NMAR (version 0.1.2)

exptilt_nonparam_engine: Nonparametric exponential tilting engine for NMAR

Description

Constructs a configuration for the nonparametric exponential tilting estimator under nonignorable nonresponse. This engine implements the "Fully Nonparametric Approach" from **Appendix 2** of Riddles et al. (2016). The estimator uses an Expectation-Maximization (EM) algorithm to directly estimate the nonresponse odds \(O(x_1, y)\) for aggregated, categorical data.

Usage

exptilt_nonparam_engine(refusal_col = "", max_iter = 100, tol_value = 1e-06)

Value

An engine object of class c("nmar_engine_exptilt_nonparam","nmar_engine"). This is a configuration list; it is not a fit. Pass it to nmar.

Arguments

refusal_col

character; the column name in data that contains the aggregated counts of non-respondents (refusals).

max_iter

integer; the maximum number of iterations for the EM algorithm.

tol_value

numeric; the convergence tolerance for the EM algorithm. The loop stops when the sum of absolute changes in the odds matrix is less than this value.

Details

This engine is designed for cases where all variables (outcomes $Y$, response predictors $X_1$, and instrumental variables $X_2$) are categorical, and the input data is pre-aggregated into strata.

The method assumes an instrumental variable \(X_2\) is available. The response probability is assumed to depend on \(X_1\) and $Y$, but *not* on \(X_2\).

The EM algorithm iteratively solves for the nonresponse odds: $$ O^{(t+1)}(x_1^*, y^*) = \frac{M_{y^*x_1^*}^{(t)}}{N_{y^*x_1^*}} $$ where \(M_{y^*x_1^*}^{(t)}\) is the expected count of non-respondents (calculated in the E-step) and \(N_{y^*x_1^*}\) is the observed count of respondents for a given stratum $(x_1, y)$.

The final output from the nmar call is an object containing data_to_return, an aggregated data frame where the original 'refusal' counts have been redistributed into the outcome columns (e.g., 'Voted_A', 'Voted_B') as expected non-respondent counts.

References

Minsun Kim Riddles, Jae Kwang Kim, Jongho Im A Propensity-score-adjustment Method for Nonignorable Nonresponse Journal of Survey Statistics and Methodology, Volume 4, Issue 2, June 2016, Pages 215–245. (See **Appendix 2** for this specific method).

Examples

# Test data (Riddles 2016, Table 9)
voting_data_example <- data.frame(
  Gender = rep(c("Male", "Male", "Male", "Male", "Female", "Female", "Female", "Female"), 1),
  Age_group = c("20-29", "30-39", "40-49", ">=50", "20-29", "30-39", "40-49", "50+"),
  Voted_A = c(93, 104, 146, 560, 106, 129, 170, 501),
  Voted_B = c(115, 233, 295, 350, 159, 242, 262, 218),
  Other = c(4, 8, 5, 3, 8, 5, 5, 7),
  Refusal = c(28, 82, 49, 174, 62, 70, 69, 211),
  Total = c(240, 427, 495, 1087, 335, 446, 506, 937)
)

np_em_config <- exptilt_nonparam_engine(
  refusal_col = "Refusal",
  max_iter = 100,
  tol_value = 0.001
)

# Formula: Y1 + Y2 + ... ~ X1_vars | X2_vars
# Here, Y = Voted_A, Voted_B, Other
#      x1 = Gender (response model)
#      x2 = Age_group (instrumental variable)
em_formula <- Voted_A + Voted_B + Other ~ Gender | Age_group

# \donttest{
results_em_np <- nmar(
  formula = em_formula,
  data = voting_data_example,
  engine = np_em_config,
  trace_level = 0
)

# View the final adjusted counts
# (Original counts + expected non-respondent counts)
print(results_em_np$data_final)
# }