# cvamPrior: Data-Augmentation Prior for Coarsened Factor Loglinear Model In cvam: Coarsened Variable Modeling

## 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

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

## 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.

## 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.

## Value

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

## Author(s)

Joe Schafer Joseph.L.Schafer@census.gov

## References

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

`cvam`, `coarsened`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```# 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 ) ```