Re: asymptotic standard error of lambda

[Ben Pfaff]

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.
>>
>>
>>
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