MAIVE: Meta-Analysis Instrumental Variable Estimator

Spurious Precision in Meta-Analysis of Observational Research
by Zuzana Irsova, Pedro R. D. Bom, Tomas Havranek, and Heiko Rachinger

Project Website: https://meta-analysis.cz/maive/

Overview

MAIVE addresses a fundamental problem in meta-analysis of observational research: spurious precision.

Traditional meta-analysis assigns more weight to studies with lower standard errors, assuming higher precision. However, in observational research, precision can be manipulated through p-hacking and other questionable research practices, invalidating:

• Inverse-variance weighting schemes
• Traditional bias-correction methods (funnel plots, trim-and-fill)
• Selection models for publication bias

MAIVE implements an instrumental variable approach to limit bias caused by spurious precision in meta-analysis.

Installation

From CRAN (coming soon)

install.packages("MAIVE")

Development version

install.packages("devtools")
devtools::install_github("meta-analysis-es/maive")

Load package

library(MAIVE)

Quick Start

# Prepare your data
data <- data.frame(
  bs = c(...),        # Effect sizes
  sebs = c(...),      # Standard errors
  Ns = c(...),        # Sample sizes
  study_id = c(...)   # Study IDs (optional)
)

# Run MAIVE with defaults (PET-PEESE, instrumented SEs, no weights)
result <- maive(
  dat = data,
  method = 3,      # PET-PEESE (default)
  weight = 0,      # No weights (default)
  instrument = 1,  # Instrument SEs (default)
  studylevel = 2,  # Cluster-robust (default)
  SE = 3,          # Wild bootstrap (default)
  AR = 1           # Anderson-Rubin CI (default)
)

# View results
print(result$Estimate)    # MAIVE estimate
print(result$SE)          # Standard error
print(result$Hausman)     # Hausman test
print(result$`F-test`)    # First-stage F-test

Data Structure

The maive() function expects a data frame with:

Key Features

Methods

• PET (Precision-Effect Test)
• PEESE (Precision-Effect Estimate with Standard Error)
• PET-PEESE (Conditional method, default)
• EK (Endogenous Kink)

Weighting Schemes

• No weights (recommended when spurious precision is a concern)
• Inverse-variance weights
• MAIVE-adjusted weights (using instrumented SEs)
• WAIVE (more aggressive correction via waive() function - downweights spurious precision and outliers) - Details

Robust Inference

• Study-level correlation (fixed effects, clustering, or both)
• Multiple SE estimators (CR0, CR1, CR2, wild bootstrap)
• Anderson-Rubin confidence intervals for weak instruments
• First-stage specification options (levels or log transformation)

Output

The function returns:

• MAIVE point estimate and standard error
• Standard (non-IV) estimate for comparison
• Hausman-type test statistic
• First-stage F-test of instrument strength
• Anderson-Rubin confidence interval
• Publication bias test p-value
• Instrumented standard errors

Documentation

• Getting Started Guide: See vignette("introduction")
• Function Reference: ?maive and ?waive
• Guided interactive workflow: https://www.easymeta.org
• Development Workflow: .github/DEVELOPMENT-WORKFLOW.md
• CRAN Submission: .github/CRAN-SUBMISSION.md
• Project Page: https://meta-analysis.cz/maive/

Example

# Create example data
set.seed(123)
data <- data.frame(
  bs = rnorm(50, mean = 0.3, sd = 0.2),
  sebs = runif(50, min = 0.05, max = 0.3),
  Ns = sample(100:1000, 50, replace = TRUE),
  study_id = rep(1:10, each = 5)
)

# Run MAIVE
result <- maive(data, method = 3, weight = 0, instrument = 1, 
                studylevel = 2, SE = 3, AR = 1)

# Compare with standard estimate
cat("MAIVE Estimate:", result$Estimate, "\n")
cat("Standard Estimate:", result$StdEstimate, "\n")
cat("Hausman Test:", result$Hausman, "\n")

# Use WAIVE for more aggressive correction (downweights spurious precision + outliers)
result_waive <- waive(data, method = 3, instrument = 1,
                      studylevel = 2, SE = 3, AR = 1)
cat("WAIVE Estimate:", result_waive$Estimate, "\n")

Citation

If you use MAIVE in your research, please cite:

Irsova, Z., Bom, P.R.D., Havranek, T., & Rachinger, H. (2025). Spurious precision in meta-analysis of observational research. Nature Communications, 16, 8454. https://doi.org/10.1038/s41467-025-63261-0

References

Keane, M., & Neal, T. (2023). Instrument strength in IV estimation and inference: A guide to theory and practice. Journal of Econometrics, 235(2), 1625-1653. https://doi.org/10.1016/j.jeconom.2022.12.009

Tipton, E. (2015). Small sample adjustments for robust variance estimation with cluster-correlated data. Psychological Methods, 20(3), 375–389. https://doi.org/10.1037/met0000019

Contributing

We welcome contributions! Please see our GitHub repository for:

• Bug reports and feature requests (use Issues)
• Code contributions (submit Pull Requests)
• Questions and discussions

License

MIT License - see LICENSE file for details.

Authors

• Zuzana Irsova - Charles University, Prague
• Pedro R. D. Bom - University of Deusto, Bilbao
• Tomas Havranek - Charles University, Prague; CEPR, London; METRICS, Stanford
• Petr Cala (Maintainer) - Charles University, Prague
• Heiko Rachinger - University of the Balearic Islands, Palma

Questions? Contact the maintainer or visit our project website.