This function computes the Rand Index(RI) of an estimated mu vector(mu_est) against the target mu vector(mu_target).
RSAVS_RI(mu_est, mu_target, detail = FALSE)numerical vector of the estimated subgroup effect.
n = length(mu_est).
numerical vector of the target(real) subgroup effect.
n = length(mu_target).
whether or not should the function computes the details(TP, TN, FP, FN)
of these 2 identifications(mu_est and mu_target).
Default value is FALSE.
numerical value of Rand Index if detail = FALSE.
Otherwise a list containing RI, TP, TN, FP, FN.
mu_est and mu_target must have the same length.
For a subgroup identification of n observations,
there are \(n * (n - 1) / 2\) pairs of different observations.
The Rand Index describes how these two subgroup identifications are
based on these observation pairs and it is given by
$$RI = (#TP + #TN) / (#TP + #TN + #FP + #FN),$$
where for any two observation i and j,
TP(True Positive): these two observations belong to the same subgroup in both these two identification.
TN(True Negative): these two observations belong to different subgroups in both these two identification.
FP(False Positive):
these two observations belong to the same subgropu in mu_est.
But they belong to different subgroups in mu_target.
FN(False Negative):
these two observations belong to different subgroups in mu_est.
But they belong to the same subgroup in mu_target.
Therefore RI ranges from 0 to 1 and RI = 1 if and only if these two identifications are identical.
Note: if detail = TRUE, the function also returns the number of TP, TN, FP and FN.
n <- 50 # number of observations
k <- 2 # k subgroup effect, centered at 0
group_center <- seq(from = 0, to = 2 * (k - 1), by = 2) - (k - 1)
# subgroup effect vector
alpha1 <- sample(group_center, size = n, replace = TRUE)
# another subgroup effect vector
alpha2 <- sample(group_center, size = n, replace = TRUE)
RSAVS_RI(alpha1, alpha2)
#> [1] 0.5102041
RSAVS_RI(alpha1, alpha2, detail = TRUE)
#> $RI
#> [1] 0.5102041
#>
#> $TP
#> [1] 325
#>
#> $TN
#> [1] 300
#>
#> $FP
#> [1] 276
#>
#> $FN
#> [1] 324
#>