Calibration estimation of population total using multi-auxiliary information in the presence of non-response

This paper considers the problem of estimation of the population total under probability proportional to size (PPS) sampling scheme when complete data is not available due to the presence of missing observations or non-response. The suggested estimators are developed based on available multi-auxiliary information for the response group and non-response group utilizing the calibration approach. The variances of the suggested estimators have been derived up to the first order of approximation. A simulation study done on a real dataset using R software also supports the performance of the suggested estimators. The empirical percentage absolute relative biases (%ARB) and percentage relative root mean squared errors (%RRMSE) are computed for the suggested estimators. The developed estimators are compared with the estimators of the population total due to the design-based Horvitz and Thompson (HT) estimator and calibration HT type estimator obtained on the available complete response units along with the design-based Hansen and Hurwitz (HH) estimator in the presence of non-response.

Simulation analysis of non-respondent information in context of small domain

In the real-world, there are various situations when all units are not accessible of the respondent called unit non-response. The effect of unit non-response is a tricky matter for estimating the total number of unit. The present work highlights the interest about subpopulations (domains) in two affairs: i. if domains total of the supportive information is accessible ii. if domains total of the supportive variable does not access. The government needs to be introducing the actual facilities in these small domains. The supportive information is used to find out the estimate of the non respondent information and to apply this information for desired domains. Sometimes, it has been found that the accessible auxiliary variable for the domains might be positive shape. Therefore, it develops an appropriate model that has positive skewness. The present context highlighted the indirect method using a power-based estimation with calibration approach. By combining power based estimation and calibration technique, it is possible to obtain more accurate estimates for intended small domains. Even the supportive information is positively biased. This approach helps us in mitigating the effect of non-respondent and improving the overall reliability of the estimators. The simulation was conducted for different sizes 70 and 90 when nonresponse variable in the study variable. The results show that investigated power-based estimate provides better option over relevant exponential, ratio, and generalized regression estimators for intended domains.

Instability of inverse probability weighting methods and a remedy for nonignorable missing data

Inverse probability weighting (IPW) methods are commonly used to analyze nonignorable missing data (NIMD) under the assumption of a logistic model for the missingness probability. However, solving IPW equations numerically may involve nonconvergence problems when the sample size is moderate and the missingness probability is high. Moreover, those equations often have multiple roots, and identifying the best root is challenging. Therefore, IPW methods may have low efficiency or even produce biased results. We identify the pitfall in these methods pathologically: they involve the estimation of a moment-generating function (MGF), and such functions are notoriously unstable in general. As a remedy, we model the outcome distribution given the covariates of the completely observed individuals semiparametrically. After forming an induced logistic regression (LR) model for the missingness status of the outcome and covariate, we develop a maximum conditional likelihood method to estimate the underlying parameters. The proposed method circumvents the estimation of an MGF and hence overcomes the instability of IPW methods. Our theoretical and simulation results show that the proposed method outperforms existing competitors greatly. Two real data examples are analyzed to illustrate the advantages of our method. We conclude that if only a parametric LR is assumed but the outcome regression model is left arbitrary, then one has to be cautious in using any of the existing statistical methods in problems involving NIMD.

Matrix completion under complex survey sampling

Multivariate nonresponse is often encountered in complex survey sampling, and simply ignoring it leads to erroneous inference. In this paper, we propose a new matrix completion method for complex survey sampling. Different from existing works either conducting row-wise or column-wise imputation, the data matrix is treated as a whole which allows for exploiting both row and column patterns simultaneously. A column-space-decomposition model is adopted incorporating a low-rank structured matrix for the finite population with easy-to-obtain demographic information as covariates. Besides, we propose a computationally efficient projection strategy to identify the model parameters under complex survey sampling. Then, an augmented inverse probability weighting estimator is used to estimate the parameter of interest, and the corresponding asymptotic upper bound of the estimation error is derived. Simulation studies show that the proposed estimator has a smaller mean squared error than other competitors, and the corresponding variance estimator performs well. The proposed method is applied to assess the health status of the U.S. population.

Generalised calibration with latent variables for the treatment of unit nonresponse in sample surveys

Sample surveys may suffer from nonignorable unit nonresponse. This happens when the decision of whether or not to participate in the survey is correlated with variables of interest; in such a case, nonresponse produces biased estimates for parameters related to those variables, even after adjustments that account for auxiliary information. This paper presents a method to deal with nonignorable unit nonresponse that uses generalised calibration and latent variable modelling. Generalised calibration enables to model unit nonresponse using a set of auxiliary variables (instrumental or model variables), that can be different from those used in the calibration constraints (calibration variables). We propose to use latent variables to estimate the probability to participate in the survey and to construct a reweighting system incorporating such latent variables. The proposed methodology is illustrated, its properties discussed and tested on two simulation studies. Finally, it is applied to adjust estimates of the finite population mean wealth from the Italian Survey of Household Income and Wealth.

Double-calibration estimators accounting for under-coverage and nonresponse in socio-economic surveys

Under-coverage and nonresponse problems are jointly present in most socio-economic surveys. The purpose of this paper is to propose an estimation strategy that accounts for both problems by performing a two-step calibration. The first calibration exploits a set of auxiliary variables only available for the units in the sampled population to account for nonresponse. The second calibration exploits a different set of auxiliary variables available for the whole population, to account for under-coverage. The two calibrations are then unified in a double-calibration estimator. Mean and variance of the estimator are derived up to the first order of approximation. Conditions ensuring approximate unbiasedness are derived and discussed. The strategy is empirically checked by a simulation study performed on a set of artificial populations. A case study is derived from the European Union Statistics on Income and Living Conditions survey data. The strategy proposed is flexible and suitable in most situations in which both under-coverage and nonresponse are present.

Combining Multiple Observational Data Sources to Estimate Causal Effects

The era of big data has witnessed an increasing availability of multiple data sources for statistical analyses. We consider estimation of causal effects combining big main data with unmeasured confounders and smaller validation data with supplementary information on these confounders. Under the unconfoundedness assumption with completely observed confounders, the smaller validation data allow for constructing consistent estimators for causal effects, but the big main data can only give error-prone estimators in general. However, by leveraging the information in the big main data in a principled way, we can improve the estimation efficiencies yet preserve the consistencies of the initial estimators based solely on the validation data. Our framework applies to asymptotically normal estimators, including the commonly used regression imputation, weighting, and matching estimators, and does not require a correct specification of the model relating the unmeasured confounders to the observed variables. We also propose appropriate bootstrap procedures, which makes our method straightforward to implement using software routines for existing estimators. Supplementary materials for this article are available online.

Calibrated propensity score method for survey nonresponse in cluster sampling

Weighting adjustment is commonly used in survey sampling to correct for unit nonresponse. In cluster sampling, the missingness indicators are often correlated within clusters and the response mechanism is subject to cluster-specific nonignorable missingness. Based on a parametric working model for the response mechanism that incorporates cluster-specific nonignorable missingness, we propose a method of weighting adjustment. We provide a consistent estimator of the mean or totals in cases where the study variable follows a generalized linear mixed-effects model. The proposed method is robust in the sense that the consistency of the estimator does not require correct specification of the functional forms of the response and outcome models. A consistent variance estimator based on Taylor linearization is also proposed. Numerical results, including a simulation and a real-data application, are presented.