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 <[email protected]> wrote: > > > ---------- 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 > _______________________________________________ pspp-dev mailing list [email protected] https://lists.gnu.org/mailman/listinfo/pspp-dev
