Nonparametric checks for varying coefficient models with missing response at random

In this paper, we propose a test on the parametric form of the coefficient functions in the varying coefficient model with missing response. Two groups of completed data sets are constructed by using imputation and inverse probability weighting methods respectively. By noting that the coefficient part can be a regression function for a specific model, we construct two empirical process-based tests. The asymptotical distributions of the proposed tests under null and local alternative hypothesis are investigated respectively. Simulation study is carried out to show the power performance of the test. We illustrate the proposed approaches with an environmental data set.     

A toolkit in SAS for the evaluation of multiple imputation methods

This paper outlines a strategy to validate multiple imputation methods. Rubin's criteria for proper multiple imputation are the point of departure. We describe a simulation method that yields insight into various aspects of bias and efficiency of the imputation process. We propose a new method for creating incomplete data under a general Missing At Random (MAR) mechanism. Software implementing the validation strategy is available as a SAS/IML module. The method is applied to investigate the behavior of polytomous regression imputation for categorical data.     

Fractional imputation for incomplete two-way contingency tables

Imputation procedures such as fully efficient fractional imputation (FEFI) or multiple imputation (MI) create multiple versions of the missing observations, thereby reflecting uncertainty about their true values. Multiple imputation generates a finite set of imputations through a posterior predictive distribution. Fractional imputation assigns weights to the observed data. The focus of this article is the development of FEFI for partially classified two-way contingency tables. Point estimators and variances of FEFI estimators of population proportions are derived. Simulation results, when data are missing completely at random or missing at random, show that FEFI is comparable in performance to maximum likelihood estimation and multiple imputation and superior to simple stochastic imputation and complete case anlaysis. Methods are illustrated with four data sets.     

Evaluating a sequential tree-based procedure for multivariate imputation of complex missing data structures

Item nonresponse in survey data can pose significant problems for social scientists carrying out statistical modeling using a large number of explanatory variables. A number of imputation methods exist but many only deal with univariate imputation, or relatively simple cases of multivariate imputation, often assuming a monotone pattern of missingness. In this paper we evaluate a tree-based approach for multivariate imputation using real data from the 1970 British Cohort Study, known for its complex pattern of nonresponse. The performance of this tree-based approach is compared to mode imputation and a sequential regression based approach within a simulation study.     

基于PMM多重插补法的线性模型系数估计量的模拟研究

在利用含无回答的经济数据建立线性回归模型,选择PMM多重插补法给出无回答的插补值。模拟结果显示,在任意无回答机制下,随着插补重数增大,系数估计量的偏差和均方误差减小不显著。对于任意无回答率,建议插补重数为5。在完全随机无回答机制下,随着无回答率增加,系数估计量的偏差或均方误差增大往往不显著。然而,在随机无回答机制下或在非随机无回答机制下,随着无回答率增加,系数估计量的偏差和均方误差增大往往显著。     

Imputation: Methods, Simulation Experiments and Practical Examples

When conducting surveys, two kinds of nonresponse may cause incomplete data files: unit nonresponse (complete nonresponse) and item nonresponse (partial nonresponse). The selectivity of the unit nonresponse is often corrected for. Various imputation techniques can be used for the missing values because of item nonresponse. Several of these imputation techniques are discussed in this report. One is the hot deck imputation. This paper describes two simulation experiments of the hot deck method. In the first study, data are randomly generated, and various percentages of missing values are then non-randomly'added'to the data. The hot deck method is used to reconstruct the data in this Monte Carlo experiment. The performance of the method is evaluated for the means, standard deviations, and correlation coefficients and compared with the available case method. In the second study, the quality of an imputation method is studied by running a simulation experiment. A selection of the data of the Dutch Housing Demand Survey is perturbed by leaving out specific values on a variable. Again hot deck imputations are used to reconstruct the data. The imputations are then compared with the true values. In both experiments the conclusion is that the hot deck method generally performs better than the available case method. This paper also deals with the questions which variables should be imputed and what the duration of the imputation process is. Finally the theory is illustrated by the imputation approaches of the Dutch Housing Demand Survey, the European Community Household Panel Survey (ECHP) and the new Dutch Structure of Earnings Survey (SES). These examples illustrate the levels of missing data that can be experienced in such surveys and the practical problems associated with choosing an appropriate imputation strategy for key items from each survey.     

Proper and Improper Multiple Imputation

Multiple imputation has become viewed as a general solution to missing data problems in statistics. However, in order to lead to consistent asymptotically normal estimators, correct variance estimators and valid tests, the imputations must be proper . So far it seems that only Bayesian multiple imputation, i.e. using a Bayesian predictive distribution to generate the imputations, or approximately Bayesian multiple imputations has been shown to lead to proper imputations in some settings. In this paper, we shall see that Bayesian multiple imputation does not generally lead to proper multiple imputations. Furthermore, it will be argued that for general statistical use, Bayesian multiple imputation is inefficient even when it is proper.     

