Hald

hald

The Hald data have been used in many books and papers to illustrate variable
selection. The data relate to an engineering application that was concerned
with the effect of the composition of cement on heat evolved during
hardening. The response variable Y is the heat evolved in a
cement mix. The four explanatory variables are ingredients of the mix, X1:
tricalcium aluminate, X2: tricalcium silicate, X3:
tetracalcium alumino ferrite, X4: dicalcium silicate. An
important feature of these data is that the variables X1 and X3 are highly
correlated, as well as the variables X2 and X4. Thus we should expect any
subset of (X1,X2,X3,X4) that includes one variable from highly correlated
pair to do as any subset that also includes the other member.

datasets

Package for Bayesian Variable Selection and Model Averaging
in linear models and generalized linear models using stochastic or
deterministic sampling without replacement from posterior
distributions. Prior distributions on coefficients are
from Zellner's g-prior or mixtures of g-priors
corresponding to the Zellner-Siow Cauchy Priors or the
mixture of g-priors from Liang et al (2008)
<DOI:10.1198/016214507000001337>
for linear models or mixtures of g-priors from Li and Clyde
(2019) <DOI:10.1080/01621459.2018.1469992> in generalized linear models.
Other model selection criteria include AIC, BIC and Empirical Bayes
estimates of g. Sampling probabilities may be updated based on the sampled
models using sampling w/out replacement or an efficient MCMC algorithm which
samples models using a tree structure of the model space
as an efficient hash table. See Clyde, Ghosh and Littman (2010)
<DOI:10.1198/jcgs.2010.09049> for details on the sampling algorithms.
Uniform priors over all models or beta-binomial prior distributions on
model size are allowed, and for large p truncated priors on the model
space may be used to enforce sampling models that are full rank.
The user may force variables to always be included in addition to imposing
constraints that higher order interactions are included only if their
parents are included in the model.
This material is based upon work supported by the National Science
Foundation under Division of Mathematical Sciences grant 1106891.
Any opinions, findings, and
conclusions or recommendations expressed in this material are those of
the author(s) and do not necessarily reflect the views of the
National Science Foundation.

Merlise Clyde

Bayesian Variable Selection and Model Averaging using Bayesian
Adaptive Sampling

Michael Littman

Joyee Ghosh

Yingbo Li

Betsy Bersson

Don van de Bergh

Quanli Wang

Hald function

<code>hald</code> is a dataframe with 13 observations and 5 variables
(columns),
Y: Heat evolved per gram of cement (in calories) X1: Amount of tricalcium
aluminate X2: Amount of tricalcium silicate X3: Amount of tetracalcium
alumino ferrite X4: Amount of dicalcium silicate

Format

Hald Data — Hald

Hald Data

Hald: Hald Data

Description

Arguments

Format