OK. Whether a user has interacted with A is a sample from a binomial distribution with an unknown parameter p_A. Likewise with B and p_B. The two binomial distributions may or may not be independent.
The LLR is measuring the degree evidence against independence. On Thu, May 1, 2014 at 12:50 AM, Mario Levitin <[email protected]>wrote: > Ted, I understand how the contingency table is constructed, and how to > compute the LLR value. What I cannot understand is how to link this with > binomial distributions. > > > On Thu, May 1, 2014 at 1:02 AM, Ted Dunning <[email protected]> wrote: > > > The contingency table is constructed by looking at how many users have > > expressed preference or interest in two items. If the items are A and B, > > the pertinent counts are > > > > k11 - the number of users who interacted with both A and B > > k12 - the number of users who interacted with A but not B > > k21 - the number of users who interacted with B but not A > > k22 - the number of users who interacted with neither A nor B. > > > > These values are values that go into the contingency table and are all > that > > is needed to compute the LLR value. > > > > See http://tdunning.blogspot.de/2008/03/surprise-and-coincidence.htmlfor > > a > > detailed description. > > > > > > > > > > On Wed, Apr 30, 2014 at 11:31 PM, Mario Levitin <[email protected] > > >wrote: > > > > > Hi Ted, > > > I have read the paper. I understand the "Likelihood Ratio for Binomial > > > Distributions" part. > > > However, I cannot make a connection with this part and the contingency > > > table. > > > > > > In order to calculate Likelihood Ratio for two Binomial Distributions > you > > > need the values: p, p1, p2, k1, k2, n1, n2. > > > But the information contained in the contingency table are different > from > > > these values. So, again, I do not understand how the information > > contained > > > in the contingency table is linked with Likelihood Ratio for Binomial > > > Distributions. > > > > > > In order to find the similarity between two users I tend to think of > the > > > boolean preferences of user1 as a sample from a binomial distribution > and > > > the boolean preferences of user2 as another sample from a binomial > > > distribution. Then use the LLR to assess how likely these distributions > > are > > > the same. But I don't think this is correct since this calculation does > > not > > > use the contingency table. > > > > > > I hope my question is clear. > > > Thanks. > > > > > > > > > > > > On Mon, Apr 28, 2014 at 2:41 AM, Ted Dunning <[email protected]> > > > wrote: > > > > > > > Excellent. Look forward to hearing your reactions. > > > > > > > > On Mon, Apr 28, 2014 at 1:14 AM, Mario Levitin < > [email protected] > > > > >wrote: > > > > > > > > > Not yet, but I will. > > > > > > > > > > > > > > > > > Have you read my original paper on the topic of LLR? It explains > > the > > > > > > connection with chi^2 measures of association. > > > > > > > > > > > > > > >
