pymare.stats.q_profile

q_profile(y, v, X, alpha=0.05)

Get the CI for tau^2 via the Q-Profile method.

Parameters:

• y (numpy.ndarray of shape (K,)) – 1d array of study-level estimates

• v (numpy.ndarray of shape (K,)) – 1d array of study-level variances

• X (numpy.ndarray of shape (K[, P])) – 1d or 2d array containing study-level predictors (including intercept); has dimensions K x P, where K is the number of studies and P is the number of predictor variables.

• alpha (float, optional) – alpha value defining the coverage of the CIs, where width(CI) = 1 - alpha. Default = 0.05.

Returns:

A dictionary with keys ‘ci_l’ and ‘ci_u’, corresponding to the lower and upper bounds of the tau^2 confidence interval, respectively.

Return type:

dict

Notes

Following the Viechtbauer[1] implementation, this method returns the interval that gives an equal probability mass at both tails (i.e., P(tau^2 <= lower_bound)  == P(tau^2 >= upper_bound) == alpha/2), and not the smallest possible range of tau^2 values that provides the desired coverage.

References

[1]

Wolfgang Viechtbauer. Confidence intervals for the amount of heterogeneity in meta-analysis. Statistics in medicine, 26(1):37–52, 2007. URL: https://doi.org/10.1002/sim.2514, doi:10.1002/sim.2514.