R: Compute the Posterior Distribution for a Linear Model
linearmodel
R Documentation
Compute the Posterior Distribution for a Linear Model
Description
Given a vector of data and a design matrix, describing how these
data are thought to relate to some predictors in a linear model, the
posterior for the parameters of this linear model is found, using a
flat prior.
Usage
linearmodel(data, design)
Arguments
data
A vector with data values.
design
A design matrix. The number of rows must be equal to the length of
the data vector. The number of columns corresponds to the number of
explanatory variables.
Details
If y_i is the i'th data value and β_j is the
j'th unknown parameter, and if x_{ij} is the value in the i'th row
and j'th column of the design matrix, then one assumes that y_i
is normally distributed with exptectation
x_{i1}β_1 + x_{i2}β_2 + … + x_{ik}β_k
and logged standard deviation λ. The computed probability
distribution is then the posterior for the joint distribution of
(β_1,β_2,…,β_k,λ)
.
Value
If k is the number of columns in the design matrix and if k>1,
then the output is a multivariate Normal-ExpGamma distribution representing
the posterior for the corresponding k values and the logged scale
parameter in the linear model. If k=1, the output is a Normal-ExpGamma
distribution representing the posterior.