cvam (version 0.9.3)

cvamPrior: Data-Augmentation Prior for Coarsened Factor Loglinear Model

Description

The cvam function fits loglinear models to coarsened categorical variables. The cvamPrior function creates an object to pass to cvam to represent prior information that is incorporated into the model fit.

Usage

cvamPrior(obj = list(), flatten = 0, ridge = 0, intensity = 1)

Value

an object of class "cvamPrior", designed for use by the function cvam.

Arguments

obj

a list of prior information nuggets to apply to the complete-data frequency table; see DETAILS.

flatten

a prior information nugget to be divided equally across all cells of the complete-data frequency table; see DETAILS.

ridge

a ridge factor to apply to the log-linear coefficients; see DETAILS.

intensity

a factor applied simultaneously to all prior information to scale it up or down; see DETAILS.

Author

Joe Schafer

Details

An object produced by this function, when passed to cvam through its prior argument, incorporates prior information as

• a flattening constant, a positive value that is divided equally among all non-structural zero cells of the complete-data table, and

• prior nuggets, which take the form of coarsened-data frequencies that are assigned to selected cells or groups of cells.

Log-linear models fit with saturated=FALSE can also accept a ridge factor, which acts upon the coefficients in a manner similar to ridge regression, shrinking the estimated coefficients toward zero and stabilizing its estimated covariance matrix. The added information is equivalent to a multivariate normal prior density centered at zero with prior precision (inverse covariance) matrix equal to the ridge factor times the identity matrix.

The intensity factor provides a simple way to strengthen or weaken the overall amount of prior information, which is useful for sensitivity analyses. The flattening constant, nugget frequencies and ridge factor are all multiplied by intensity. Setting intensity=2 doubles the prior information, intensity=.5 cuts it in half, and so on.

References

For more information, refer to the package vignette Log-Linear Modeling with Missing and Coarsened Values Using the cvam Package.

See Also

cvam, coarsened

Examples

# fit a saturated model to a four-way table
fit <- cvam( ~ Sex*CenRace*Hisp*Party, data=abortion2000,
 saturated=TRUE )
# add a flattening constant
fit <- cvam( ~ Sex*CenRace*Hisp*Party, data=abortion2000,
 saturated=TRUE, prior=cvamPrior( flatten=10 ) )

# fit with saturated=FALSE and no prior information, and
# notice how large the SEs are
fit <- cvam( ~ Sex*CenRace*Hisp*Party, data=abortion2000,
 saturated=FALSE )
head( get.coef(fit, withSE=TRUE) )
# add a very mild ridge factor and notice how the SEs
# have become reasonable
fit <- cvam( ~ Sex*CenRace*Hisp*Party, data=abortion2000,
 saturated=FALSE, prior=cvamPrior( ridge=.1 ) )
head( get.coef(fit, withSE=TRUE) )

# add s few prior nuggets to stabilize the distribution
# of Party within a rare category
nuggetList <- list(
   list( CenRace="Black", Hisp="Hisp", Party="Dem", freq=1 ),
   list( CenRace="Black", Hisp="Hisp", Party="Rep", freq=1 ),
   list( CenRace="Black", Hisp="Hisp", Party="Ind/Oth", freq=1 ) )
myPrior <- cvamPrior( nuggetList, flatten=10 )
summary(myPrior)
fit <- cvam( ~ Sex*CenRace*Hisp*Party, data=abortion2000,
 saturated=FALSE, prior=myPrior )