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Volume II incorporates all the situations presented in Volume I, except for Section V, and adds the condition of missing observations of the covariate and/or response variables. Volume II presents the theoretical development of the analysis of multivariate covariance in which missing values occur among both dependent and independent variables and presents an example.

The influence of method of handling missing data on estimates produced by a structural equation model of the effects of part-time work on high-school student achievement was investigated. Missing data methods studied were listwise deletion, pairwise deletion, the expectation maximization (EM) algorithm, regression, and response pattern. The 26 variables selected from the National Educational Longitudinal Survey of 1988 database were those previously used by K. Singh and M. Ozturk (1999) in an analysis of part-time work. Results indicate the data was not missing completely at random, and although the covariance matrices, measurement models, and structural models using the five missing data methods were not significantly different statistically, the individual best fitting structural model for each missing data method differed substantively. Results are discussed. (Contains 4 figures, 3 tables, and 20 references.) (Author/SLD)

The influence of method of handling missing data on estimates produced by a structural equation model of the effects of part-time work on high-school student achievement was investigated. Missing data methods studied were listwise deletion, pairwise deletion, the expectation maximization (EM) algorithm, regression, and response pattern. The 26 variables selected from the National Educational Longitudinal Survey of 1988 database were those previously used by K. Singh and M. Ozturk (1999) in an analysis of part-time work. Results indicate the data was not missing completely at random, and although the covariance matrices, measurement models, and structural models using the five missing data methods were not significantly different statistically, the individual best fitting structural model for each missing data method differed substantively. Results are discussed. (Contains 4 figures, 3 tables, and 20 references.) (Author/SLD)

With the prevalence of missing data in social science research, it is necessary to use methods for handling missing data. One framework in which data with missing values can still be used for parameter estimation is the Bayesian framework. In this tutorial, different missing data mechanisms including Missing Completely at Random, Missing at Random, and Missing Not at Random are introduced. Methods for estimating models with missing values under the Bayesian framework for both ignorable and non-ignorable missingness are also discussed. A structural equation model on data from the Advanced Cognitive Training for Independent and Vital Elderly study is used as an illustration on how to fit missing data models in JAGS.

This report reviews the theoretical framework which permits analysis of multivariate covariance data in which missing values occur among both dependent and independent variables. A flow chart and program listing is given for a computer program which will estimate the block and treatment parameters, as well as the regression coefficients for the covariates. The program will also calculate test statistics for testing hypotheses which are supplied by the user. It should be pointed out that this program allows for only two categories of design indicator variables, namely a block effect and a treatment effect which are assumed to be additive. The program is thus suitable for the usual randomized block model with additive block and treatment effects, or a general two-factor additive effects model (i.e., no interaction), or the usual one-way classification model (i.e., several treatments but only one block). It will not accommodate more complex designs such as a Latin Square Layout with a multivariate response and one or more covariates. User instructions and a worked example are provided in this volume. (Author)

This article is from Trials , volume 15 . Abstract The aim of this review was to establish the frequency with which trials take into account missingness, and to discover what methods trialists use for adjustment in randomised controlled trials with longitudinal measurements. Failing to address the problems that can arise from missing outcome data can result in misleading conclusions. Missing data should be addressed as a means of a sensitivity analysis of the complete case analysis results. One hundred publications of randomised controlled trials with longitudinal measurements were selected randomly from trial publications from the years 2005 to 2012. Information was extracted from these trials, including whether reasons for dropout were reported, what methods were used for handing the missing data, whether there was any explanation of the methods for missing data handling, and whether a statistician was involved in the analysis. The main focus of the review was on missing data post dropout rather than missing interim data. Of all the papers in the study, 9 (9%) had no missing data. More than half of the papers included in the study failed to make any attempt to explain the reasons for their choice of missing data handling method. Of the papers with clear missing data handling methods, 44 papers (50%) used adequate methods of missing data handling, whereas 30 (34%) of the papers used missing data methods which may not have been appropriate. In the remaining 17 papers (19%), it was difficult to assess the validity of the methods used. An imputation method was used in 18 papers (20%). Multiple imputation methods were introduced in 1987 and are an efficient way of accounting for missing data in general, and yet only 4 papers used these methods. Out of the 18 papers which used imputation, only 7 displayed the results as a sensitivity analysis of the complete case analysis results. 61% of the papers that used an imputation explained the reasons for their chosen method. Just under a third of the papers made no reference to reasons for missing outcome data. There was little consistency in reporting of missing data within longitudinal trials.

