zlm {BMS} | R Documentation |

Used to fit the Bayesian normal-conjugate linear model with Zellner's g prior and mean zero coefficent priors. Provides an object similar to the `lm`

class.

zlm(formula, data = NULL, subset = NULL, g = "UIP")

`formula` |
an object of class "formula" (or one that can be coerced to that class), such as a data.frame - cf. |

`data` |
an optional |

`subset` |
an optional vector specifying a subset of observations to be used in the fitting process. |

`g` |
specifies the hyperparameter on Zellner's g-prior for the regression coefficients. |

`zlm`

estimates the coefficents of the following model *y = α + X β + ε* where *ε* ~ *N(0,σ^2)* and *X* is the design matrix

The priors on the intercept *α* and the variance *σ* are improper: *alpha \propto 1*, *sigma \propto σ^{-1}*

Zellner's g affects the prior on coefficients: *beta* ~ *N(0, σ^2 g (X'X)^{-1})*.

Note that the prior mean of coefficients is set to zero by default and cannot be adjusted. Note moreover that `zlm`

always includes an intercept.

Returns a list of class `zlm`

that contains at least the following elements (cf. `lm`

):

`coefficients` |
a named vector of posterior coefficient expected values |

`residuals` |
the residuals, that is response minus fitted values |

`fitted.values` |
the fitted mean values |

`rank` |
the numeric rank of the fitted linear model |

`df.residual` |
the residual degrees of freedom |

`call` |
the matched call |

`terms` |
the |

`model` |
the model frame used |

`coef2moments` |
a named vector of coefficient posterior second moments |

`marg.lik` |
the log marginal likelihood of the model |

`gprior.info` |
a list detailing information on the g-prior, cf. output value |

Stefan Zeugner

The representation follows Fernandez, C. E. Ley and M. Steel (2001): Benchmark priors for Bayesian model averaging. Journal of Econometrics 100(2), 381–427

See also http://bms.zeugner.eu for additional help.

The methods `summary.zlm`

and `predict.lm`

provide additional insights into `zlm`

output.

The function `as.zlm`

extracts a single out model of a `bma`

object (as e.g. created through`bms`

).

Moreover, `lm`

for the standard OLS object, `bms`

for the application of `zlm`

in Bayesian model averaging.

Check http://bms.zeugner.eu for additional help.

data(datafls) #simple example foo = zlm(datafls) summary(foo) #example with formula and subset foo2 = zlm(y~GDP60+LifeExp, data=datafls, subset=2:70) #basic model, omitting three countries summary(foo2)

[Package *BMS* version 0.3.1 Index]