| linearmodel {lestat} | 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 \beta_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}\beta_1 + x_{i2}\beta_2 + \dots + x_{ik}\beta_k
and logged standard deviation \lambda. The computed probability
distribution is then the posterior for the joint distribution of
(\beta_1,\beta_2,\dots,\beta_k,\lambda)
.
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.
Author(s)
Petter Mostad <mostad@chalmers.se>
See Also
fittedvalues, leastsquares,
linearpredict
Examples
data1 <- simulate(normal(3.3, log(2)), 9)
data2 <- simulate(normal(4.5, log(2)), 8)
data3 <- simulate(normal(2.9, log(2)), 7)
design <- designManyGroups(c(9,8,7))
posterior <- linearmodel(c(data1, data2, data3), design)
plot(posterior)