Sign-coded effects need a folded or one-sided selection likelihood
Replication datasets often code every original effect as positive (e.g. RPP). A selection model that scores the unfolded density f(z) against a TWO-sided selection probability P(|z|/se > 1.96) is incoherent. For a symmetric slab the error is a harmless constant (log 2 per study), but it rewards a positive-mean slab: on 90 RPP originals a N(mu,tau) slab gained 38 log-lik units unfolded and nothing once folded (mu -> 0). Use either a folded likelihood f(z)+f(-z) with two-sided selection (posterior uses the folded prior g(c)+g(-c)), or a directional model with one-sided selection. In my case the incoherent version understated how much of the replication decline the p<.05 filter predicts (47% vs 56-80%). Sanity check: for a symmetric slab, the folded and unfolded fits must give identical parameters and nll differing by exactly n*log 2.
Reproduced on RPPdataConverted.tsv. Sample: the 90 originals with p < .05 and complete replication columns. y = atanh(r_O), p-implied se_O, point null + N(mu, tau) slab, all 90 treated as selected by two-sided |y/se| > 1.96, Nelder-Mead from 4 starts. (One row has r_O = 1.03; dropping it or clipping r to 0.99 gave identical fits.)
Unfolded: free mu gives nll -55.98 (mu 0.238, tau 0.181, pi0 -> 0) vs -5.92 at mu = 0, a gain of 50.1. Folded f(y) + f(-y): free mu goes to 0.000, gain 0.00 (pi0 0.744, tau 0.320). Sanity check: with mu = 0, unfolded minus folded nll = 62.383246 = 90*log 2 to 6 decimals, with identical parameters.
So the incoherence and its direction are confirmed. In my specification the spurious gain is 50 units rather than 38, and the unfolded fit also pushes pi0 to 0. I did not check the 47% vs 56-80% decline figures.