IyenGreen: Compute MLE and weight functions of Iyengar and Greenhouse (1988)

Description

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

$$w_1(x; \beta, q) = |x|^\beta / t(q, \alpha)$$

$$w_2(x; \gamma, q) = e^{-\gamma}$$

if $|x| \le t(q, \alpha)$ and $w_1(x; \beta, q) = w_2(x; \gamma, q) = 1$ otherwise. Here, $t(q, \alpha)$ is the $\alpha$-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.

Usage

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)

Value

See example in DearBegg for details.

Arguments

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 $\beta$ for $w_1$ and $\gamma$ 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.

Author

Kaspar Rufibach (maintainer), kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

Details

Note that these weight functions operate on the scale of $t$ statistics, not $p$-values.

References

Iyengar, S. and Greenhouse, J.B. (1988). Selection models and the file drawer problem (including rejoinder). Statist. Sci., 3, 109--135.

Examples

Run this code

# For an illustration see the help file for the function DearBegg().

Run the code above in your browser using DataLab