Estimation of single index model with missing response at random

Under missing at random, we estimate the unknown link function and the direction parameter in a single index model. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, the optimal convergence rate for the estimator of the link function is obtained and simulation results support the theoretical results of the paper.     

Multistage Sampling Designs and Estimating Equations

In some applications it is cost efficient to sample data in two or more stages. In the first stage a simple random sample is drawn and then stratified according to some easily measured attribute. In each subsequent stage a random subset of previously selected units is sampled for more detailed and costly observation, with a unit's sampling probability determined by its attributes as observed in the previous stages. This paper describes multistage sampling designs and estimating equations based on the resulting data. Maximum likelihood estimates (MLEs) and their asymptotic variances are given for designs using parametric models. Horvitz–Thompson estimates are introduced as alternatives to MLEs, their asymptotic distributions are derived and their strengths and weaknesses are evaluated. The designs and the estimates are illustrated with data on corn production.     

CANONICAL VARIATE ANALYSIS—A GENERAL MODEL FORMULATION

A general model, specifying the population means as a function of the population canonical vectors, provides a natural basis for considering many aspects of canonical variate analysis. These aspects include: estimation for elliptical densities, and robust estimation; estimation of missing values; adequacy of hypothetical variables; regression in dummy variable space; and comparison of solutions.     

Structural effects of network sampling coverage I: Nodes missing at random

Network measures assume a census of a well-bounded population. This level of coverage is rarely achieved in practice, however, and we have only limited information on the robustness of network measures to incomplete coverage. This paper examines the effect of node-level missingness on 4 classes of network measures: centrality, centralization, topology and homophily across a diverse sample of 12 empirical networks. We use a Monte Carlo simulation process to generate data with known levels of missingness and compare the resulting network scores to their known starting values. As with past studies (0035 and 0135), we find that measurement bias generally increases with more missing data. The exact rate and nature of this increase, however, varies systematically across network measures. For example, betweenness and Bonacich centralization are quite sensitive to missing data while closeness and in-degree are robust. Similarly, while the tau statistic and distance are difficult to capture with missing data, transitivity shows little bias even with very high levels of missingness. The results are also clearly dependent on the features of the network. Larger, more centralized networks are generally more robust to missing data, but this is especially true for centrality and centralization measures. More cohesive networks are robust to missing data when measuring topological features but not when measuring centralization. Overall, the results suggest that missing data may have quite large or quite small effects on network measurement, depending on the type of network and the question being posed.     

Missing Data: A Comparison of Online and Classroom Data Collection Methods With Social Work Students

ABSTRACT

Missing data (item nonresponse) is prevalent in survey research and likely regardless of the researcher's efforts. Problems associated with missing data include but are not limited to low statistical power, biased results, and limited external validity. The present study compared online (n = 125) and classroom (n = 74) data collection methods to determine the extent of missing data between the two cohorts. The total sample consisted of 199 master's of social work and bachelor's of social work students, each of whom were asked to respond to 91 survey items (the majority of which pertained to research in social work practice). A logistic regression model demonstrated a significant relationship between the total number of completed survey items and the data collection methods. The study shows an empirical association between the classroom data collection method and the lower levels of missing data. Study limitations are discussed, and recommendations for future research are made.     

Power of double-sampling tests for General Linear Hypotheses

In this paper, testing procedures based on double-sampling are proposed that yield gains in terms of power for the tests of General Linear Hypotheses. The distribution of a test statistic, involving both the measurements of the outcome on the smaller sample and of the covariates on the wider sample, is first derived. Then, approximations are provided in order to allow for a formal comparison between the powers of double-sampling and single-sampling strategies. Furthermore, it is shown how to allocate the measurements of the outcome and the covariates in order to maximize the power of the tests for a given experimental cost.     

Stratified Logrank Test of No Randomized Treatment Effect with Missing Stratum Information

A major objective in many clinical trials is to compare several competing treatments in a randomized experiment. In such studies, it is often necessary to adjust for some other important factor that affects the event rates in the treatment groups. When this factor is discrete, one usual approach uses a stratified version of the logrank test. In this article, we consider the problem that arises when the factor giving rise to the strata is missing at random for some of the study subjects. This article proposes a modified version of the stratified logrank test, in which the unobserved stratum indicators are replaced by an estimate of their conditional expectation given available auxiliary covariate measurements. The null asymptotic distribution of the proposed test statistic is investigated. Simulation experiments are also conducted to examine the finite-sample behavior of this test under both null and alternative hypotheses. Simulations indicate that the proposed test performs well, even under some moderate deviations to the at-random missingness assumption.     

Estimators for the Population Mean in the Case of Missing Data

We propose a class of estimators for the population mean when there are missing data in the data set. Obtaining the mean square error equations of the proposed estimators, we show the conditions where the proposed estimators are more efficient than the sample mean, ratio-type estimators, and the estimators in Singh and Horn (2000 Singh , S. , Horn , S. ( 2000 ). Compromised imputation in survey sampling . Metrika 51 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) and Singh and Deo (2003 Singh , S. , Deo , B. (2003). Imputation by power transformation. Statist. Pap. 44:555–579.[Crossref], [Web of Science ®] , [Google Scholar]) in the case of missing data. These conditions are also supported by a numerical example.     

Nonignorable Attrition in Multi-Period Panels With Refreshment Samples

In panel surveys, some observation units drop out before the end of the observation period. This panel attrition should not be ignored if it is related to the variables of interest. Hirano, Imbens, Ridder, and Rubin proposed the additively nonignorable (AN) attrition model to correct for the potential selectivity of the attrition in panels with two periods. If a refreshment sample is available in the second period, their model nonparametrically just-identifies the population distribution and the observation probability. We propose the sequential additively nonignorable attrition model that just-identifies the population distribution and the sequence of observation hazards for panels with more than two periods.     

EM Algorithm Estimation of Simultaneous Equation Model with Limited Variables: An Example of Cigarette Consumption

The two-part model and Heckman's sample selection model are often used in economic studies which involve analyzing the demand for limited variables. This study proposed a simultaneous equation model (SEM) and used the expectation-maximization algorithm to obtain the maximum likelihood estimate. We then constructed a simulation to compare the performance of estimates of price elasticity using SEM with those estimates from the two-part model and the sample selection model. The simulation shows that the estimates of price elasticity by SEM are more precise than those by the sample selection model and the two-part model when the model includes limited independent variables. Finally, we analyzed a real example of cigarette consumption as an application. We found an increase in cigarette price associated with a decrease in both the propensity to consume cigarettes and the amount actually consumed.