BAS (version 1.2.2)

fitted.bas: Fitted values for a BAS BMA objects

Description

Calculate fitted values for a BAS BMA object

Usage

"fitted"(object,  type="HPM", top=NULL, ...)

Arguments

object

An object of class 'bma' as created by bas

type

type of fitted value to return. Options include 'HPM' the highest probability model 'BMA' Bayesian model averaging, using optionally only the 'top' models 'MPM' the median probability model of Barbieri and Berger. 'BPM' the model that is closest to BMA predictions under squared error loss

top

optional argument specifying that the 'top' models will be used in constructing the BMA prediction, if NULL all models will be used. If top=1, then this is equivalent to 'HPM'

...

optional arguments, not used currently

Value

Details

Calcuates fitted values at observed design matrix using either the highest probability model, 'HPM', the posterior mean (under BMA) 'BMA', the median probability model 'MPM' or the best predictive model 'BPM". The median probability model is defined by including variable where the marginal inclusion probability is greater than or equal to 1/2. For type="BMA", the weighted average may be based on using a subset of the highest probability models if an optional argument is given for top. By default BMA uses all sampled models, which may take a while to compute if the number of variables or number of models is large. The "BPM" is found be computing the squared distance of the vector of fitted values for a model and the fitted values under BMA and returns the model with the smallest distance. In the presence of multicollinearity this may be quite different from the MPM, with extreme collinearity may drop relevant predictors.

References

Barbieri, M. and Berger, J.O. (2004) Optimal predictive model selection. Annals of Statistics. 32, 870-897. http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.aos/1085408489 Clyde, M. Ghosh, J. and Littman, M. (2010) Bayesian Adaptive Sampling for Variable Selection and Model Averaging. Journal of Computational Graphics and Statistics. 20:80-101 http://dx.doi.org/10.1198/jcgs.2010.09049

See Also

predict.bas

Examples

data(Hald)
hald.gprior =  bas.lm(Y~ ., data=Hald, prior="ZS-null", initprobs="Uniform")
plot(Hald$Y, fitted(hald.gprior, type="HPM"))
plot(Hald$Y, fitted(hald.gprior, type="BMA"))
plot(Hald$Y, fitted(hald.gprior, type="MPM"))
plot(Hald$Y, fitted(hald.gprior, type="BPM"))