R: Fitted values for a BAS BMA objects

fitted.bas {BAS} | R Documentation

## Fitted values for a BAS BMA objects

### Description

Calculate fitted values for a BAS BMA object

### Usage

    ## S3 method for class 'bas'
    fitted(
      object,
      type = "link",
      estimator = "BMA",
      top = NULL,
      na.action = na.pass,
      ...
    )

### Arguments

`object` | An object of class 'bas' as created by `bas`
`type` | type equals "response" or "link" in the case of GLMs (default is 'link')
`estimator` | estimator type of fitted value to return. Default is to use BMA with all models. 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'
`na.action` | function determining what should be done with missing values in newdata. The default is to predict NA.
`...` | optional arguments, not used currently

### Details

Calculates 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.

### Value

A vector of length n of fitted values.

### Author(s)

Merlise Clyde clyde@duke.edu

### References

Barbieri, M. and Berger, J.O. (2004) Optimal predictive model selection. Annals of Statistics. 32, 870-897.
https://projecteuclid.org/euclid.aos/1085408489&url=/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
doi: 10.1198/jcgs.2010.09049

### See Also

`predict.bas` `predict.basglm`

Other bas methods: `BAS`, `bas.lm()`, `coef.bas()`, `confint.coef.bas()`, `confint.pred.bas()`, `diagnostics()`, `force.heredity.bas()`, `image.bas()`, `plot.confint.bas()`, `predict.basglm()`, `predict.bas()`, `summary.bas()`, `update.bas()`, `variable.names.pred.bas()`

Other predict methods: `predict.basglm()`, `predict.bas()`, `variable.names.pred.bas()`

### Examples

    data(Hald)
    hald.gprior =  bas.lm(Y~ ., data=Hald, prior="ZS-null", initprobs="Uniform")
    plot(Hald$Y, fitted(hald.gprior, estimator="HPM"))
    plot(Hald$Y, fitted(hald.gprior, estimator="BMA", top=3))
    plot(Hald$Y, fitted(hald.gprior, estimator="MPM"))
    plot(Hald$Y, fitted(hald.gprior, estimator="BPM"))

[Package BAS version 1.6.2 Index]