Break-even sensitivity values and identified sets from a tilt profile

For each lagged coefficient reports the smallest \(|\delta|\) on the grid at which the sign of the estimate changes or the confidence interval starts (or stops) covering zero, and the identified set (range of the estimate) over \(|\delta| \le \delta_{max}\).

Usage

break_even(profile, delta_max = max(abs(profile$delta_grid)))

Arguments

profile: A tilt_profile.
delta_max: Half-width of the plausible sensitivity interval.

Value

A data frame with one row per lagged coefficient and the columns

coef, estimate_0 (the estimate at \(\delta = 0\)),

significant_0 (whether its confidence interval excludes zero there), sign_flip_delta and significance_flip_delta (the grid values nearest zero at which the sign and the significance status change; NA = never on the grid), set_lower and

set_upper (the identified set: the range of the estimate over

\(|\delta| \le \delta_{max}\)) and band_lower and

band_upper (the band: the range of the confidence limits over the same interval). A significance change is a dichotomous criterion; the sign change and the band are the primary quantities.

Examples

sim <- simulate_ema(N = 40, n_prompts = 30, motifs = "M2", delta = -1, seed = 1)
prof <- tilt_profile(sim$data, sim$vars, delta_grid = c(-1, -0.5, 0, 0.5))
be <- break_even(prof, delta_max = 1)
be[be$coef == "NegA<-NegA", ]
#>         coef estimate_0 significant_0 sign_flip_delta significance_flip_delta
#> 6 NegA<-NegA    0.27203          TRUE              NA                      NA
#>   set_lower set_upper band_lower band_upper
#> 6   0.27203  0.299884  0.1807127  0.4022882
# a narrower plausible interval gives a narrower identified set
break_even(prof, delta_max = 0.5)[1, c("set_lower", "set_upper")]
#>   set_lower set_upper
#> 1 0.3132909 0.3200395