mmm {CIAAWconsensus} | R Documentation |

## Multivariate meta-analysis of correlated effects

### Description

This function provides meta-analysis of multivariate correlated data using the marginal method of moments with working independence assumption as described by Chen et al (2016). As such, the meta-analysis does not require correlations between the outcomes within each dataset.

### Usage

```
mmm(y, uy, knha = TRUE, verbose = TRUE)
```

### Arguments

`y` |
A matrix of results from each of the |

`uy` |
A matrix with uncertainties of the results given in |

`knha` |
(Logical) Allows for the adjustment of consensus uncertainties using the Birge ratio (Knapp-Hartung adjustment) |

`verbose` |
(Logical) Requests annotated summary output of the results |

### Details

The marginal method of moments delivers the inference for correlated effect sizes using multiple univariate meta-analyses.

### Value

`studies` |
The number of independent studies |

`beta` |
The consensus estimates for all outcomes |

`beta.u` |
Standard uncertainties of the consensus estimates |

`beta.U95` |
Expanded uncertainties of the consensus estimates corresponding to 95% confidence |

`beta.cov` |
Covariance matrix of the consensus estimates |

`beta.cor` |
Correlation matrix of the consensus estimates |

`H` |
Birge ratios (Knapp-Hartung adjustment) which were applied to adjust the standard uncertainties of each consensus outcome |

`I2` |
Relative total variability due to heterogeneity (in percent) for each outcome |

### Author(s)

Juris Meija <juris.meija@nrc-cnrc.gc.ca> and Antonio Possolo

### References

Y. Chen, Y. Cai, C. Hong, and D. Jackson (2016) Inference for correlated effect sizes using multiple univariate meta-analyses. *Statistics in Medicine*, 35, 1405-1422

J. Meija and A. Possolo (2017) Data reduction framework for standard atomic weights and isotopic compositions of the elements. *Metrologia*, 54, 229-238

### Examples

```
## Consensus isotope amount ratios for platinum
df=normalize.ratios(platinum.data, "platinum", "195Pt")
mmm(df$R, df$u.R)
```

*CIAAWconsensus*version 1.3 Index]