With three sources, the data set needed for the capture-recapture application becomes more complicated. The necessary information for the capture-recapture analysis includes:

a = number of cases identified by source 1 only;

b = number of cases identified by source 2 only;

c = number of cases identified by source 3 only;

d = number of cases identified by sources 1 and 2 but not by source 3;

e = number of cases identified by sources 1 and 3 but not by sources 2;

f = number of cases identified by sources 2 and 3 but not by source 1;

g = number of cases identified by all three sources.

The numbers of cases from different source combination can also be arranged in a 2³ contingency table with one missing cell:

If we use "0" to represent "identified" and "1" to represent "not identified", then the data can also be arranged as :

          Source1   Source2     Source3 No. of Cases
         ============================================================
             0      0         0         g
             1      0         0         f
             0      1         0         e
             1      1         0         c
             0      0         1         d
             1      0         1         b
             0      1         1         a
             1      1         1         ?

With the above information available, log-linear model could be applied to estimate the number of cases not identified by all three sources.

Three sources were employed to identify the incidence of dog bite injury in Pittsburgh in 1993. They were reports from animal control, reports from hospitals and reports from police/victims. The numbers of cases identified by different source combinations were listed below.

     Animal   Hospital   Police/   # Cases
     Control             Victim
      (p1)      (p2)     (p3)         (r)
 ============================================
     0      0     0       1
     1      0     0       7
     0      1     0      15
     1      1     0     326
     0      0     1      27
     1      0     1     323
     0      1     1      91
     1      1     1       ?

In the following, we demonstrated how to use GLIM (Generalized Linear Interactive Model) program to conduct log-linear modelling for the capture-recapture analysis.

      
GLIM without macro

      
GLIM using macro created by Dr. Richard Cormack