IyenGreen: Compute MLE and weight functions of Iyengar and Greenhouse...
In selectMeta: Estimation of Weight Functions in Meta Analysis

Description Usage Arguments Details Value Author(s) References See Also Examples

Two parameteric weight functions for selection models were introduced in Iyengar and Greenhouse (1988):

w_1(x; β, q) = |x|^β / t(q, α)

w_2(x; γ, q) = e^{-γ}

if |x| ≤ t(q, α) and w_1(x; β, q) = w_2(x; γ, q) = 1 otherwise. Here, t(q, α) is the α-quantile of a t distribution with q degrees of freedom. The functions w_1 and w_2 are used to model the selection process that may be present in a meta analysis, in a model where effect sizes are assumed to follow a t distribution. We have implemented estimation of the parameters in this model in IyenGreenMLE and plotting in IyenGreenWeight. The functions normalizeT and IyenGreenLoglikT are used in computation of ML estimators and not intended to be called by the user. For an example how to use IyenGreenMLE and IyenGreenWeight we refer to the help file for DearBegg.

normalizeT(s, theta, b, q, N, type = 1, alpha = 0.05)
IyenGreenLoglikT(para, t, q, N, type = 1)
IyenGreenMLE(t, q, N, type = 1, alpha = 0.05)
IyenGreenWeight(x, b, q, type = 1, alpha = 0.05)

`s`	Quantile where normalizing integrand should be computed.
`theta`	Vector containing effect size estimates of the meta analysis.
`b`	Parameter that governs shape of the weight function. Equals β for w_1 and γ for w_2.
`q`	Degrees of freedom in the denominator of w_1, w_2. Must be a real number.
`N`	Number of observations in each trial.
`type`	Type of weight function in Iyengar & Greenhouse (1988). Either 1 (for w_1) or 2 (for w_2).
`alpha`	Quantile to be used in the denominator of w_1, w_2.
`para`	Vector in R^2 over which log-likelihood function is maximized.
`t`	Vector of real numbers, t test statistics.
`x`	Vector of real numbers where weight function should be computed at.