This article is from Trials , volume 15 . Abstract The aim of this review was to establish the frequency with which trials take into account missingness, and to discover what methods trialists use for adjustment in randomised controlled trials with longitudinal measurements. Failing to address the problems that can arise from missing outcome data can result in misleading conclusions. Missing data should be addressed as a means of a sensitivity analysis of the complete case analysis results. One hundred publications of randomised controlled trials with longitudinal measurements were selected randomly from trial publications from the years 2005 to 2012. Information was extracted from these trials, including whether reasons for dropout were reported, what methods were used for handing the missing data, whether there was any explanation of the methods for missing data handling, and whether a statistician was involved in the analysis. The main focus of the review was on missing data post dropout rather than missing interim data. Of all the papers in the study, 9 (9%) had no missing data. More than half of the papers included in the study failed to make any attempt to explain the reasons for their choice of missing data handling method. Of the papers with clear missing data handling methods, 44 papers (50%) used adequate methods of missing data handling, whereas 30 (34%) of the papers used missing data methods which may not have been appropriate. In the remaining 17 papers (19%), it was difficult to assess the validity of the methods used. An imputation method was used in 18 papers (20%). Multiple imputation methods were introduced in 1987 and are an efficient way of accounting for missing data in general, and yet only 4 papers used these methods. Out of the 18 papers which used imputation, only 7 displayed the results as a sensitivity analysis of the complete case analysis results. 61% of the papers that used an imputation explained the reasons for their chosen method. Just under a third of the papers made no reference to reasons for missing outcome data. There was little consistency in reporting of missing data within longitudinal trials.

This paper discusses a novel algorithm for solving a missing data problem in the machine learning pre-processing stage. A model built to help lenders evaluate home loans based on numerous factors by learning from available user data, is adopted in this paper as an example. If one of the factors is missing for a person in the dataset, the currently used methods delete the whole entry therefore reducing the size of the dataset and affecting the machine learning model accuracy. The novel algorithm aims to avoid losing entries for missing factors by breaking the dataset into multiple subsets, building a different machine learning model for each subset, then combining the models into one machine learning model. In this manner, the model makes use of all available data and only neglects the missing values. Overall, the new algorithm improved the prediction accuracy by 5% from 93% accuracy to 98% in the home loan example.

Cost-Effectiveness Analyses (CEAs) alongside randomised controlled trials (RCTs) are increasingly often designed to collect resource use and preference-based health status data for the purpose of healthcare technology assessment. However, because of the way these measures are collected, they are prone to missing data, which can ultimately affect the decision of whether an intervention is good value for money. We examine how missing cost and effect outcome data are handled in RCT-based CEAs, complementing a previous review (covering 2003-2009, 88 articles) with a new systematic review (2009-2015, 81 articles) focussing on two different perspectives. First, we review the description of the missing data, the statistical methods used to deal with them, and the quality of the judgement underpinning the choice of these methods. Second, we provide guidelines on how the information about missingness and related methods should be presented to improve the reporting and handling of missing data. Our review shows that missing data in within-RCT CEAs are still often inadequately handled and the overall level of information provided to support the chosen methods is rarely satisfactory.

