calculating delta K

[Jennifer Petersen]

Dear STRUCTURE Group;

We have a question about the calculation of delta K. 

In order to determine this value for a given value of K, one needs to calculate first L’K, the average difference between likelihood values for n number of runs at K and n number of runs at K-1, and then L”K, the absolute value of the difference (or is it the average absolute value of the difference? – this is the crux of our question) between L’K at K +1 and L’K at K. For L’K, taking the difference between the average L(K) yields the same value of L’K as taking average difference between all pairwise L(K)s or as pairing each value of L(K) at K with a value at K-1, though the variances on L’K will be different depending on which of the latter two approaches one takes. 

But for L”K, since absolute values are involved, it matters whether you take the absolute value of the difference between the averages, the average absolute value of all pairwise differences, or the average absolute value of n pairwise differences. The last approach, which seems to be what Structure Harvester uses, does not seem appropriate for either L’K or L”K, since there is no reason why a given run at K should be paired with a given run at K +1 (or K -1). So how should delta K be calculated? Any insights, corrections to our logic, etc. would be greatly appreciated. 

Thanks in advance for any help with these calculations,

Jennifer