scholarly journals Empirical likelihood and Wilks phenomenon for data with nonignorable missing values

2019 ◽  
Vol 46 (4) ◽  
pp. 1003-1024 ◽  
Author(s):  
Puying Zhao ◽  
Lei Wang ◽  
Jun Shao
Keyword(s):  
Empirical Likelihood ◽  
Missing Values ◽  
Wilks Phenomenon ◽  
Nonignorable Missing

Semiparametric inverse propensity weighting for nonignorable missing data

Biometrika ◽  
2016 ◽  
Vol 103 (1) ◽  
pp. 175-187 ◽  
Author(s):  
Jun Shao ◽  
Lei Wang
Keyword(s):  
Missing Data ◽  
Missing Values ◽  
Generalized Method Of Moments ◽  
Estimating Equations ◽  
Real Data ◽  
Population Parameters ◽  
Finite Sample ◽  
External Data ◽  
Nonignorable Missing ◽  
Inverse Propensity Weighting

Abstract To estimate unknown population parameters based on data having nonignorable missing values with a semiparametric exponential tilting propensity, Kim & Yu (2011) assumed that the tilting parameter is known or can be estimated from external data, in order to avoid the identifiability issue. To remove this serious limitation on the methodology, we use an instrument, i.e., a covariate related to the study variable but unrelated to the missing data propensity, to construct some estimating equations. Because these estimating equations are semiparametric, we profile the nonparametric component using a kernel-type estimator and then estimate the tilting parameter based on the profiled estimating equations and the generalized method of moments. Once the tilting parameter is estimated, so is the propensity, and then other population parameters can be estimated using the inverse propensity weighting approach. Consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the estimators is studied through simulation, and a real-data example is also presented.

scholarly journals A Mixture IRTree Model for Performance Decline and Nonignorable Missing Data

2020 ◽  
Vol 80 (6) ◽  
pp. 1168-1195
Author(s):  
Hung-Yu Huang
Keyword(s):  
Item Response ◽  
International Student ◽  
Missing Values ◽  
Student Assessment ◽  
Response Behavior ◽  
Parameter Recovery ◽  
Test Items ◽  
International Student Assessment ◽  
Performance Decline ◽  
Nonignorable Missing

In educational assessments and achievement tests, test developers and administrators commonly assume that test-takers attempt all test items with full effort and leave no blank responses with unplanned missing values. However, aberrant response behavior—such as performance decline, dropping out beyond a certain point, and skipping certain items over the course of the test—is inevitable, especially for low-stakes assessments and speeded tests due to low motivation and time limits, respectively. In this study, test-takers are classified as normal or aberrant using a mixture item response theory (IRT) modeling approach, and aberrant response behavior is described and modeled using item response trees (IRTrees). Simulations are conducted to evaluate the efficiency and quality of the new class of mixture IRTree model using WinBUGS with Bayesian estimation. The results show that the parameter recovery is satisfactory for the proposed mixture IRTree model and that treating missing values as ignorable or incorrect and ignoring possible performance decline results in biased estimation. Finally, the applicability of the new model is illustrated by means of an empirical example based on the Program for International Student Assessment.

scholarly journals Imputation-based strategies for clinical trial longitudinal data with nonignorable missing values

2008 ◽  
Vol 27 (15) ◽  
pp. 2826-2849 ◽  
Author(s):  
Xiaowei Yang ◽  
Jinhui Li ◽  
Steven Shoptaw
Keyword(s):  
Clinical Trial ◽  
Longitudinal Data ◽  
Missing Values ◽  
Nonignorable Missing

scholarly journals Empirical Likelihood for Multidimensional Linear Model with Missing Responses

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Liping Zhu
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Missing Values ◽  
Probability Function ◽  
Likelihood Ratio Statistic ◽  
Selection Probability ◽  
Missing Responses ◽  
Chi Squared ◽  
Multidimensional Linear

Imputation is a popular technique for handling missing data especially for plenty of missing values. Usually, the empirical log-likelihood ratio statistic under imputation is asymptotically scaled chi-squared because the imputing data are not i.i.d. Recently, a bias-corrected technique is used to study linear regression model with missing response data, and the resulting empirical likelihood ratio is asymptotically chi-squared. However, it may suffer from the “the curse of high dimension” in multidimensional linear regression models for the nonparametric estimator of selection probability function. In this paper, a parametric selection probability function is introduced to avoid the dimension problem. With the similar bias-corrected method, the proposed empirical likelihood statistic is asymptotically chi-squared when the selection probability is specified correctly and even asymptotically scaled chi-squared when specified incorrectly. In addition, our empirical likelihood estimator is always consistent whether the selection probability is specified correctly or not, and will achieve full efficiency when specified correctly. A simulation study indicates that the proposed method is comparable in terms of coverage probabilities.

scholarly journals When Nonresponse Mechanisms Change: Effects on Trends and Group Comparisons in International Large-Scale Assessments

2019 ◽  
Vol 79 (4) ◽  
pp. 699-726 ◽  
Author(s):  
Karoline A. Sachse ◽  
Nicole Mahler ◽  
Steffi Pohl
Keyword(s):  
Missing Data ◽  
Large Scale ◽  
Missing Values ◽  
Parameter Estimates ◽  
Assessment Data ◽  
Change Over Time ◽  
International Student Assessment ◽  
Large Scale Assessments ◽  
Nonignorable Missing ◽  
Over Time

Mechanisms causing item nonresponses in large-scale assessments are often said to be nonignorable. Parameter estimates can be biased if nonignorable missing data mechanisms are not adequately modeled. In trend analyses, it is plausible for the missing data mechanism and the percentage of missing values to change over time. In this article, we investigated (a) the extent to which the missing data mechanism and the percentage of missing values changed over time in real large-scale assessment data, (b) how different approaches for dealing with missing data performed under such conditions, and (c) the practical implications for trend estimates. These issues are highly relevant because the conclusions hold for all kinds of group mean differences in large-scale assessments. In a reanalysis of PISA (Programme for International Student Assessment) data from 35 OECD countries, we found that missing data mechanisms and numbers of missing values varied considerably across time points, countries, and domains. In a simulation study, we generated data in which we allowed the missing data mechanism and the amount of missing data to change over time. We showed that the trend estimates were biased if differences in the missing-data mechanisms were not taken into account, in our case, when omissions were scored as wrong, when omissions were ignored, or when model-based approaches assuming a constant missing data mechanism over time were used. The results suggest that the most accurate estimates can be obtained from the application of multiple group models for nonignorable missing values when the amounts of missing data and the missing data mechanisms changed over time. In an empirical example, we furthermore showed that the large decline in PISA reading literacy in Ireland in 2009 was reduced when we estimated trends using missing data treatments that accounted for changes in missing data mechanisms.

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