Handling of missed data is one of the main tasks in data preprocessing especially in large public service datasets. We have analysed data from the Trauma Audit and Research Network (TARN) database, the largest trauma database in Europe. For the analysis we used 165,559 trauma cases. Among them, there are 19,289 cases (13.19%) with unknown outcome. We have demonstrated that these outcomes are not missed `completely at random' and, hence, it is impossible just to exclude these cases from analysis despite the large amount of available data. We have developed a system of non-stationary Markov models for the handling of missed outcomes and validated these models on the data of 15,437 patients which arrived into TARN hospitals later than 24 hours but within 30 days from injury. We used these Markov models for the analysis of mortality. In particular, we corrected the observed fraction of death. Two na\"ive approaches give 7.20% (available case study) or 6.36% (if we assume that all unknown outcomes are `alive'). The corrected value is 6.78%. Following the seminal paper of Trunkey (1983) the multimodality of mortality curves has become a much discussed idea. For the whole analysed TARN dataset the coefficient of mortality monotonically decreases in time but the stratified analysis of the mortality gives a different result: for lower severities the coefficient of mortality is a non-monotonic function of the time after injury and may have maxima at the second and third weeks. The approach developed here can be applied to various healthcare datasets which experience the problem of lost patients and missed outcomes.

Handling of missed data is one of the main tasks in data preprocessing especially in large public service datasets. We have analysed data from the Trauma Audit and Research Network (TARN) database, the largest trauma database in Europe. For the analysis we used 165,559 trauma cases. Among them, there are 19,289 cases (13.19%) with unknown outcome. We have demonstrated that these outcomes are not missed `completely at random' and, hence, it is impossible just to exclude these cases from analysis despite the large amount of available data. We have developed a system of non-stationary Markov models for the handling of missed outcomes and validated these models on the data of 15,437 patients which arrived into TARN hospitals later than 24 hours but within 30 days from injury. We used these Markov models for the analysis of mortality. In particular, we corrected the observed fraction of death. Two na\"ive approaches give 7.20% (available case study) or 6.36% (if we assume that all unknown outcomes are `alive'). The corrected value is 6.78%. Following the seminal paper of Trunkey (1983) the multimodality of mortality curves has become a much discussed idea. For the whole analysed TARN dataset the coefficient of mortality monotonically decreases in time but the stratified analysis of the mortality gives a different result: for lower severities the coefficient of mortality is a non-monotonic function of the time after injury and may have maxima at the second and third weeks. The approach developed here can be applied to various healthcare datasets which experience the problem of lost patients and missed outcomes.

Restorer is a visualization technique for indicating the location of missing data in a scientific visualization. Rather than filling missing data regions with interpolated data colored with the same scale as real data or simply leaving such regions empty, the restorer technique fills the regions with interpolated data colored with a color table with only luminance values. This technique allows missing data to be indicated clearly without distracting from the content of the real data. Note: A narrated video describing the restorer technique and giving several examples. Animator: Ray Twiddy (Hughes STX), John Cavallo (Hughes STX), Shahram Shiri (NASA). Scientist: Ray Twiddy (Hughes STX). Platforms/Sensors/Data Sets: Nimbus-7/TOMS.

When survey data are statistically analyzed, many times some of the data is missing. If the missing values are not correctly handled, results of the analysis may be dubious and publication may jeopardize the credibility of the organization preparing the report. This study examined four of the more commonly used methods of handling missing data. The following techniques were compared: (1) listwise deletion; (2) pairwise deletion; (3) mean substitution; and (4) regression imputation of missing data. Comparisons were made using a sample selected from the General Social Survey--1984 of the National Opinion Research Center. The sample of 829 cases was randomly divided into two sample groups: Sample 1, with 415 cases; and Sample 2, with 414 cases, which was reduced to only non-missing cases at 283. Sample 1 was used to develop regression equations after treatment by each technique. Sample 2 was used to compare the efficiency of these regression equations in predicting the criterion variable by comparing the actual criterion mean to the predicted mean using Dunnett's test for contrasts. There was a statistically significant difference between the actual mean and the mean predicted by mean substitution with the significance level at 0.01. The other methods exhibited no significant differences. Mean substitution appears inappropriate as a way of handling missing data. A seven-item list of references is included. Three data tables are provided. (SLD)

