Visibility from a clique tie

The exact rule, and the default everywhere. Reproduces calculate_sib_ind_visibility() bit for bit: an alter who is on the frame has visibility y.F, and an alter who is not has y.F + 1.

Usage

vis_from_clique(ego.in.group = TRUE)

Arguments

ego.in.group

is ego a member of the group ego reports about? TRUE for siblings and households. Setting it FALSE drops the + 1, which is what makes this the general clique rule rather than a sibling-specific one

Value

a visibility_rule

Details

This is a theorem, not a definition, and it is worth being precise about what buys it. It follows when three things hold:

• the tie partitions the population into disjoint groups (it is an equivalence relation, so it is transitive – siblingship is, cousinship is not);

• ego is a member of the group ego reports about (ego.in.group);

• reporting within the group is complete.

Given those, ego's own roster is sufficient to recover the visibility of every alter, including alters whose neighbourhood ego cannot observe. Siblings and households satisfy all three. Cousins, parents and neighbours do not, and need vis_from_donor() or a rule yet to be written.

The asymmetry between on-frame and off-frame alters is not a detail. A dead alter is never on the frame, so every death is divided by y.F + 1, while exposure is a mixture of both cases. That asymmetry is the only way visibility survives into a rate, which is a ratio; a rule that assigned one number to every alter in a cell would cancel out and reduce exactly to the aggregate estimator.

Examples

rule <- vis_from_clique()
rule
#> <visibility_rule: clique>
#>   requires:     y.F, .sib.in.F
#>   is_estimated: FALSE  (fit once; frozen across bootstrap replicates)
#>   parameters:
#>     ego.in.group = TRUE
#>   assumptions:
#>     - the tie partitions the population into disjoint groups
#>     - ego is a member of the group ego reports about
#>     - reporting within the group is complete