MC3.REG.logpost {BMA}

Helper function to MC3.REG

Description

Helper function to MC3.REG that calculates the posterior model probability (up to a constant).

Usage

MC3.REG.logpost(Y, X, model.vect, p, i, K, nu, lambda, phi)

Arguments

Y

the vector of scaled responses.

X

the matrix of scaled covariates.

model.vect

logical vector indicating which variables are to be included in the model

p

number of variables in model.vect

i

vector of possible outliers

K

a hyperparameter indicating the outlier inflation factor

nu

regression hyperparameter. Default value is 2.58 if r2 for the full model is less than 0.9 or 0.2 if r2 for the full model is greater than 0.9.

lambda

regression hyperparameter. Default value is 0.28 if r2 for the full model is less than 0.9 or 0.1684 if r2 for the full model is greater than 0.9.

phi

regression hyperparameter. Default value is 2.85 if r2 for the full model is less than 0.9 or 9.2 if r2 for the full model is greater than 0.9.

Value

The log-posterior distribution for the model (up to a constant).

Note

The implementation here differs from the Splus implentation. The Splus implementation uses global variables to contain the state of the current model and the history of the Markov-Chain. This implentation passes the current state and history to the function and then returns the updated state.

Author(s)

Jennifer Hoeting [e-mail] with the assistance of Gary Gadbury. Translation from Splus to R by Ian Painter [e-mail].

References

Bayesian Model Averaging for Linear Regression Models Adrian E. Raftery, David Madigan, and Jennifer A. Hoeting (1997). Journal of the American Statistical Association, 92, 179-191.

A Method for Simultaneous Variable and Transformation Selection in Linear Regression Jennifer Hoeting, Adrian E. Raftery and David Madigan (2002). Journal of Computational and Graphical Statistics 11 (485-507)

A Method for Simultaneous Variable Selection and Outlier Identification in Linear Regression Jennifer Hoeting, Adrian E. Raftery and David Madigan (1996). Computational Statistics and Data Analysis, 22, 251-270

Earlier versions of these papers are available via the World Wide Web using the url: https://www.stat.colostate.edu/~jah/papers/

See Also

MC3.REG, For.MC3.REG, MC3.REG.choose