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Re: asymptotic standard error of lambda
From: |
Ben Pfaff |
Subject: |
Re: asymptotic standard error of lambda |
Date: |
Tue, 6 May 2014 08:47:30 -0700 |
Thank you very much! I implemented this formula and checked it against
a few examples by hand.
On Tue, May 6, 2014 at 7:48 AM, Douglas Bonett <address@hidden> wrote:
>
>
> ---------- Forwarded message ----------
> From: Douglas Bonett <address@hidden>
> Date: Mon, May 5, 2014 at 10:31 PM
> Subject: Re: asymptotic standard error of lambda
> To: John Darrington <address@hidden>
>
>
> 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
> <address@hidden> 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
>> <address@hidden> 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.
>>
>>
>> _______________________________________________
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>>
>
>
>
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- asymptotic standard error of lambda, Ben Pfaff, 2014/05/05
- Re: asymptotic standard error of lambda, John Darrington, 2014/05/05
- Re: asymptotic standard error of lambda, Ben Pfaff, 2014/05/05
- Re: asymptotic standard error of lambda, John Darrington, 2014/05/05
- Re: asymptotic standard error of lambda, Ben Pfaff, 2014/05/05
- Re: asymptotic standard error of lambda, John Darrington, 2014/05/05
- Re: asymptotic standard error of lambda, Ben Pfaff, 2014/05/06
- Message not available
- Fwd: asymptotic standard error of lambda, Douglas Bonett, 2014/05/06
- Re: asymptotic standard error of lambda,
Ben Pfaff <=