1. The Conditional Random-Effects Variance Component in Meta-regression
Michael T. Brannick
Guy Cafri
University of South Florida

2. Background What is the random-effects variance component (REVC)?
What is the conditional random-effects variance component (CREVC)?
Who cares? (Tells whether we are done!)

3. Fixed and Mixed Regression
CREVC = 0
CREVC > 0

4. Items of Interest Point Estimators of the CREVC Significance tests
Method of Moments (WLS)
Maximum Likelihood (iterated WLS)
Significance tests
Fixed chi-square
Random chi-square (2 of these)
Lower bound > 0 (3 of these)
Confidence Intervals (3 types)
ML, bootstrap, bootstrap adjusted
Bias
RMSE
Type I error
Power
Coverage probability
Width

5. Monte Carlo Method Effect size: d Conditions (based on literature)
REVC: 0, .04, .10, .19, .35, .52
Proportion A/C: 0, .02, .18, .50
K studies: 13, 22, 30, 69, 112, 234
Average N (skewed): 53, 231, 730
Reps: 10k times each for 378 cells

6. Results – Point Estimates
Note: results are averages over cells
Method of moments is less biased than max like until k > 100

7. Results – Point Estimates
Meta-analysis results for one cell
(10k trials for each method)

8. Results – Significance Tests
CREVC
ML ran
Chi-sq
CI ml
CI bs
CI bc
.045
.002
.004
.044
.02
.732
.507
.537
.710
.04
.859
.674
.696
.845
.10
.960
.837
.849
.952

9. Results – Confidence Intervals
Bias corrected bootstrap has best coverage; similar width
Coverage
Width

10. Implications
Slight preference for method of moments WLS when k is small
Use the fixed-effects chi-square for testing the CREVC
Use the bias-corrected bootstrap for constructing confidence intervals

11. Conclusions
Please indicate the uncertainty of the estimates when reporting a meta-analysis (confidence intervals and/or standard errors of parameter estimates)
Free software: