Creates field fix in pi design data and either sets to NA to be estimated or 1 if intercept or 0 if not possible. It uses observed data at initial entry to decide the appropriate fix values.
initiate_pi(data, ddl)ddl with fix field added to pi dataframe
Processed data list; resulting value from process.data
design data list created by make.design.data
Jeff Laake
It is possible that the state will be known for some individuals and unknown for others. The function initiate_pi modifies the design data for pi by adding the field fix which can be used to fix the value of pi for an individual with known state at release. It also sets up the mlogit structure for pi by setting one of the fixed values to 1 such that the value for pi is computed by subtraction. By default it chooses the first factor level of each of the state variables that is unknown. If some of the state variables are known but others are not, it sets fix to 0 for the values of the known state variables that don't match the known value.
For example, with a bivariate case with first state A,B or C and second variable 1 or 2. Only the second variable can be unknown. There are 6 possible combinations of the state variables: A1,A2,B2,B2,C1,C2. Assume a capture history is 0,Au,0,B1,B2. There will be 6 records in the design data for this record with strata A1,A2,B2,B2,C1,C2. The occ (occasion field) will be 2 because pi is only for the first occasion. After running initiate_pi, the fix values will be 1,NA,0,0,0,0. A1 will be the intercept and computed by subtraction (fix=1), the value for A2 will be estimated (NA) and all of the others are not possible (0) because it is known to be in A.
If both can be uncertain, and the capture history was 0,uu,0,B1,B2, then the fix values will be 1,NA,NA,NA,NA,NA. With a mix of partially known and completely unknown the formulation for the mlogit could get complicated making it difficult to specify an understandable formula because the restrictions on the mlogit will change, so think hard and long about what you are doing. It may be necessary to construct "multiple" formula in the sense that you use indicator variables (0/1) as interactions.