set_datamod_miscount: Specify Miscount Data Model

In bage: Bayesian Estimation and Forecasting of Age-Specific Rates

Specify Miscount Data Model

Description

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

Usage

set_datamod_miscount(mod, prob, rate)

Arguments

mod	An object of class "bage_mod_pois", created with mod_pois().
prob	The prior for the probability that a person or event in the target population will correctly enumerated. A data frame with a variable called "mean", a variable called "disp", and, optionally, one or more 'by' variables.
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.

Details

The miscount data model is essentially a combination of the undercount and overcount data models. It assumes that reported outcome is the sum of two quantities:

1. Units from target population, undercounted People or events belonging to the target population, in which each unit's inclusion probability is less than 1.

2. Overcount People or events that do not belong to target population, or that are counted more than once.

If, for instance, a census enumerates 91 people from a true population of 100, but also mistakenly enumerates a further 6 people, then

• the true value for the outcome variable is 100

• the value for the undercounted target population is 91,

• the value for the overcount is 6, and

• the observed value for the outcome variable is 91 + 6 = 97.

Value

A revised version of mod.

The prob argument

The prob argument specifies a prior distribution for the probability that a person or event in the target population is included in the reported outcome. prob is a data frame with a variable called "mean", a variable called "disp", and, optionally, one or more 'by' variables. For instance, a prob of

data.frame(sex = c("Female", "Male"),
           mean = c(0.95, 0.92),
           disp = c(0.02, 0.015))

implies that the expected value for the inclusion probability is 0.95 for females and 0.92 for males, with slightly more uncertainty for females than for males.

The rate 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(mean = 0.03, disp = 0.1)

implies that the expected value for the overcoverage rate is 0.03, with a dispersion of 0.1. Since no 'by' variables are included, the same mean and dispersion values are applied to all cells.

Mathematical details

The model for the observed outcome is

y_i^{\text{obs}} = u_i + v_i

u_i \sim \text{Binomial}(y_i^{\text{true}}, \pi_{g[i]})

v_i \sim \text{Poisson}(\kappa_{h[i]} \gamma_i w_i)

\pi_g \sim \text{Beta}(m_g^{(\pi)} / d_g^{(\pi)}, (1-m_g^{(\pi)}) / d_g^{(\pi)})

\kappa_h \sim \text{Gamma}(1/d_h^{(\kappa)}, 1/(d_h^{(\kappa)} m_h^{(\kappa)}))

where

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

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

• \gamma_i is the rate for cell i;

• w_i is exposure for cell i;

• \pi_{g[i]} is the probability that a member of the target population in cell i is correctly enumerated in that cell;

• \kappa_{h[i]} is the overcoverage rate for cell i;

• m_g^{(\pi)} is the expected value for \pi_g (specified via prob);

• d_g^{(\pi)} is disperson for \pi_g (specified via prob);

• m_h^{(\kappa)} is the expected value for \kappa_h (specified via rate); and

• d_h^{(\kappa)} is disperson for \kappa_h (specified via rate).

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_overcount() An overcount-only data model

• datamods All data models implemented in bage

• confidential Confidentialization procedures modeled in bage

• Mathematical Details vignette

Examples

## specify 'prob' and 'rate'
prob <- data.frame(sex = c("Female", "Male"),
                   mean = c(0.95, 0.97),
                   disp = c(0.05, 0.05))
rate <- data.frame(mean = 0.03, disp = 0.15)

## specify model
mod <- mod_pois(divorces ~ age * sex + time,
                data = nzl_divorces,
                exposure = population) |>
  set_datamod_miscount(prob = prob, rate = 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 undercoverage and
## overcoverage
mod <- mod |>
 set_confidential_rr3() |>
 fit()
mod

bage documentation built on Nov. 5, 2025, 5:33 p.m.