Abscent of records generally termed as missing data which should be treated properly before analysis procedes in data analysis. There were many researchers who undoubtedly mislead their research findings without proper treatment of missing data, therefore this review research try to explain the best ways of missing data handling using r programming. Generally, many researchers apply mean and median imputation but this sometimes creates bios in many  situations, therefore, the researcher tries to explain some basic  association among other research variables with treating missing data using r programming. The imputation process suggests five alternatives be replaced for missing data values were generated automatically and substituted easily  at the process of data cleaning and data preparation. Here researcher explains two sample data for missing treatment  and explains many ways for  graphical interpretation  of them. The first data set with 12 observation describes the easiest way of missing replacement and the second  vehicle failure data from internet of 1624 records, whose missing pattern were calculated and replaced with to the respective data sets before analysis. Yagyanath Rimal. (2020). Multivariate imputation for missing data handling a case study on small and large data sets. International Journal of Human Computing Studies, 2(1), 5-11. https://doi.org/10.31149/ijhcs.v2i1.352 Pdf Url : https://journals.researchparks.org/index.php/IJHCS/article/view/352/341 Paper Url : https://journals.researchparks.org/index.php/IJHCS/article/view/352

Abscent of records generally termed as missing data which should be treated properly before analysis procedes in data analysis. There were many researchers who undoubtedly mislead their research findings without proper treatment of missing data, therefore this review research try to explain the best ways of missing data handling using r programming. Generally, many researchers apply mean and median imputation but this sometimes creates bios in many  situations, therefore, the researcher tries to explain some basic  association among other research variables with treating missing data using r programming. The imputation process suggests five alternatives be replaced for missing data values were generated automatically and substituted easily  at the process of data cleaning and data preparation. Here researcher explains two sample data for missing treatment  and explains many ways for  graphical interpretation  of them. The first data set with 12 observation describes the easiest way of missing replacement and the second  vehicle failure data from internet of 1624 records, whose missing pattern were calculated and replaced with to the respective data sets before analysis. Yagyanath Rimal. (2020). Multivariate imputation for missing data handling a case study on small and large data sets. International Journal of Human Computing Studies, 2(1), 5-11. https://doi.org/10.31149/ijhcs.v2i1.352 Pdf Url : https://journals.researchparks.org/index.php/IJHCS/article/view/352/341 Paper Url : https://journals.researchparks.org/index.php/IJHCS/article/view/352

The last 20 years has seen an uptick in research on missing data problems, and most software applications now implement one or more sophisticated missing data handling routines (e.g., multiple imputation or maximum likelihood estimation). Despite their superior statistical properties (e.g., less stringent assumptions, greater accuracy and power), the adoption of these modern analytic approaches is not uniform in psychology and related disciplines. Thus, the primary goal of this manuscript is to describe and illustrate the application of multiple imputation. Although maximum likelihood estimation is perhaps the easiest method to use in practice, psychological data sets often feature complexities that are currently difficult to handle appropriately in the likelihood framework (e.g., mixtures of categorical and continuous variables), but relatively simple to treat with imputation. The paper describes a number of practical issues that clinical researchers are likely to encounter when applying multiple imputation, including mixtures of categorical and continuous variables, item-level missing data in questionnaires, significance testing, interaction effects, and multilevel missing data. Analysis examples illustrate imputation with software packages that are freely available on the internet. [This paper was published in "Behaviour Research and Therapy" v98 p4-18 2017.]

