Which deterrence partial effects a design can identify — morie_deterrence_design

For the linear response \(y = \beta_0 + \beta_p p + \beta_s s + \beta_c c\) over the observed sanction regimes, a dimension that never varies has an unidentified coefficient: another coefficient vector reproduces every fitted value (Research.P8.constant_dimension_not_identified). More generally the coefficients are identified exactly when the design columns (1, p, s, c) are linearly independent (Research.P8.identified_iff_injective). This function reports the rank of the design and, for each dimension, whether its partial effect is identified given the others.

Usage

morie_deterrence_design_check(p, s, c)

Arguments

p, s, c: Certainty, severity and celerity of the observed regimes.

Value

A list with rank, identified (logical per dimension), n_regimes, and theorem.

Examples

# certainty varied at fixed severity and celerity: only certainty is identified
morie_deterrence_design_check(p = c(0.1, 0.3, 0.5), s = c(2, 2, 2), c = c(30, 30, 30))
#> $rank
#> [1] 2
#> 
#> $identified
#> certainty  severity  celerity 
#>      TRUE     FALSE     FALSE 
#> 
#> $n_regimes
#> [1] 3
#> 
#> $constant
#> certainty  severity  celerity 
#>     FALSE      TRUE      TRUE 
#> 
#> $theorem
#> [1] "Research.P8.constant_dimension_not_identified"
#> 
# all three varied off a base regime: all identified
morie_deterrence_design_check(p = c(0, 1, 0, 0), s = c(0, 0, 1, 0), c = c(0, 0, 0, 1))
#> $rank
#> [1] 4
#> 
#> $identified
#> certainty  severity  celerity 
#>      TRUE      TRUE      TRUE 
#> 
#> $n_regimes
#> [1] 4
#> 
#> $constant
#> certainty  severity  celerity 
#>     FALSE     FALSE     FALSE 
#> 
#> $theorem
#> [1] "Research.P8.constant_dimension_not_identified"
#>