基于EMB多重插补法的线性模型系数估计量的模拟研究

基于EMB多重插补法的线性模型系数估计量,分析其统计性质,并与PMM多重插补法以及DA插补法进行比较。模拟结果显示,随着无回答率增加,系数估计量的偏差绝对值、均方误差呈递增趋势,估计方差的递增趋势相对更显著。在完全随机无回答机制或随机无回答机制下,建议插补重数为15。在依赖被解释变量的非随机无回答机制下,建议插补重数可适当增大。在依赖其他变量的非随机无回答机制下,估计量的均方误差和估计方差的差异大,使用EMB多重插补法要谨慎。     

Methods for the Analysis of Explanatory Linear Regression Models with Missing Data Not at Random

Since the work of Little and Rubin (1987) not substantial advances in the analysisof explanatory regression models for incomplete data with missing not at randomhave been achieved, mainly due to the difficulty of verifying the randomness ofthe unknown data. In practice, the analysis of nonrandom missing data is donewith techniques designed for datasets with random or completely random missingdata, as complete case analysis, mean imputation, regression imputation, maximumlikelihood or multiple imputation. However, the data conditions required to minimizethe bias derived from an incorrect analysis have not been fully determined. In thepresent work, several Monte Carlo simulations have been carried out to establishthe best strategy of analysis for random missing data applicable in datasets withnonrandom missing data. The factors involved in simulations are sample size,percentage of missing data, predictive power of the imputation model and existenceof interaction between predictors. The results show that the smallest bias is obtainedwith maximum likelihood and multiple imputation techniques, although with lowpercentages of missing data, absence of interaction and high predictive power ofthe imputation model (frequent data structures in research on child and adolescentpsychopathology) acceptable results are obtained with the simplest regression imputation.     

Predictive mean matching imputation of semicontinuous variables

Multiple imputation methods properly account for the uncertainty of missing data. One of those methods for creating multiple imputations is predictive mean matching (PMM), a general purpose method. Little is known about the performance of PMM in imputing non‐normal semicontinuous data (skewed data with a point mass at a certain value and otherwise continuously distributed). We investigate the performance of PMM as well as dedicated methods for imputing semicontinuous data by performing simulation studies under univariate and multivariate missingness mechanisms. We also investigate the performance on real‐life datasets. We conclude that PMM performance is at least as good as the investigated dedicated methods for imputing semicontinuous data and, in contrast to other methods, is the only method that yields plausible imputations and preserves the original data distributions.     

A comparison of multiple imputation with EM algorithm and MCMC method for quality of life missing data

This study investigated the performance of multiple imputations with Expectation-Maximization (EM) algorithm and Monte Carlo Markov chain (MCMC) method in missing data imputation. We compared the accuracy of imputation based on some real data and set up two extreme scenarios and conducted both empirical and simulation studies to examine the effects of missing data rates and number of items used for imputation. In the empirical study, the scenario represented item of highest missing rate from a domain with fewest items. In the simulation study, we selected a domain with most items and the item imputed has lowest missing rate. In the empirical study, the results showed there was no significant difference between EM algorithm and MCMC method for item imputation, and number of items used for imputation has little impact, either. Compared with the actual observed values, the middle responses of 3 and 4 were over-imputed, and the extreme responses of 1, 2 and 5 were under-represented. The similar patterns occurred for domain imputation, and no significant difference between EM algorithm and MCMC method and number of items used for imputation has little impact. In the simulation study, we chose environmental domain to examine the effect of the following variables: EM algorithm and MCMC method, missing data rates, and number of items used for imputation. Again, there was no significant difference between EM algorithm and MCMC method. The accuracy rates did not significantly reduce with increase in the proportions of missing data. Number of items used for imputation has some contribution to accuracy of imputation, but not as much as expected.     

Using the Fraction of Missing Information to Identify Auxiliary Variables for Imputation Procedures via Proxy Pattern‐mixture Models

In many surveys, imputation procedures are used to account for non‐response bias induced by either unit non‐response or item non‐response. Such procedures are optimised (in terms of reducing non‐response bias) when the models include covariates that are highly predictive of both response and outcome variables. To achieve this, we propose a method for selecting sets of covariates used in regression imputation models or to determine imputation cells for one or more outcome variables, using the fraction of missing information (FMI) as obtained via a proxy pattern‐mixture (PMM) model as the key metric. In our variable selection approach, we use the PPM model to obtain a maximum likelihood estimate of the FMI for separate sets of candidate imputation models and look for the point at which changes in the FMI level off and further auxiliary variables do not improve the imputation model. We illustrate our proposed approach using empirical data from the Ohio Medicaid Assessment Survey and from the Service Annual Survey.     

Taking ‘Don’t Knows’ as Valid Responses: A Multiple Complete Random Imputation of Missing Data

Incomplete data is a common problem of survey research. Recent work on multiple imputation techniques has increased analysts’ awareness of the biasing effects of missing data and has also provided a convenient solution. Imputation methods replace non-response with estimates of the unobserved scores. In many instances, however, non-response to a stimulus does not result from measurement problems that inhibit accurate surveying of empirical reality, but from the inapplicability of the survey question. In such cases, existing imputation techniques replace valid non-response with counterfactual estimates of a situation in which the stimulus is applicable to all respondents. This paper suggests an alternative imputation procedure for incomplete data for which no true score exists: multiple complete random imputation, which overcomes the biasing effects of missing data and allows analysts to model respondents’ valid ‘I don’t know’ answers.     

