function to estimate the hierarchical sparsity parameter for a desired level of sparsity for simulated hierarchical coefficients

function to estimate the hierarchical sparsity parameter for a desired level of sparsity for simulated hierarchical coefficients

estimate.hier.sparsity.param(
  ncats,
  nvars,
  avg.hier.zeros = 0.3,
  nsims = 150,
  effect.size.max = 0.5,
  misspecification.prop = 0
)

Arguments

ncats	number of categories to stratify on
nvars	number of variables
avg.hier.zeros	desired percent of zero variables among the variables with hierarchical zero patterns.
nsims	number of simulations to estimate the average sparsity. A larger number will be more accurate but take much longer.
effect.size.max	maximum magnitude of the true effect sizes
misspecification.prop	proportion of variables with hierarchical missingness misspecified

Examples

set.seed(123)


# estimate hier.sparsity.param for 0.15 total proportion of nonzero variables
# among vars with hierarchical zero patterns
if (FALSE) {
hsp <- estimate.hier.sparsity.param(ncats = 3, nvars = 25, avg.hier.zeros = 0.15, nsims = 100)
}
# the above results in the following value
hsp <- 0.6341772

# check that this does indeed achieve the desired level of sparsity
mean(replicate(100, mean(genHierSparseBeta(ncats = 3,
                           nvars = 25, hier.sparsity.param = hsp) != 0)  ))
#> [1] 0.14565

sparseBeta <- genHierSparseBeta(ncats = 3, nvars = 25, hier.sparsity.param = hsp)


if (FALSE) {
hsp2 <- estimate.hier.sparsity.param(ncats = 2, nvars = 100,
                        avg.hier.zeros = 0.30, nsims = 50) # 0.5778425
hsp3 <- estimate.hier.sparsity.param(ncats = 3, nvars = 100,
                        avg.hier.zeros = 0.30, nsims = 50) # 0.4336312
hsp4 <- estimate.hier.sparsity.param(ncats = 4, nvars = 100,
                        avg.hier.zeros = 0.30, nsims = 50) # 0.2670061
hsp5 <- estimate.hier.sparsity.param(ncats = 5, nvars = 100,
                        avg.hier.zeros = 0.30, nsims = 50) # 0.146682
}
# 0.07551241 for hsp6