bayespolr: Bayesian Ordered Logistic or Probit Regression

Description

Bayesian functions for ordered logistic or probit modeling with independent normal, t, or Cauchy prior distribution for the coefficients.

Usage

bayespolr(formula, data, weights, start, ..., 
    subset, na.action, contrasts = NULL, 
    Hess = TRUE, model = TRUE, 
    method = c("logistic", "probit", "cloglog", "cauchit"), 
    prior.mean = 0, prior.scale = 2.5, prior.df = 1, 
    scaled = TRUE, prior.mean.for.cutpoints = 0, 
    prior.scale.for.cutpoints = 10, prior.df.for.cutpoints = 1,
    n.iter = 100)

Arguments

formula

a formula expression as for regression models, of the form 'response ~ predictors'. The response should be a factor (preferably an ordered factor), which will be interpreted as an ordinal response, with levels ordered as i

data

an optional data frame in which to interpret the variables occurring in 'formula'.

weights

optional case weights in fitting. Default to 1.

start

initial values for the parameters. This is in the format 'c(coefficients, zeta)'

...

additional arguments to be passed to 'optim', most often a 'control' argument.

subset

expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.

na.action

a function to filter missing data.

contrasts

a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.

Hess

logical for whether the Hessian (the observed information matrix) should be returned.

model

logical for whether the model matrix should be returned.

method

logistic or probit or complementary log-log or cauchit (corresponding to a Cauchy latent variable and only available in R >= 2.1.0).

prior.mean

prior mean for the coefficients: default is 0. Can be a vector of length equal to the number of predictors (not counting the intercepts). If it is a scalar, it is expanded to the length of this vector.

prior.scale

prior scale for the coefficients: default is 2.5. Can be a vector of length equal to the number of predictors (not counting the intercepts). If it is a scalar, it is expanded to the length of this vector.

prior.df

for t distribution: default is 1 (Cauchy). Set to Inf to get normal prior distributions. Can be a vector of length equal to the number of predictors (not counting the intercepts). If it is a scalar, it is expanded to the length of this

scaled

if scaled = TRUE, then the prior distribution is rescaled. Can be a vector of length equal to the number of cutpoints (intercepts). If it is a scalar, it is expanded to the length of this vector.

prior.mean.for.cutpoints

prior mean for cutpoints: default is 0. Can be a vector of length equal to the number of cutpoints (intercepts). If it is a scalar, it is expanded to the length of this vector.

prior.scale.for.cutpoints

prior scale for cutpoints: default is 10. Can be a vector of length equal to the number of cutpoints (intercepts). If it is a scalar, it is expanded to the length of this vector.

prior.df.for.cutpoints

for t distribution: default is 1 (Cauchy). Can be a vector of length equal to the number of cutpoints (intercepts). If it is a scalar, it is expanded to the length of this vector.

n.iter

default is 100.

Value

See polr for details.

Details

The program is a simple alteration of polr() that augments the loglikelihood with the log of the t prior distributions for the coefficients. We use Student-t prior distributions for the coefficients. The prior distributions for the intercepts (the cutpoints) are set so they apply to the value when all predictors are set to their mean values. If scaled=TRUE, the scales for the prior distributions of the coefficients are determined as follows: For a predictor with only one value, we just use prior.scale. For a predictor with two values, we use prior.scale/range(x). For a predictor with more than two values, we use prior.scale/(2*sd(x)).

Examples

Run this code

M1 <- polr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing)
    display (M1)
    
    M2 <- bayespolr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing,
        prior.scale=Inf, prior.df=Inf) # Same as M1
    display (M2)
    
    M3 <- bayespolr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing)
    display (M3)
    
    M4 <- bayespolr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing,
        prior.scale=2.5, prior.df=1)  # Same as M3
    display (M4)   
    
    M5 <- bayespolr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing,
        prior.scale=2.5, prior.df=7)
    display (M5)

    M6 <- bayespolr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing,
        prior.scale=2.5, prior.df=Inf)
    display (M6)