by SPSS for
> asymmetric
> > lambda). It's ASE1, displayed as "Asymp. Std. Error", that
> PSPP gets
> > wrong.
> >
> > Ahh. I was calculating ASE0.
> >
> > ASE1 like you say seems wierd and results in an imaginary number.
> I can only imagine
> > that this is a mistake in the SPSS documentation. Unfortunately I
> haven't been able
> > to find any other references on how to calculate this value.
> >
> > Another issue: if we have T, we should be able to calculate the
> significance. We just
> > need to know the degrees of freedom. I wonder how these are
> calculated?
> >
> > Unfortunately the litereature on these values seems to be scarce.
>
> https://v8doc.sas.com/sashtml/stat/chap28/sect20.htm has a different
> formula,
> but I don't understand how to interpret r_i|l_i = l.
>
> The text below it says:
> Also, let li be the unique value of j such that ri=nij, and let l be the
> unique value of j such that r = n·j.
>
> I interpret this to mean that r_i is summed for all i where the condition
> l_i == l is true.
>
>
>
> --
> PGP Public key ID: 1024D/2DE827B3
> fingerprint = 8797 A26D 0854 2EAB 0285 A290 8A67 719C 2DE8 27B3
> See http://sks-keyservers.net or any PGP keyserver for public key.
>
>
> _______________________________________________
> pspp-dev mailing list
> [email protected]
> https://lists.gnu.org/mailman/listinfo/pspp-dev
>
>
_______________________________________________
pspp-dev mailing list
[email protected]
https://lists.gnu.org/mailman/listinfo/pspp-dev
