bage (version 0.10.2)

set_datamod_overcount: Specify Overcount Data Model

Description

Specify a data model for the outcome in a Poisson model, where the outcome is subject to overcount

Usage

set_datamod_overcount(mod, rate)

Value

A revised version of mod.

Arguments

mod

An object of class "bage_mod_pois", created with mod_pois().

rate

The prior for the overcoverage rate. A data frame with a variable called "mean", a variable called "disp", and, optionally, one or more 'by' variables.

The <code>rate</code> argument

The rate argument specifies a prior distribution for the overcoverage rate. rate is a data frame with a variable called "mean", a variable called "disp", and, optionally, one or more 'by' variables. For instance, a rate of

data.frame(sex = c("Female", "Male"),
           mean = c(0.05, 0.03),
           disp = c(0.1, 0.15))

implies that the reported value for the outcome is expected to overstate the true value by about 5% for females, and about 3% for females, with greater unceratinty for males than females.

Mathematical details

The model for the observed outcome is

$$y_i^{\text{obs}} = y_i^{\text{true}} + \epsilon_i$$ $$\epsilon_i \sim \text{Poisson}(\kappa_{g[i]} \gamma_i w_i)$$ $$\kappa_g \sim \text{Gamma}(1/d_g, 1/(d_g m_g))$$

where

• \(y_i^{\text{obs}}\) is the observed outcome for cell \(i\);

• \(y_i^{\text{true}}\) is the true outcome for cell \(i\);

• \(\epsilon_i\) overcount in cell \(i\);

• \(\gamma_i\) is the rate for cell \(i\);

• \(w_i\) is exposure for cell \(i\);

• \(\kappa_{g[i]}\) is the overcoverage rate for cell \(i\);

• \(m_g\) is the expected value for \(\kappa_g\) (specified via rate); and

• \(d_g\) is disperson for \(\kappa_g\) (specified via rate).

Details

The overcount data model assumes that reported values for the outcome overstate the actual values. The reported values might be affected by double-counting, for instance, or might include some people or events that are not in the target population.

See Also

• mod_pois() Specify a Poisson model

• augment() Original data plus estimated values, including estimates of true value for the outcome variable

• components() Estimated values for model parameters, including inclusion probabilities and overcount rates

• set_datamod_undercount() An undercount-only data model

• set_datamod_miscount() An undercount-and-overcount data model

• datamods All data models implemented in bage

• confidential Confidentialization procedures modeled in bage

• Mathematical Details vignette

Examples

## specify 'rate'
rate <- data.frame(sex = c("Female", "Male"),
                   mean = c(0.1, 0.13),
                   disp = c(0.2, 0.2))

## specify model
mod <- mod_pois(divorces ~ age * sex + time,
                data = nzl_divorces,
                exposure = population) |>
  set_datamod_overcount(rate)
mod

## fit model
mod <- mod |>
  fit()
mod

## original data, plus imputed values for outcome
mod |>
  augment()

## parameter estimates
library(dplyr)
mod |>
  components() |>
  filter(term == "datamod")

## the data have in fact been confidentialized,
## so we account for that, in addition
## to accounting for overcoverage
mod <- mod |>
 set_confidential_rr3() |>
 fit()
mod