`qqnorm.rma.Rd`

Function to create normal QQ plots for objects of class `"rma.uni"`

, `"rma.mh"`

, and `"rma.peto"`

.

# S3 method for rma.uni qqnorm(y, type="rstandard", pch=19, envelope=TRUE, level=y$level, bonferroni=FALSE, reps=1000, smooth=TRUE, bass=0, label=FALSE, offset=0.3, pos=13, lty, ...) # S3 method for rma.mh qqnorm(y, type="rstandard", pch=19, label=FALSE, offset=0.3, pos=13, ...) # S3 method for rma.peto qqnorm(y, type="rstandard", pch=19, label=FALSE, offset=0.3, pos=13, ...) # S3 method for rma.glmm qqnorm(y, ...) # S3 method for rma.mv qqnorm(y, ...)

y | an object of class |
---|---|

type | character string (either |

pch | plotting symbol to use for the observed effect sizes or outcomes. By default, a solid circle is used. See |

envelope | logical to specify whether a pseudo confidence envelope should be simulated and added to the plot (the default is |

level | numeric value between 0 and 100 to specify the level of the pseudo confidence envelope (the default is to take the value from the object). |

bonferroni | logical to specify whether the bounds of the envelope should be Bonferroni corrected. |

reps | numeric value to specify the number of iterations to use for simulating the pseudo confidence envelope (the default is 1000). |

smooth | logical to specify whether the results from the simulation should be smoothed (the default is |

bass | numeric value that controls the degree of smoothing (the default is 0). |

label | argument to control the labeling of the points (the default is |

offset | argument to control the distance between the points and the corresponding labels. |

pos | argument to control the position of the labels. |

lty | optional character string to specify the line type for the diagonal line and the pseudo confidence envelope (if unspecified, the function sets this to |

... | other arguments. |

The plot shows the theoretical quantiles of a normal distribution on the horizontal axis against the observed quantiles for either the standardized residuals (`type="rstandard"`

, the default) or the externally standardized residuals (`type="rstudent"`

) on the vertical axis (see `residuals.rma`

for details on the definition of these residual types).

For reference, a line is added to the plot with slope of 1, going through the (0,0) point.

For objects of class `"rma.uni"`

, it is also possible to add a pseudo confidence envelope to the plot. The envelope is created based on the quantiles of sets of pseudo residuals simulated from the given model (for details, see Cook & Weisberg, 1982). The number of sets simulated can be controlled with the `reps`

argument. When `smooth=TRUE`

, the simulated bounds are smoothed with Friedman's SuperSmoother (see `supsmu`

). The `bass`

argument can be set to a number between 0 and 10, with higher numbers indicating increasing smoothness. If `bonferroni=TRUE`

, the envelope bounds are Bonferroni corrected, so that the envelope can be regarded as a confidence region for all \(k\) residuals simultaneously. The default however is `bonferroni=FALSE`

, which makes the plot more sensitive to deviations from normality.

With the `label`

argument, one can control whether points in the plot will be labeled (e.g., to identify outliers). If `label="all"`

(or `label=TRUE`

), all points in the plot will be labeled. If `label="out"`

, points falling outside of the confidence envelope will be labeled (only available for objects of class `"rma.uni"`

). Finally, one can also set this argument to a numeric value (between 1 and \(k\)), indicating how many of the most extreme points should be labeled (for example, with `label=1`

only the most extreme point would be labeled, while with `label=3`

, the most extreme, and the second and third most extreme points would be labeled). With the `offset`

argument, the distance between the labels and the corresponding points can be controlled. The `pos`

argument is the position specifier for the labels (`1`

, `2`

, `3`

, and `4`

, respectively indicate positions below, to the left of, above, and to the right of the points; `13`

places the labels below the points for points that fall below the reference line and above otherwise; `24`

places the labels to the left of the points for points that fall above the reference line and to the right otherwise).

A list with components:

the x coordinates of the points that were plotted.

the y coordinates of the points that were plotted.

Wolfgang Viechtbauer wvb@metafor-project.org http://www.metafor-project.org

Cook, R. D., & Weisberg, S. (1982). *Residuals and influence in regression*. London: Chapman and Hall.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. *Journal of Statistical Software*, **36**(3), 1--48. https://doi.org/10.18637/jss.v036.i03

Wang, M. C., & Bushman, B. J. (1998). Using the normal quantile plot to explore meta-analytic data sets. *Psychological Methods*, **3**(1), 46--54. https://doi.org/10.1037/1082-989X.3.1.46

### meta-analysis of the log risk ratios using a random-effects model res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg) qqnorm(res)### mixed-effects model with absolute latitude as a moderator res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, mods = ~ ablat, data=dat.bcg) qqnorm(res)