PEPBVS (version 2.2)

peptest: Bayes factor for model comparison

Description

Given two models to be compared (the one nested to the other), computes the corresponding Bayes factor.

Usage

peptest(formula1, formula2, data, intrinsic = FALSE, reference.prior = TRUE)

Value

peptest returns the Bayes factor, i.e., a numeric value. For the ratio, the marginal likelihood of the more complex model (nominator) with respect to that of the simpler one (denominator) is computed. Both marginal likelihoods are computed with respect to the intercept--only model (reference model).

Arguments

formula1

One of the two formulas/models to be compared.

formula2

The second formula/model. The one model needs to be nested to the other.

data

A data frame (of numeric values), containing the data.

intrinsic

Logical, indicating whether the PEP (FALSE) or the intrinsic --- which is a special case of it --- (TRUE) should be used as prior on the regression parameters. Default value=FALSE.

reference.prior

Logical, indicating whether the reference prior (TRUE) or the dependence Jeffreys prior (FALSE) is used as baseline. Default value=TRUE.

Details

This function can be used to perform hypothesis testing indirectly. More specifically, for the interpretation of the result (Bayes factor), the table in Kass and Raftery (1995) can be used.

The function works when \(p\leq n-2\), where \(p\) is the number of explanatory variables in the more complex model and \(n\) is the sample size.

The case of missing data (i.e., presence of NA's either in the data matrix corresponding to the explanatory variables of the more complex model or the response vector) is not currently supported. Further, the explanatory variables of the more complex model need to be quantitative.

If \(p>1\), the explanatory variables of the more complex model cannot have an exact linear relationship (perfect multicollinearity).

References

Kass, R. and Raftery, A. (1995) Bayes Factors. Journal of the American Statistical Association, 90(430): 773–795. tools:::Rd_expr_doi("10.1080/01621459.1995.10476572")

Examples

data(UScrime_data)
resBF1 <- peptest(y~1,y~M+Ed,UScrime_data)
resBF1i <- peptest(y~1,y~M+Ed,UScrime_data, intrinsic=TRUE)
resBF2j <- peptest(y~M+Ed+Po1+Po2,y~M+Ed,UScrime_data,
                   reference.prior=FALSE)
resBF2ij <- peptest(y~M+Ed+Po1+Po2,y~M+Ed,UScrime_data,
                    intrinsic=TRUE, reference.prior=FALSE)