sim1

The simulated data set <code>sim1</code> illustrates a setting with 500 observations from a linear 
regression model with normal response, 4 ordinal and 4 nominal predictors. Two regressors 
have 8 and two have 4 categories for each type of covariate (ordinal and nominal). Regression 
effects are set to \(\beta_1 = (0, 1, 1, 2, 2, 4, 4)\) and \(\beta_3 = (0, -2, -2)\) for the 
ordinal and \(\beta_5 = (0, 1, 1, 1, 1, -2, -2)\) and \(\beta_7 = (0, 2, 2)\) for the nominal 
covariates, and \(\beta_h = 0\) for h = 2, 4, 6, 8. Levels of the predictors are generated with 
probabilities \(\pi_h = (0.1, 0.1, 0.2, 0.05, 0.2, 0.1, 0.2, 0.05)\) and \(\pi_h = (0.1, 0.4, 
0.2, 0.3)\) for regressors with 8 and 4 levels, respectively. For more details on the 
simulation setting see Pauger and Wagner (2019).

datasets

Variable selection and Bayesian effect fusion for categorical predictors in linear and
logistic regression models. Effect fusion aims at the question which categories have a similar
effect on the response and therefore can be fused to obtain a sparser representation of the model.
Effect fusion and variable selection can be obtained either with a prior that has an interpretation
as spike and slab prior on the level effect differences or with a sparse finite mixture prior on
the level effects. The regression coefficients are estimated with a flat uninformative prior after
model selection or by taking model averages. Posterior inference is accomplished by an MCMC
sampling scheme which makes use of a data augmentation strategy (Polson, Scott & Windle
(2013) <doi:10.1080/01621459.2013.829001>) based on latent Polya-Gamma random variables
in the case of logistic regression. The code for data augmentation is taken from Polson et al. (2013)
<doi:10.1080/01621459.2013.829001>, who own the copyright.

Magdalena Leitner

effectFusion

Bayesian Effect Fusion for Categorical Predictors

Daniela Pauger

Helga Wagner

Gertraud Malsiner-Walli

Nicholas G. Polson

James G. Scott

Jesse Windle

Bettina Gr<c3><bc>n

sim1 function

A named list containing the following four variables:<dl class="dl-horizontal">
 <dt><code>y</code></dt><dd>vector with 500 observations of a normal response variable</dd>
 <dt><code>X</code></dt><dd>matrix with 8 categorical predictors</dd>
 <dt><code>beta</code></dt><dd>vector with coefficients used for data generation</dd>
 <dt><code>types</code></dt><dd>character vector with types of covariates, 'o' for ordinal and 'n' for 
 nominal covariates</dd>
</dl>

Format

Simulated data set 1 — sim1

A named list containing the following four variables:<dl class='dl-horizontal'>
 <dt><code>y</code></dt><dd>vector with 500 observations of a normal response variable</dd>
 <dt><code>X</code></dt><dd>matrix with 8 categorical predictors</dd>
 <dt><code>beta</code></dt><dd>vector with coefficients used for data generation</dd>
 <dt><code>types</code></dt><dd>character vector with types of covariates, 'o' for ordinal and 'n' for 
 nominal covariates</dd>
</dl>

Simulated data set 1

sim1: Simulated data set 1

Description

Usage

Arguments

Format

References

See Also