R: Bayesian analysis for a parametric linear regression model

Plm {DPpackage} | R Documentation

## Bayesian analysis for a parametric linear regression model

### Description

This function generates a posterior density sample from a parametric linear regression model using a normal distribution of the errors.

### Usage

    Plm(formula,prior,mcmc,state,status,
         data=sys.frame(sys.parent()),na.action=na.fail)

### Arguments

`formula` | a two-sided linear formula object describing the model fit, with the response on the left of a `~` operator and the terms, separated by `+` operators, on the right.
`prior` | a list giving the prior information. The list includes the following parameter: `tau1` and `tau2` giving the hyperparameters for the prior distribution of the error variance, `beta0` and `Sbeta0` giving the hyperparameters of the normal prior distribution for the regression coefficients.
`mcmc` | a list giving the MCMC parameters. The list must include the following integers: `nburn` giving the number of burn-in scans, `nskip` giving the thinning interval, `nsave` giving the total number of scans to be saved, and `ndisplay` giving the number of saved scans to be displayed on the screen (the function reports on the screen when every `ndisplay` iterations have been carried out).
`state` | a list giving the current value of the parameters. This list is used if the current analysis is the continuation of a previous analysis.
`status` | a logical variable indicating whether this run is new (`TRUE`) or the continuation of a previous analysis (`FALSE`). In the latter case the current value of the parameters must be specified in the object `state`.
`data` | data frame.
`na.action` | a function that indicates what should happen when the data contain `NA`s. The default action (`na.fail`) causes `Plm` to print an error message and terminate if there are any incomplete observations.

### Details

This generic function fits a linear regression model:

yi = Xi beta + Vi, i=1,…,n

Vi | sigma2 ~ N(0,sigma2)

To complete the model specification, independent hyperpriors are assumed,

beta | beta0, Sbeta0 ~ N(beta0,Sbeta0)

sigma^-2 | tau1, tau2 ~ Gamma(tau1/2,tau2/2)

### Value

An object of class `Plm` representing the parametric linear regression model fit. Generic functions such as `print`, `plot`, `summary`, and `anova` have methods to show the results of the fit. The results include `beta`, and `sigma2`.

The list `state` in the output object contains the current value of the parameters necessary to restart the analysis. If you want to specify different starting values to run multiple chains set `status=TRUE` and create the list state based on this starting values. In this case the list `state` must include the following objects:

`beta` | giving the value of the regression coefficients.
`sigma2` | giving the error variance.

### Author(s)

Alejandro Jara <atjara@uc.cl>

### Examples

    ## Not run:

        ############################################
        # The Australian Institute of Sport's data
        ############################################
          data(sports)
          attach(sports)

        # Initial state
          state <- NULL

        # MCMC parameters

          nburn <- 5000
          nsave <- 10000
          nskip <- 20
          ndisplay <- 100
          mcmc <- list(nburn=nburn,nsave=nsave,nskip=nskip,
                       ndisplay=ndisplay)

        # Prior information
          prior <- list(beta0=rep(0,3),
                        Sbeta0=diag(1000,3),
                        tau1=0.01,
                        tau2=0.01)

        # Fit the model

          fit <- Plm(formula=bmi~lbm+gender,prior=prior,mcmc=mcmc,
                      state=state,status=TRUE)

        # Summary with HPD and Credibility intervals
          summary(fit)
          summary(fit,hpd=FALSE)

        # Plot model parameters (to see the plots gradually set ask=TRUE)
          plot(fit)
          plot(fit,nfigr=2,nfigc=2)

        # Table of Pseudo Contour Probabilities
          anova(fit)

    ## End(Not run)

[Package DPpackage version 1.1-7.4 Index]