familyPrior {WALS}

Family Objects for Prior Distributions in WALS

Description

"familyPrior" objects provide a convenient way to specify the prior distribution used for the Bayesian posterior mean estimation of the WALS estimators in wals, walsGLM and walsNB

Usage

familyPrior(object, ...)

weibull(q = 0.887630085544086, b = log(2))

subbotin(q = 0.799512530172489, b = 0.937673273794677)

laplace(b = log(2))

## S3 method for class 'familyPrior'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'wals'
familyPrior(object, ...)

Arguments

object, x

Object of of class "familyPrior" or "wals". The function familyPrior() accesses the "familyPrior" objects that are stored in objects of class "wals".

...

Further arguments passed to methods.

q

q in Magnus and De Luca (2016). Parameter of reflected generalized gamma distribution. See below for details.

b

c in Magnus and De Luca (2016). Parameter of reflected generalized gamma distribution. See below for details.

digits

The number of significant digits to display.

Details

familyPrior() is a generic function that extracts the family used in "wals" objects.

The density function of the reflected generalized gamma distribution is

\pi(x) = \frac{q c^{(1 - \alpha)/q}}{2 \Gamma((1 - \alpha)/q)} |x|^{-\alpha} \exp(-c |x|^{q}).

The double (reflected) Weibull, Subbotin and Laplace distributions are all special cases of the reflected generalized gamma distribution. The Laplace distribution is also a special case of the double Weibull and of the Subbotin distribution.

The double (reflected) Weibull density sets q = 1 - \alpha, the Subbotin density sets \alpha = 0 and the Laplace density sets \alpha = 0 and q = 1.

The default values for the parameters q and b are minimax regret solutions for the corresponding priors. The double (reflected) Weibull and Subbotin prior are both neutral and robust. In contrast, the Laplace prior is only neutral but not robust. See section 9 "Enter Bayes: Neutrality and Robustness" of Magnus and De Luca (2016) for details and Table 1 for the optimal parameter values.

Value

An object of class "familyPrior" to be used in wals, walsGLM and walsNB. This is a list with the elements

q

Parameter q.

alpha

Parameter \alpha (of the reflected generalized gamma distribution).

b

Parameter c.

delta

Parameter \delta = (1 - \alpha)/q.

printPars

vector. Contains the parameters that are shown in printing functions, e.g. print.familyPrior().

prior

String with the name of the prior distribution.

laplace() returns an object of the specialized class "familyPrior_laplace" that inherits from "familyPrior". This allows separate processing of the Laplace prior in the estimation functions as closed-form formulas exists for its posterior mean and variance. The list elements are the same as for objects of class "familyPrior".

References

Magnus JR, De Luca G (2016). “Weighted-average least squares (WALS): A survey.” Journal of Economic Surveys, 30(1), 117-148. doi:10.1111/joes.12094.

See Also

wals, walsGLM, walsNB, computePosterior, ddweibull, dsubbotin, dlaplace.

Examples

## Use in wals():
fit <- wals(gdpgrowth ~ lgdp60 + equipinv + school60 + life60 + popgrowth |
            law + tropics + avelf + confucian, data = GrowthMPP,
            prior = weibull(q = 0.8, b = log(1.8)))
summary(fit)