Description

Bootstrap model effects (standardised coefficients) and optional SEM correlated errors.

Usage

Arguments

Details

bootEff uses the boot function (primarily) to bootstrap standardised effects from a fitted model or list of models (calculated using stdEff). Bootstrapping is typically nonparametric, i.e. model effects are calculated from data where the rows have been randomly sampled with replacement. 10,000 such resamples should provide accurate coverage for confidence intervals in most situations, with fewer sufficing in some cases. To ensure that data is resampled in the same way across individual bootstrap operations within the same run (e.g. models in a list), the same seed is set per operation, with the value saved as an attribute to the matrix of bootstrapped values (for reproducibility). The seed can either be user-supplied or a randomly-generated five-digit number (default), and is always re-initialised on exit (i.e. set.seed(NULL)).

Where weights are specified, bootstrapped effects will be a weighted average across the set of candidate models for each response variable, calculated after each model is first refit to the resampled dataset (specifying weights = "equal" will use a simple average instead - see avgEst). If no weights are specified and mod is a nested list of models, the function will throw an error, as it will be expecting weights for a presumed model averaging scenario. If instead the user wishes to bootstrap each individual model, they should recursively apply the function using rMapply (remember to set a seed).

Where names of models with correlated errors are specified to cor.err, the function will also return bootstrapped Pearson correlated errors (weighted residuals) for those models. If weights are supplied and mod is a nested list, residuals will first be averaged across candidate models. If any two models (or candidate sets) with correlated errors were fit to different subsets of data observations, both models/sets are first refit to data containing only the observations in common.

For nonparametric bootstrapping of mixed models, resampling should occur at the group-level, as individual observations are not independent. The name of the random effect to resample must be supplied to ran.eff. For nested random effects, this should be the highest-level group (Davison & Hinkley 1997, Ren et al. 2010). This form of resampling will result in differently-sized datasets if observations are unbalanced across groups; however this should not generally be an issue, as the number of independent units (groups), and hence the 'degrees of freedom', remains unchanged.

For mixed models with non-nested random effects, nonparametric resampling will not be appropriate. In these cases, (semi-)parametric bootstrapping can be performed instead via bootMer in the lme4 package (with additional arguments passed to that function as necessary). NOTE: As bootMer takes only a fitted model as its first argument, any model averaging is calculated 'post-hoc' using the estimates in boot objects for each candidate model, rather than during the bootstrapping process itself (i.e. the default procedure via boot). Results are then returned in a new boot object for each response variable or correlated error estimate.

If supplied a list containing both mixed and non-mixed models, bootEff with nonparametric bootstrapping will still work and will treat all models as mixed for resampling (with a warning). This is probably a relatively rare scenario, but may occur where the user decides that non-mixed models perform similarly and/or cause less issues than their mixed counterparts for at least some response variables (e.g. where random effect variance estimates are at or near zero). If nonparametric bootstrapping is not used however, an error will occur, as bootMer will only accept mixed models.

Parallel processing is used by default via the parallel package and option parallel = "snow" (and is generally recommended), but users can specify the type of parallel processing to use, or none. If "snow", a cluster of workers is created using makeCluster, and the user can specify the number of system cores to incorporate in the cluster (defaults to all available). bootEff then exports all required objects and functions to this cluster using clusterExport, after performing a (rough) match of all objects and functions in the current global environment to those referenced in the model call(s). Users should load any required external packages prior to calling the function.

Value

An object of class "boot" containing the bootstrapped effects, or a list/nested list of such objects.

Note

Bootstrapping mixed (or indeed any other) models may take a very long time when the number of replicates, observations, parameters, and/or models is high. To decrease processing time, it may be worth trying different optimizers and/or other options to generate faster estimates (always check results).

References

Burnham, K. P., & Anderson, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.). New York: Springer-Verlag. Retrieved from https://www.springer.com/gb/book/9780387953649

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press.

Ren, S., Lai, H., Tong, W., Aminzadeh, M., Hou, X., & Lai, S. (2010). Nonparametric bootstrapping for hierarchical data. Journal of Applied Statistics, 37(9), 1487–1498. https://doi.org/dvfzcn

Examples