The tau^2 solving generalised Q(tau^2) = k - 1. The left side is
strictly decreasing in tau^2, so the root is unique and bisection
cannot fail – unlike the likelihood-based estimators. Markedly
less downward-biased than DerSimonian-Laird, which is returned
alongside. Since the weights are 1/(v + tau^2), a different tau^2
is a different POOLED EFFECT. A Q already below its expectation at
zero gives a boundary truncation, and at_boundary says so.
Usage
morie_psy_ma_paule_mandel(yi, vi, max_iter = 200L, tol = 1e-12)
Arguments
- yi, vi
effects and within-study variances.
- max_iter, tol
bisection controls.
Value
list: tau2, tau, mu, se, ci, Q, I2, tau2_dl, at_boundary,
weights, k, method.
References
Paule and Mandel (1982), J. Research NBS 87:377-385;
Veroniki et al. (2016), Research Synthesis Methods 7:55-79.
Examples
morie_psy_ma_paule_mandel(c(0.2, 0.5, 0.1), c(0.02, 0.03, 0.04))$tau2
#> [1] 0.01131638
