Description Usage Arguments Value References Examples
The adaptive powered correlation prior extends the Zellner-Siow Cauchy g-prior by allowing the crossproduct of the
model matrix to be raised to powers other than -1 (which gives the Fisher information matrix). The power here will
be referred to as "lambda". A lambda of 0 results in an identity matrix, which results in a ridge-regression like
prior. Positive values of lambda adapt to collinearity by allowing correlated predictors to enter and exit the model
together. Negative values of lambda on the other hand favor including only one of a set of correlated predictors.
This can be understood as projecting the information matrix into a new space which leads to a model
similar in function to principal components regression (Krishna et al., 2009). In this implementation full Bayesian
inference is used for lambda, rather than searching via marginal likelihood maximization as Krishna et al. (2009) did.
The reason for this is twofold. First, full Bayesian inference means the model has to be fit only once instead of
several times over a grid of candidate values for lambda. Second, this avoids any coherency problems such as those
that arise when using fixed-g priors.
In addition, this function allows for a set of covariates that are held constant across all models.
For example, you may wish to keep variables such as age and gender constant in order to control for them,
so that the selected variables are chosen in light of the effects of age and gender on the outcome variable.
The probability that a variable has no effect is 1 - mean(delta_i), where delta_i is an indicator variable that takes on values of 1 for
inclusion and 0 for exclusion. Averaging the number of 1s over the MCMC iterations gives the posterior inclusion probability (pip), hence,
1-pip gives the posterior exclusion probability. The overall rate of inclusion for all variables is controlled by the hyperparameter
"phi". Phi is given a beta(1,1) prior which gives uniform probability to the inclusion rate.
The posterior means of the coefficients give the Bayesian Model Averaged estimates, which are the expected values of each
parameter averaged over all sampled models (Hoeting et al., 1999).
The model specification is given below. Note that the model formulae have been adjusted to reflect the fact that JAGS
parameterizes the normal and multivariate normal distributions by their precision, rater than (co)variance. For generalized
linear models plug-in pseudovariances are used.
Model Specification:
Plugin Pseudo-Variances:
1 2 3 4 | apcSpikeDC(formula, design.formula, data, family = "gaussian",
lower = NULL, upper = NULL, log_lik = FALSE, iter = 15000,
warmup = 5000, adapt = 5000, chains = 4, thin = 1,
method = "rjparallel", cl = makeCluster(2), ...)
|
formula |
the model formula |
design.formula |
formula for the design covariates. |
data |
a data frame |
family |
one of "gaussian", "binomial", or "poisson". |
lower |
lower limit on value of lambda. Is NULL by default and limits are set based on the minimum value that produces a positive definite covariance matrix. |
log_lik |
Should the log likelihood be monitored? The default is FALSE. |
iter |
How many post-warmup samples? Defaults to 10000. |
warmup |
How many warmup samples? Defaults to 5000. |
adapt |
How many adaptation steps? Defaults to 5000. |
chains |
How many chains? Defaults to 4. |
thin |
Thinning interval. Defaults to 1. |
method |
Defaults to "rjparallel". For an alternative parallel option, choose "parallel". Otherwise, "rjags" (single core run). |
cl |
Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to two cores. |
... |
Other arguments to run.jags. |
uppper |
upper limit on value of lambda. Is NULL by default and limits are set based on the maximum value that produces a positive definite covariance matrix. |
A run.jags object.
Krishna, A., Bondell, H. D., & Ghosh, S. K. (2009). Bayesian variable selection using an adaptive powered correlation prior. Journal of statistical planning and inference, 139(8), 2665–2674. doi:10.1016/j.jspi.2008.12.004
Kuo, L., & Mallick, B. (1998). Variable Selection for Regression Models. Sankhyā: The Indian Journal of Statistics, Series B, 60(1), 65-81.
Hoeting, J. , Madigan, D., Raftery, A. & Volinsky, C. (1999). Bayesian model averaging: a tutorial. Statistical Science 14 382–417.
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