This article is from BMC Medical Research Methodology , volume 12 . Abstract Background: Retaining participants in cohort studies with multiple follow-up waves is difficult. Commonly, researchers are faced with the problem of missing data, which may introduce biased results as well as a loss of statistical power and precision. The STROBE guidelines von Elm et al. (Lancet, 370:1453-1457, 2007); Vandenbroucke et al. (PLoS Med, 4:e297, 2007) and the guidelines proposed by Sterne et al. (BMJ, 338:b2393, 2009) recommend that cohort studies report on the amount of missing data, the reasons for non-participation and non-response, and the method used to handle missing data in the analyses. We have conducted a review of publications from cohort studies in order to document the reporting of missing data for exposure measures and to describe the statistical methods used to account for the missing data. Methods: A systematic search of English language papers published from January 2000 to December 2009 was carried out in PubMed. Prospective cohort studies with a sample size greater than 1,000 that analysed data using repeated measures of exposure were included. Results: Among the 82 papers meeting the inclusion criteria, only 35 (43%) reported the amount of missing data according to the suggested guidelines. Sixty-eight papers (83%) described how they dealt with missing data in the analysis. Most of the papers excluded participants with missing data and performed a complete-case analysis (n = 54, 66%). Other papers used more sophisticated methods including multiple imputation (n = 5) or fully Bayesian modeling (n = 1). Methods known to produce biased results were also used, for example, Last Observation Carried Forward (n = 7), the missing indicator method (n = 1), and mean value substitution (n = 3). For the remaining 14 papers, the method used to handle missing data in the analysis was not stated. Conclusions: This review highlights the inconsistent reporting of missing data in cohort studies and the continuing use of inappropriate methods to handle missing data in the analysis. Epidemiological journals should invoke the STROBE guidelines as a framework for authors so that the amount of missing data and how this was accounted for in the analysis is transparent in the reporting of cohort studies.

This article is from BMC Medical Research Methodology , volume 12 . Abstract Background: Retaining participants in cohort studies with multiple follow-up waves is difficult. Commonly, researchers are faced with the problem of missing data, which may introduce biased results as well as a loss of statistical power and precision. The STROBE guidelines von Elm et al. (Lancet, 370:1453-1457, 2007); Vandenbroucke et al. (PLoS Med, 4:e297, 2007) and the guidelines proposed by Sterne et al. (BMJ, 338:b2393, 2009) recommend that cohort studies report on the amount of missing data, the reasons for non-participation and non-response, and the method used to handle missing data in the analyses. We have conducted a review of publications from cohort studies in order to document the reporting of missing data for exposure measures and to describe the statistical methods used to account for the missing data. Methods: A systematic search of English language papers published from January 2000 to December 2009 was carried out in PubMed. Prospective cohort studies with a sample size greater than 1,000 that analysed data using repeated measures of exposure were included. Results: Among the 82 papers meeting the inclusion criteria, only 35 (43%) reported the amount of missing data according to the suggested guidelines. Sixty-eight papers (83%) described how they dealt with missing data in the analysis. Most of the papers excluded participants with missing data and performed a complete-case analysis (n = 54, 66%). Other papers used more sophisticated methods including multiple imputation (n = 5) or fully Bayesian modeling (n = 1). Methods known to produce biased results were also used, for example, Last Observation Carried Forward (n = 7), the missing indicator method (n = 1), and mean value substitution (n = 3). For the remaining 14 papers, the method used to handle missing data in the analysis was not stated. Conclusions: This review highlights the inconsistent reporting of missing data in cohort studies and the continuing use of inappropriate methods to handle missing data in the analysis. Epidemiological journals should invoke the STROBE guidelines as a framework for authors so that the amount of missing data and how this was accounted for in the analysis is transparent in the reporting of cohort studies.

