method_npar: Mass imputation using non-parametric model method

In nonprobsvy: Inference Based on Non-Probability Samples

Mass imputation using non-parametric model method

Description

Model for the outcome for the mass imputation estimator using loess via stats::loess. Estimation of the mean is done using the S_B probability sample.

Usage

method_npar(
  y_nons,
  X_nons,
  X_rand,
  svydesign,
  weights = NULL,
  family_outcome = "gaussian",
  start_outcome = NULL,
  vars_selection = FALSE,
  pop_totals = NULL,
  pop_size = NULL,
  control_outcome = control_out(),
  control_inference = control_inf(),
  verbose = FALSE,
  se = TRUE
)

Arguments

y_nons	target variable from non-probability sample
X_nons	a model.matrix with auxiliary variables from non-probability sample
X_rand	a model.matrix with auxiliary variables from non-probability sample
svydesign	a svydesign object
weights	case / frequency weights from non-probability sample (default NULL)
family_outcome	family for the glm model)
start_outcome	a place holder (not used in method_npar)
vars_selection	whether variable selection should be conducted
pop_totals	a place holder (not used in method_npar)
pop_size	population size from the nonprob function
control_outcome	controls passed by the control_out function
control_inference	controls passed by the control_inf function
verbose	parameter passed from the main nonprob function
se	whether standard errors should be calculated

Details

Analytical variance

The variance of the mean is estimated based on the following approach

(a) non-probability part (S_A with size n_A; denoted as var_nonprob in the result)

\hat{V}_1 = \frac{1}{N^2} \sum_{i=1}^{n_A} \left\lbrace\hat{g}_B(\boldsymbol{x}_i)\right\rbrace^{2} \hat{e}_i^2,

where \hat{e}_i=y_i - \hat{m}(x_i) is the residual and \hat{g}_B(\boldsymbol{x}_i) = \left\lbrace \pi_B(\boldsymbol{x}_i) \right\rbrace^{-1} can be estimated various ways. In the package we estimate \hat{g}_B(\boldsymbol{x}_i) using \pi_B(\boldsymbol{x}_i)=E(R | \boldsymbol{x}) as suggested by Chen et al. (2022, p. 6). In particular, we currently support this using stats::loesswith"gaussian"' family.

(b) probability part (S_B with size n_B; denoted as var_prob in the result)

This part uses functionalities of the {survey} package and the variance is estimated using the following equation:

\hat{V}_2=\frac{1}{N^2} \sum_{i=1}^{n_B} \sum_{j=1}^{n_B} \frac{\pi_{i j}-\pi_i \pi_j}{\pi_{i j}} \frac{\hat{m}(x_i)}{\pi_i} \frac{\hat{m}(x_j)}{\pi_j}.

Note that \hat{V}_2 in principle can be estimated in various ways depending on the type of the design and whether population size is known or not.

Value

an nonprob_method class which is a list with the following entries

model_fitted

fitted model object returned by stats::loess

y_nons_pred

predicted values for the non-probablity sample

y_rand_pred

predicted values for the probability sample or population totals

coefficients

coefficients for the model (if available)

svydesign

an updated surveydesign2 object (new column y_hat_MI is added)

y_mi_hat

estimated population mean for the target variable

vars_selection

whether variable selection was performed

var_prob

variance for the probability sample component (if available)

var_nonprob

variance for the non-probability sampl component

model

model type (character "npar")

References

Chen, S., Yang, S., & Kim, J. K. (2022). Nonparametric mass imputation for data integration. Journal of Survey Statistics and Methodology, 10(1), 1-24.

Examples

set.seed(123123123)
N <- 10000
n_a <- 500
n_b <- 1000
n_b1 <- 0.7*n_b
n_b2 <- 0.3*n_b
x1 <- rnorm(N, 2, 1)
x2 <- rnorm(N, 2, 1)
y1 <- rnorm(N, 0.3 + 2*x1+ 2*x2, 1)
y2 <- rnorm(N, 0.3 + 0.5*x1^2+ 0.5*x2^2, 1)
strata <- x1 <= 2
pop <- data.frame(x1, x2, y1, y2, strata)
sample_a <- pop[sample(1:N, n_a),]
sample_a$w_a <- N/n_a
sample_a_svy <- svydesign(ids=~1, weights=~w_a, data=sample_a)
pop1 <- subset(pop, strata == TRUE)
pop2 <- subset(pop, strata == FALSE)
sample_b <- rbind(pop1[sample(1:nrow(pop1), n_b1), ],
                  pop2[sample(1:nrow(pop2), n_b2), ])
res_y_npar <- nonprob(outcome = y1 + y2 ~ x1 + x2,
                      data = sample_b,
                      svydesign = sample_a_svy,
                      method_outcome = "npar")
res_y_npar

nonprobsvy documentation built on April 3, 2025, 7:08 p.m.