method_nn: Mass imputation using nearest neighbours matching method
In nonprobsvy: Inference Based on Non-Probability Samples

method_nn

R Documentation

Mass imputation using nearest neighbours matching method

Description

Mass imputation using nearest neighbours approach as described in Yang et al. (2021). The implementation is currently based on RANN::nn2 function and thus it uses Euclidean distance for matching units from S_A (non-probability) to S_B (probability). Estimation of the mean is done using S_B sample.

Usage

method_nn(
  y_nons,
  X_nons,
  X_rand,
  svydesign,
  weights = NULL,
  family_outcome = NULL,
  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
`family_outcome`	a placeholder (not used in `method_nn`)
`start_outcome`	a placeholder (not used in `method_nn`)
`vars_selection`	whether variable selection should be conducted
`pop_totals`	a placeholder (not used in `method_nn`)
`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)

This may be estimated using

\hat{V}_1 = \frac{1}{N^2}\sum_{i=1}^{S_A}\frac{1-\hat{\pi}_B(\boldsymbol{x}_i)}{\hat{\pi}_B(\boldsymbol{x}_i)}\hat{\sigma}^2(\boldsymbol{x}_i),

where \hat{\pi}_B(\boldsymbol{x}_i) is an estimator of propensity scores which we currently estimate using n_A/N (constant) and \hat{\sigma}^2(\boldsymbol{x}_i) is estimated using based on the average of (y_i - y_i^*)^2.

Chlebicki et al. (2025, Algorithm 2) proposed non-parametric mini-bootstrap estimator (without assuming that it is consistent) but with good finite population properties. This bootstrap can be applied using control_inference(nn_exact_se=TRUE) and can be summarized as follows:

Sample n_A units from S_A with replacement to create S_A' (if pseudo-weights are present inclusion probabilities should be proportional to their inverses).
Match units from S_B to S_A' to obtain predictions y^*={k}^{-1}\sum_{k}y_k.
Estimate \hat{\mu}=\frac{1}{N} \sum_{i \in S_B} d_i y_i^*.
Repeat steps 1-3 M times (we set M=50 in our simulations; this is hard-coded).
Estimate \hat{V}_1=\text{var}({\hat{\boldsymbol{\mu}}}) obtained from simulations and save it as var_nonprob.

(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 \sum_{j=1}^n \frac{\pi_{i j}-\pi_i \pi_j}{\pi_{i j}} \frac{y_i^*}{\pi_i} \frac{y_j^*}{\pi_j},

where y^*_i and y_j^* are values imputed imputed as an average of k-nearest neighbour, i.e. {k}^{-1}\sum_{k}y_k. 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: RANN::nn2 object
y_nons_pred: predicted values for the non-probablity sample (query to itself)
y_rand_pred: predicted values for the probability sample
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 (not implemented, for further development)
var_prob: variance for the probability sample component (if available)
var_nonprob: variance for the non-probability sample component
var_tot: total variance, if possible it should be var_prob+var_nonprob if not, just a scalar
model: model type (character "nn")
family: placeholder for the ⁠NN approach⁠ information

References

Yang, S., Kim, J. K., & Hwang, Y. (2021). Integration of data from probability surveys and big found data for finite population inference using mass imputation. Survey Methodology, June 2021 29 Vol. 47, No. 1, pp. 29-58

Chlebicki, P., Chrostowski, Ł., & Beręsewicz, M. (2025). Data integration of non-probability and probability samples with predictive mean matching. arXiv preprint arXiv:2403.13750.

Examples


data(admin)
data(jvs)
jvs_svy <- svydesign(ids = ~ 1,  weights = ~ weight, strata = ~ size + nace + region, data = jvs)

res_nn <- method_nn(y_nons = admin$single_shift,
                    X_nons = model.matrix(~ region + private + nace + size, admin),
                    X_rand = model.matrix(~ region + private + nace + size, jvs),
                    svydesign = jvs_svy)

res_nn

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