The effectiveness of four methods of handling missing data in reproducing the target sample covariance matrix and mean vector was tested using three levels of incomplete cases: 30%, 50%, and 70%. Data were selected from the National Education Longitudinal Study (NELS) database. Three levels of sample sizes (500, 1000, and 2000) were used. The assumption of missing data completely at random was violated in all samples. Results indicate that listless deletion was most effective in replicating the target mean vector and covariance matrix. (Contains 2 tables, 1 figure, and 19 references.) (Author/SLD)

Researchers are frequently confronted with unanswered questions or items on their questionnaires and tests, due to factors such as item difficulty, lack of testing time, or participant distraction. This paper first presents results from a poll confirming previous claims (Rietveld & van Hout, 2006; Schafer & Graham, 2002) that data replacement and deletion methods are common in research. Language researchers declared that when faced with missing answers of the yes/no type (that translate into zero or one in data tables), the three most common solutions they adopt are to exclude the participant's data from the analyses, to leave the square empty, or to fill in with zero, as for an incorrect answer. This study then examines the impact on Cronbach's a of five types of data insertion, using simulated and actual data with various numbers of participants and missing percentages. Our analyses indicate that the three most common methods we identified among language researchers are the ones with the greatest impact on Cronbach's a coefficients; in other words, they are the least desirable solutions to the missing data problem. On the basis of our results, we make recommendations for language researchers concerning the best way to deal with missing data. Given that none of the most common simple methods works properly, we suggest that the missing data be replaced either by the item's mean or by the participants' overall mean to provide a better, more accurate image of the instrument's internal consistency.

Four methods of handling missing data were applied to missing values for variables selected from the National Education Longitudinal Study of 1988. Variables used were those selected by K. Singh and M. Ozturk (1999) for a study concerning high school students' academic achievement and work. Samples selected consisted of 100 cases, 300 cases, and 500 cases. The proportion of incomplete cases was manipulated to represent 30%, 50%, and 70% for each sample. In addition, composite variables were created and tested. Results indicate the expectation maximization (EM) algorithm and regression procedures provide accurate estimates under all conditions. Listwise and pairwise deletion were effective with small proportions of missing data and when composites were created. (Contains 1 figure, 8 tables, and 19 references.) (Author/SLD)

This article is from Korean Journal of Anesthesiology , volume 64 . Abstract Even in a well-designed and controlled study, missing data occurs in almost all research. Missing data can reduce the statistical power of a study and can produce biased estimates, leading to invalid conclusions. This manuscript reviews the problems and types of missing data, along with the techniques for handling missing data. The mechanisms by which missing data occurs are illustrated, and the methods for handling the missing data are discussed. The paper concludes with recommendations for the handling of missing data.

The imbalanced data affect the accuracy of models, especially for precision and sensitivity, it makes difficult to find information on minority class. The problem is identified in the tracer study dataset Universitas Sriwijaya that has 2934 data. The label attribute is divided into several label classes, namely not tight, somewhat-tight, tight, very tight, and tightest. The number of the tightest and very tight is 27% and 38.6% of the number majority classes. In the study, the SMOTE is combined with eliminating the missing value of data to handle the imbalanced data. The method was evaluated by the classification methods KNN, ANN, and C4.5. The results of these methods show a significant increase in accuracy as a whole and a significant increase in the precision and sensitivity of minority classes. The precision and sensitivity of both the majority and minority are not too different, although the number of the minority is very less compared to the majority class. the information on minority classes can be obtained with quite high precision and sensitivity. As a conclusion, the proposed method is passably to improve accuracy and greatly affects the increase in sensitivity and precision.

Missing data is an important issue that is discussed across many fields. In order to understand the issues caused by missing data, this paper reviews the types of missing data and problems caused by missing data. Also, to understand how missing data are handled in instructional technology research, articles published in "Educational Media International,""Educational Technology Research and Development," and "Performance Improvement Quarterly" for the last 5 years are reviewed. A total of 84 quantitative research articles were identified in the 3 journals. About 42% of the reviewed studies had incomplete data sets, and in most of them, information about data completeness was clearly presented through comparisons of usable data points with the intended sample size. Overall, it was found that the awareness of missing data issues was low among the researchers in the field of instructional technology. Findings are discussed in terms of missing data mechanisms, and recommendations are presented. An appendix shows missing data methods in the three journals in table form. (Contains 19 references.) (Author/SLD)