Recent Developments in Dealing with Item Non‐response in Surveys: A Critical Review

The most common way for treating item non‐response in surveys is to construct one or more replacement values to fill in for a missing value. This process is known as imputation. We distinguish single from multiple imputation. Single imputation consists of replacing a missing value by a single replacement value, whereas multiple imputation uses two or more replacement values. This article reviews various imputation procedures used in National Statistical Offices as well as the properties of point and variance estimators in the presence of imputed survey data. It also provides the reader with newer developments in the field.     

Confidence Intervals for the Area Under the Receiver Operating Characteristic Curve in the Presence of Ignorable Missing Data

Receiver operating characteristic curves are widely used as a measure of accuracy of diagnostic tests and can be summarised using the area under the receiver operating characteristic curve (AUC). Often, it is useful to construct a confidence interval for the AUC; however, because there are a number of different proposed methods to measure variance of the AUC, there are thus many different resulting methods for constructing these intervals. In this article, we compare different methods of constructing Wald‐type confidence interval in the presence of missing data where the missingness mechanism is ignorable. We find that constructing confidence intervals using multiple imputation based on logistic regression gives the most robust coverage probability and the choice of confidence interval method is less important. However, when missingness rate is less severe (e.g. less than 70%), we recommend using Newcombe's Wald method for constructing confidence intervals along with multiple imputation using predictive mean matching.     

Multiple imputation of incomplete zero‐inflated count data

Empirical count data are often zero‐inflated and overdispersed. Currently, there is no software package that allows adequate imputation of these data. We present multiple‐imputation routines for these kinds of count data based on a Bayesian regression approach or alternatively based on a bootstrap approach that work as add‐ons for the popular multiple imputation by chained equations (mice ) software in R (van Buuren and Groothuis‐Oudshoorn , Journal of Statistical Software, vol. 45, 2011, p. 1). We demonstrate in a Monte Carlo simulation that our procedures are superior to currently available count data procedures. It is emphasized that thorough modeling is essential to obtain plausible imputations and that model mis‐specifications can bias parameter estimates and standard errors quite noticeably. Finally, the strengths and limitations of our procedures are discussed, and fruitful avenues for future theory and software development are outlined.     

List augmentation with model based multiple imputation: a case study using a mixed-outcome factor model

This study concerns list augmentation in direct marketing. List augmentation is a special case of missing data imputation. We review previous work on the mixed outcome factor model and apply it for the purpose of list augmentation. The model deals with both discrete and continuous variables and allows us to augment the data for all subjects in a company's transaction database with soft data collected in a survey among a sample of those subjects. We propose a bootstrap-based imputation approach, which is appealing to use in combination with the factor model, since it allows one to include estimation uncertainty in the imputation procedure in a simple, yet adequate manner. We provide an empirical case study of the performance of the approach to a transaction data base of a bank.     

Compromised imputation in survey sampling

In this paper, a compromised imputation procedure has been suggested. The estimator of mean obtained from compromised imputation remains better than the estimators obtained from ratio method of imputation and mean method of imputation. An idea to form “Warm Deck Method” of imputation has also been suggested. Received: July 1998     

Testing the adequacy of varying coefficient models with missing responses at random

In this paper, we investigate checking the adequacy of varying coefficient models with response missing at random. In doing so, we first construct two completed data sets based on imputation and marginal inverse probability weighted methods, respectively. The empirical process-based tests by using these two completed data sets are suggested and the asymptotic properties of the test statistics under the null and local alternative hypotheses are studied. Because the limiting null distribution is intractable, a Monte Carlo approach is applied to approximate the distribution to determine critical values. Simulation studies are carried out to examine the performance of our method, and a real data set from an environmental study is analyzed for illustration.     

Are Corporate Tax Reductions Real Benefits under Imputation Systems?

Imputation systems integrate corporate and shareholder personal income taxes to alleviate double taxation of dividend income. In this study, we empirically examine whether a corporate tax rate reduction under an imputation tax system benefits shareholders. Using Taiwan as a setting, our analyses indicate that decreasing the corporate tax rate is associated with an increase in dividend payout ratio and foreign investment. Moreover, the increase in dividend payout ratio is even greater for firms that have a higher increase in foreign ownership. Additionally, the market reacts positively to an announcement of a tax rate reduction; specifically, positive stock price reactions are stronger for firms that experienced a greater increase in foreign ownership in response to the tax rate reduction, for firms with greater liquidity constraints and more growth opportunities before the tax rate reduction, and for firms with a bigger decrease in effective tax rates after the tax rate reduction. Overall, we provide evidence that a tax rate reduction is associated with economic impacts and that foreign shareholders appear to be the main beneficiaries of a tax rate reduction under an imputation tax system.