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.     

Using data augmentation to correct for non-ignorable non-response when surrogate data are available: an application to the distribution of hourly pay

Summary.  The paper develops a data augmentation method to estimate the distribution function of a variable, which is partially observed, under a non-ignorable missing data mechanism, and where surrogate data are available. An application to the estimation of hourly pay distributions using UK Labour Force Survey data provides the main motivation. In addition to considering a standard parametric data augmentation method, we consider the use of hot deck imputation methods as part of the data augmentation procedure to improve the robustness of the method. The method proposed is compared with standard methods that are based on an ignorable missing data mechanism, both in a simulation study and in the Labour Force Survey application. The focus is on reducing bias in point estimation, but variance estimation using multiple imputation is also considered briefly.     

Foreign Exchange Intervention by the Bank of Japan: Bayesian Analysis Using a Bivariate Stochastic Volatility Model

A bivariate stochastic volatility model is employed to measure the effect of intervention by the Bank of Japan (BOJ) on daily returns and volume in the USD/YEN foreign exchange market. Missing observations are accounted for, and a data-based Wishart prior for the precision matrix of the errors to the transition equation that is in line with the likelihood is suggested. Empirical results suggest there is strong conditional heteroskedasticity in the mean-corrected volume measure, as well as contemporaneous correlation in the errors to both the observation and transition equations. A threshold model is used for the BOJ reaction function, which is estimated jointly with the bivariate stochastic volatility model via Markov chain Monte Carlo. This accounts for endogeneity between volatility in the market and the BOJ reaction function, something that has hindered much previous empirical analysis in the literature on central bank intervention. The empirical results suggest there was a shift in behavior by the BOJ, with a movement away from a policy of market stabilization and toward a role of support for domestic monetary policy objectives. Throughout, we observe “leaning against the wind” behavior, something that is a feature of most previous empirical analysis of central bank intervention. A comparison with a bivariate EGARCH model suggests that the bivariate stochastic volatility model produces estimates that better capture spikes in in-sample volatility. This is important in improving estimates of a central bank reaction function because it is at these periods of high daily volatility that central banks more frequently intervene.     

Multivariate multilevel analyses of examination results

Summary. In the study of examination results much interest centres on comparisons of curriculum subjects entered and the correlation between these at individual and institution level based on data where not every individual takes all subjects. Such `missing' data are not missing at random because individuals deliberately select subjects that they wish to study according to criteria that will be associated with their performance. In this paper we propose multivariate multilevel models for the analysis of such data, adjusting for such subject selection effects as well as for prior achievement. This then enables more appropriate institutional comparisons and correlation estimates. We analyse A- and AS-level results in different mathematics papers of 52 587 students from 2592 institutions in England in 1997. Although this paper is concerned largely with methodology, substantive findings emerge on the effects of gender, age, intakes of General Certificate of Education pupils, examination board and establishment type for A- and AS-level mathematics.     

Missing time-dependent covariates in human immunodeficiency virus dynamic models

Summary. The study of human immunodeficiency virus dynamics is one of the most important areas in research into acquired immune deficiency syndrome in recent years. Non-linear mixed effects models have been proposed for modelling viral dynamic processes. A challenging problem in the modelling is to identify repeatedly measured (time-dependent), but possibly missing, immunologic or virologic markers (covariates) for viral dynamic parameters. For missing time-dependent covariates in non-linear mixed effects models, the commonly used complete-case, mean imputation and last value carried forward methods may give misleading results. We propose a three-step hierarchical multiple-imputation method, implemented by Gibbs sampling, which imputes the missing data at the individual level but can pool information across individuals. We compare various methods by Monte Carlo simulations and find that the multiple-imputation method proposed performs the best in terms of bias and mean-squared errors in the estimates of covariate coefficients. By applying the favoured multiple-imputation method to clinical data, we conclude that there is a negative correlation between the viral decay rate (a virological response parameter) and CD4 or CD8 cell counts during the treatment; this is counter-intuitive, but biologically interpretable on the basis of findings from other clinical studies. These results may have an important influence on decisions about treatment for acquired immune deficiency syndrome patients.     

Markov structure based logistic regression for repeated measures: An application to diabetes mellitus data

In longitudinal studies, as repeated observations are made on the same individual the response variables will usually be correlated. In analyzing such data, this dependence must be taken into account to avoid misleading inferences. The focus of this paper is to apply a logistic marginal model with Markovian dependence proposed by Azzalini [A. Azzalini, Logistic regression for autocorrelated data with application to repeated measures, Biometrika 81 (1994) 767–775] to the study of the influence of time-dependent covariates on the marginal distribution of the binary response in serially correlated binary data. We have shown how to construct the model so that the covariates relate only to the mean value of the process, independent of the association parameters. After formulating the proposed model for repeated measures data, the same approach is applied to missing data. An application is provided to the diabetes mellitus data of registered patients at the Bangladesh Institute of Research and Rehabilitation in Diabetes, Endocrine and Metabolic Disorders (BIRDEM) in 1984, using both time stationary and time varying covariates.     

Empirical Likelihood in Causal Inference

This paper discusses the estimation of average treatment effects in observational causal inferences. By employing a working propensity score and two working regression models for treatment and control groups, Robins et al. (1994 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1994 ). Estimation of regression coefficients when some regressors are not always observed . Journal of the American Statistical Association 89 : 846 – 866 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 1995 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1995 ). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data . Journal of the American Statistical Association 90 : 106 – 121 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) introduced the augmented inverse probability weighting (AIPW) method for estimation of average treatment effects, which extends the inverse probability weighting (IPW) method of Horvitz and Thompson (1952 Horvitz , D. G. , Thompson , D. J. ( 1952 ). A generalization of sampling without replacement from a finite universe . Journal of the American Statistical Association 47 : 663 – 685 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]); the AIPW estimators are locally efficient and doubly robust. In this paper, we study a hybrid of the empirical likelihood method and the method of moments by employing three estimating functions, which can generate estimators for average treatment effects that are locally efficient and doubly robust. The proposed estimators of average treatment effects are efficient for the given choice of three estimating functions when the working propensity score is correctly specified, and thus are more efficient than the AIPW estimators. In addition, we consider a regression method for estimation of the average treatment effects when working regression models for both the treatment and control groups are correctly specified; the asymptotic variance of the resulting estimator is no greater than the semiparametric variance bound characterized by the theory of Robins et al. (1994 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1994 ). Estimation of regression coefficients when some regressors are not always observed . Journal of the American Statistical Association 89 : 846 – 866 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 1995 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1995 ). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data . Journal of the American Statistical Association 90 : 106 – 121 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Finally, we present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification.     

An algorithm for weighted bilinear regression

Bilinear models in which the expectation of a two-way array is the sum of products of parameters are widely used in spectroscopy. In this paper we present an algorithm called combined-vector successive overrelaxation (COV-SOR) for bilinear models, and compare it with methods like alternating least squares, singular value decomposition, and the Marquardt procedure. Comparisons are done for missing data also.