Description Usage Arguments Details Value Note Author(s) References See Also Examples

This method function computes (empirical) best linear unbiased predictions from fitted random-effects meta-analytical models represented in objects of class `"mixmeta"`

. Quantities can represent prediction of outcomes given both fixed and random effects, or just random-effects residuals from the fixed-effects estimates. Predictions are optionally accompanied by standard errors, prediction intervals or the entire (co)variance matrix of the predicted outcomes.

1 2 3 |

`object ` |
an object of class |

`se ` |
logical switch indicating if standard errors must be included. |

`pi ` |
logical switch indicating if prediction intervals must be included. |

`vcov ` |
logical switch indicating if the (co)variance matrix must be included. |

`pi.level ` |
a numerical value between 0 and 1, specifying the confidence level for the computation of prediction intervals. |

`type ` |
the type of prediction. This can be either |

`level ` |
level of random-effects grouping for which predictions are to be computed. Default to the highest (inner) level, with 0 corresponding to fixed-effects predictions obtained through |

`format ` |
the format for the returned results. See Value. |

`aggregate ` |
when |

`... ` |
further arguments passed to or from other methods. |

The method function `blup`

produces (empirical) best linear unbiased predictions from `mixmeta`

objects. These can represent outcomes, given by the sum of fixed and random parts, or just random-effects residuals representing deviations from the fixed-effects estimated outcomes. In non-standard models with multiple hierarchies of random effects, the argument `level`

can be used to determine the level of grouping for which predictions are to be computed.

These predictions are a shrunk version of unit-specific realizations, where unit-specific estimates borrow strength from the assumption of an underlying (potentially multivariate) distribution of outcomes or residuals in a (usually hypothetical) population. The amount of shrinkage depends from the relative size of the within and between-unit covariance matrices reported as components `S`

and `Psi`

in `mixmeta`

objects (see `mixmetaObject`

).

Fixed-effects models do not assume random effects, and the results of `blup`

for these models are identical to `predict`

(for `type="oucome"`

) or just 0's (for `type="residuals"`

).

How to handle predictions for units removed from estimation due to invalid missing pattern is determined by the `na.action`

argument used in `mixmeta`

to produce `object`

. If `na.action=na.omit`

, units excluded from estimation will not appear, whereas if `na.action=na.exclude`

they will appear, with values set to `NA`

for all the outcomes. This step is performed by `napredict`

. See Note below.

In the presence of missing values in the outcomes `y`

of the fitted model, correspondent values of point estimates and covariance terms are set to 0, while the variance terms are set to `1e+10`

. In this case, in practice, the unit-specific estimates do not provide any information (their weight is virtually 0), and the prediction tends to the value returned by `predict`

with `interval="prediction"`

, when applied to a new but identical set of predictors. See also Note below.

(Empirical) best linear unbiased predictions of outcomes or random-effects residuals. The results may be aggregated in matrices (the default), or returned as lists, depending on the argument `format`

. For multivariate models, the aggregation is ruled by the argument `aggregate`

, and the results may be grouped by statistic or by outcome. If `vcov=TRUE`

, lists are always returned.

The definition of missing in model frames used for estimation in `mixmeta`

is different than that commonly adopted in other regression models such as `lm`

or `glm`

. See info on `missing values`

in `mixmeta`

.

Differently from `predict`

, this method function computes the predicted values in the presence of partially missing outcomes. Interestingly, BLUPs for missing outcomes may be slightly different than predictions returned by `predict`

on a new but identical set of predictors, as the BLUP also depends on the random part of the model. Specifically, the function uses information from the random-effects (co)variance to predict missing outcomes given the observed ones.

Antonio Gasparrini <antonio.gasparrini@lshtm.ac.uk> and Francesco Sera <francesco.sera@lshtm.ac.uk>

Sera F, Armstrong B, Blangiardo M, Gasparrini A (2019). An extended mixed-effects framework for meta-analysis.*Statistics in Medicine*. 2019;38(29):5429-5444. [Freely available **here**].

Verbeke G, Molenberghs G. *Linear Mixed Models for Longitudinal Data*. Springer; 1997.

See `predict`

for standard predictions. See `mixmeta-package`

for an overview of the package and modelling framework.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
# RUN THE MODEL
model <- mixmeta(cbind(PD,AL) ~ 1, S=berkey98[5:7], data=berkey98)
# ONLY BLUP
blup(model)
# BLUP AND SE
blup(model, se=TRUE)
# SAME AS ABOVE, AGGREGATED BY OUTCOME, WITH PREDICTION INTERVALS
blup(model, se=TRUE, pi=TRUE, aggregate="outcome")
# WITH VCOV, FORCED TO A LIST
blup(model, se=TRUE, pi=TRUE, vcov=TRUE, aggregate="outcome")
# PREDICTING ONLY THE RANDOM-EFFECT RESIDUALS
blup(model, type="residual")
``` |

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