# cvamEstimate: Obtain Estimated Probabilities from a Fitted Model In cvam: Coarsened Variable Modeling

## Description

After fitting a log-linear model with `cvam`, the fitted model object may be passed to this function to obtain estimated marginal and conditional probabilities for model factors.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```cvamEstimate(estimate, obj, meanSeries = TRUE, confidence = obj\$control\$confidence, probRound = obj\$control\$probRound, probDigits = obj\$control\$probDigits, ...) ## S3 method for class 'cvamEstimate' print(x, showHeader = TRUE, ...) ## S3 method for class 'cvamEstimateList' print(x, showHeader = TRUE, ...) ```

## Arguments

 `estimate` a formula or list of formulas indicating the desired probabilities; see DETAILS. `obj` an object produced by `cvam` containing results from a model fit `meanSeries` applies when `obj` contains results from a simulation run. If `TRUE`, then the requested estimates are computed based on a running mean of cell probabilities over all iterations after the burn-in period. If `FALSE`, then the requested estimates are based only on the cell probabilities from the final iteration, and (assuming the run was sufficiently long, if it is MCMC) can be regarded as a single draw from their posterior distribution. `confidence` confidence coefficient for asymmetric interval estimates; see DETAILS. `probRound` if TRUE, probabilities will be rounded. `probDigits` number of digits for rounding probabilities. `x` a set of estimates to be printed. `showHeader` if `TRUE`, a descriptive header is printed. `...` additional arguments to be passed to `print`.

## Details

The argument `estimate` should be a one-sided formula or a list of one-sided formulas, with variables separated by '`+`', and variables to be conditioned on appearing after '`|`'. For example, `~ A` requests marginal probabilities for every level of `A`; `~ A + B | C + D` requests conditional probabilities for every level combination of `A` and `B` given every level combination of `C` and `D`.

• If `obj` was produced with `saturated=FALSE` and `method="EM"`, then standard errors for all probabilities are computed using Taylor linearization, also known as the delta method, based on the asymptotic covariance matrix for the log-linear coefficients.

• If `obj` was produced with `saturated=FALSE` and `method="MCMC"` or `"approxBayes"`, then standard errors are computed with Taylor linearization, based on the covariance matrix for the simulated log-linear coefficients from all iterations after the burn-in period.

• If `obj` was produced with `saturated=TRUE`, then standard errors are not computed.

A symmetric confidence interval for a probability may be problematic, especially if the estimate is close to zero or one. Asymmetric confidence intervals are computed by applying a normal approximation on the logistic (log-odds) scale and translating the endpoints back to the probability scale.

## Value

if `estimate` is a single formula, this function returns a data frame containing estimated probabilities, standard errors, and endpoints of approximate confidence intervals. If `estimate` is a list of formulas, then a list of data frames is returned.

## Note

Estimates may also be requested when fitting a model with `cvam`, by providing a formula or list of formulas to the optional argument `estimate`.

## 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` `cvamPredict` `cvamImpute` `cvamLik`
 ```1 2``` ```fit <- cvam( ~ Sex * PolViews * AbAny, data=abortion2000 ) cvamEstimate( list( ~ AbAny | Sex, ~ AbAny | PolViews ), fit ) ```