Calculate a weighted average of model estimates (e.g. effects, fitted values, residuals) for a set of models.
A list or nested list of numeric vectors, comprising the model estimates. In the latter case, these should correspond to estimates for candidate models for each of a set of different response variables.
An optional numeric vector of weights to use for model
averaging, or a named list of such vectors. The former should be supplied
An optional vector of names used to extract and/or sort estimates from the output.
This function can be used to calculate a weighted average of model estimates such as effects, fitted values, or residuals, where models are typically competing candidate models fit to the same response variable. Weights are typically a 'weight of evidence' type metric such as Akaike model weights (Burnham & Anderson 2002, Burnham et al. 2011), which can be conveniently calculated in R using packages such as MuMIn or AICcmodavg. However, numeric weights of any sort can be used. If none are supplied, a simple average is calculated instead.
Averaging is performed via the 'full'/'zero' rather than 'subset'/'conditional'/'natural' method, meaning that zero is substituted for estimates for any 'missing' parameters (e.g. effects) prior to calculations. This provides a form of shrinkage and thus reduces estimate bias (Burnham & Anderson 2002, Grueber et al. 2011).
A numeric vector of the model-averaged estimates, or a list of such vectors.
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
Burnham, K. P., Anderson, D. R., & Huyvaert, K. P. (2011). AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons. Behavioral Ecology and Sociobiology, 65(1), 23-35. doi: 10/c4mrns
Dormann, C. F., Calabrese, J. M., Guillera-Arroita, G., Matechou, E., Bahn, V., Barton, K., ... Hartig, F. (2018). Model averaging in ecology: a review of Bayesian, information-theoretic, and tactical approaches for predictive inference. Ecological Monographs, 88(4), 485-504. doi: 10/gfgwrv
Grueber, C. E., Nakagawa, S., Laws, R. J., & Jamieson, I. G. (2011). Multimodel inference in ecology and evolution: challenges and solutions. Journal of Evolutionary Biology, 24(4), 699-711. doi: 10/b7b5d4
Walker, J. A. (2019). Model-averaged regression coefficients have a straightforward interpretation using causal conditioning. BioRxiv, 133785. doi: 10/c8zt
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