post_mu_fe | R Documentation |

This function computes the mean and the standard deviation of the normal posterior distribution for the overall mean parameter mu in the fixed effects model.

```
post_mu_fe(df, mu.mean = 0, mu.sd = 4)
```

`df` |
data frame with one column "y" containing the (transformed) effect estimates for the individual studies and one column "sigma" containing the standard errors of these estimates. |

`mu.mean` |
mean of the normal prior for the overall mean parameter mu. Defaults to 0. |

`mu.sd` |
standard deviation of the normal prior for the overall mean parameter mu. Defaults to 4. |

For the fixed effects model, the normal posterior for the overall mean parameter mu can be computed analytically (under the common assumption of a normal prior on mu)
since this is a conjugate Bayesian normal-normal model.
See for example Ott et al. (2021), Equation (2) for the formula
(`mu.mean`

corresponds to `\nu`

and `mu.sd`

corresponds to `\gamma`

).

The default values for `mu.mean`

and `mu.sd`

are suitable for effects mu on the log odds (ratio) scale (Roever, 2020).

A list with two elements: the first element "mean" and the second element "sd", which refer to the mean and the standard deviation of the normal posterior of mu.

Ott, M., Plummer, M., Roos, M. (2021). How vague is vague?
How informative is informative? Reference analysis for
Bayesian meta-analysis. *Statistics in Medicine* **40**, 4505–4521.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.9076")}

Roever C. Bayesian random-effects meta-analysis using the bayesmeta R package (2020). *Journal of Statistical Software* **93(6)**, 1–51.

```
# load the aurigular acupuncture (AA) data set
data(aa)
# normal prior for log odds ratios suggested by Roever (2020)
post_mu_fe(df=aa, mu.mean=0, mu.sd=4)
```

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