Hot Deck Research Articles

Correlation-Based Ensemble Feature Selection Using Bioinspired Algorithms and Classification Using Backpropagation Neural Network.

A framework for clinical diagnosis which uses bioinspired algorithms for feature selection and gradient descendant backpropagation neural network for classification has been designed and implemented. The clinical data are subjected to data preprocessing, feature selection, and classification. Hot deck imputation has been used for handling missing values and min-max normalization is used for data transformation. Wrapper approach that employs bioinspired algorithms, namely, Differential Evolution, Lion Optimization, and Glowworm Swarm Optimization with accuracy of AdaBoostSVM classifier as fitness function has been used for feature selection. Each bioinspired algorithm selects a subset of features yielding three feature subsets. Correlation-based ensemble feature selection is performed to select the optimal features from the three feature subsets. The optimal features selected through correlation-based ensemble feature selection are used to train a gradient descendant backpropagation neural network. Ten-fold cross-validation technique has been used to train and test the performance of the classifier. Hepatitis dataset and Wisconsin Diagnostic Breast Cancer (WDBC) dataset from University of California Irvine (UCI) Machine Learning repository have been used to evaluate the classification accuracy. An accuracy of 98.47% is obtained for Wisconsin Diagnostic Breast Cancer dataset, and 95.51% is obtained for Hepatitis dataset. The proposed framework can be tailored to develop clinical decision-making systems for any health disorders to assist physicians in clinical diagnosis.

CHOOSING APPROPRIATE IMPUTATION METHODS FOR MISSING DATA: A DECISION ALGORITHM ON METHODS FOR MISSING DATA

Missing values commonly happen in the realm of medical research, which is regarded creating a lot of bias in case it is neglected with poor handling. However, while dealing with such challenges, some standard statistical methods have been already developed and available, yet no credible method is available so far to infer credible estimates. The existing data size gets lowered, apart from a decrease in efficiency happens when missing values is found in a dataset. A number of imputation methods have addressed such challenges in early scholarly works for handling missing values. Some of the regular methods include complete case method, mean imputation method, Last Observation Carried Forward (LOCF) method, Expectation-Maximization (EM) algorithm, and Markov Chain Monte Carlo (MCMC), Mean Imputation (Mean), Hot Deck (HOT), Regression Imputation (Regress), K-nearest neighbor (KNN),K-Mean Clustering, Fuzzy K-Mean Clustering, Support Vector Machine, and Multiple Imputation (MI) method. In the present paper, a simulation study is attempted for carrying out an investigative exploration into the efficacy of the above mentioned archetypal imputation methods along with longitudinal data setting under missing completely at random (MCAR). We took out missingness from three cases in a block having low missingness of 5% as well as higher levels at 30% and 50%. With this simulation study, we concluded LOCF method having more bias than the other methods in most of the situations after carrying out a comparison through simulation study.

Missing Data Imputation Using Morphoscopic Traits and Their Performance in the Estimation of Ancestry

Missing data are an inherent problem in biological anthropology for both reference data sets and individual cases. The goal of data imputation for forensic anthropological applications is to accurately estimate missing values by using other, observed values. To quantify the accuracy of macromorphoscopic data in conditions with slight (10%), moderate (25%), and severe (50%, 75%, and 90%) amounts of missing data, we selected four data-imputation techniques: Hot Deck, iterative robust model-based imputation (IRMI), k-nearest neighbor (k-NN), and the variable medians. Hefner’s Macromorphoscopic Databank was used (Hefner 2018); the full sample consisted of 688 individuals from 3 U.S. populations (Blacks, Hispanics, and Whites). Six cranial macromorphoscopic variants were scored in accordance with Hefner (2009). The five data sets with missing data were randomly simulated over multiple iterations (N = 500 each) from the original data. These data sets were compared for agreement using weighted Cohen’s kappa and correct classification accuracies over multiple iterations (N = 500) calculated for the original data set. The latter comparisons were also used to examine the effects of imputed data on classification accuracies. Results suggest that IRMI is the most accurate method for imputing missing data, followed by k-NN, in each of the comparisons for nearly all of the variables imputed.

Missing behavior data in longitudinal network studies: the impact of treatment methods on estimated effect parameters in stochastic actor oriented models

Research into missing network data is growing, with a focus on the impact of missing ties on network statistics or network model parameters. Longitudinal network studies using stochastic actor-oriented models (SAOMs) focus on the co-evolution of network structure and behavior/attributes to disentangle influence and selection mechanisms. Still little is known about the impact of missing behavior data on estimated effect parameters in SAOMs. This paper examines seven different methods that are currently available to deal with missing behavior data: complete cases, three single imputation procedures (imputing the mean, random hot deck, nearest neighbor hot deck), one multiple imputation procedure (based on predictive mean matching), and two methods available in the RSIENA software to estimate SAOMs (default method based on imputation and available cases, and a method based on dummy variables). In a simulation study based on four real-life data sets, the impact of these methods on estimated parameters of SAOMS was investigated. Missing behavior data were created under different conditions (proportions, mechanisms), and the missing data methods were used to estimate SAOMs on the incomplete data. The effect of the missing data methods was inspected using three criteria: model convergence, parameter bias, and parameter coverage. The results show that, in general, the default method available in the RSIENA software gives the best outcomes for all three criteria. The dummy-based method generally performed worse than the default method, as did the imputation procedures. The multiple imputation procedure sometimes outperformed the single imputations and the three single imputation methods often gave the same results. The effects of missing data mechanism and data set were small.

A new approach for processing climate missing databases applied to daily rainfall data in Soummam watershed, Algeria

Missing data is a very frequent problem in climatology, it influences on the quality of results that will afford in hydrological studies, as well as water resources management. This paper proposes a new imputation algorithm, based on the optimization of some regression methods, which are hot deck, k-nearest-neighbors imputation, weighted k-nearest-neighbors imputation, multiple imputation, linear regression and simple average method. The choice of these methods was justified by qualitative and quantitative statistical tests analysis. However, the reliability of obtained results depends mainly on percentage of missing data, choice of neighboring stations and data missingness mechanism which should be missing at random. During the study it was found that the most of stations in Soummam watershed don't have a good correlation because the large loss in rainfall data or the geology of watershed which gives a relationship between station position and rainfall variability. For this case, principal component analysis is applied on a set of stations; it showed a positive impact of altitude, latitude and longitude on correlation index between selected stations. The graphical analysis of the normal law on RMSE values, which were obtained by applying the proposed technique in several random cases of missingness, that are 4%, 8%, 12% and 16% respectively, it confirmed the validity and the performance of this approach.

Health behaviour, social support, socio-economic status and the 5-year progression of multimorbidity: Results from the MultiCare Cohort Study.

Background:Multimorbidity in elderly patients is a major challenge for physicians, because of a high prevalence of and associations with many adverse outcomes. However, the mechanisms of progressing multimorbidity are not well-understood. The aim of our study was to determine if the progression of multimorbidity is influenced by health behaviour and social support and to analyse if the patients’ socio-economic status had an effect on these prognostic factors.Methods:The study was designed as prospective cohort study based on interviews of 158 GPs and 3189 patients randomly selected from GP records (response rate: 46.2%). Patients were aged 65–85 years at recruitment and observed in four waves of data collection (dropout rate: 41.5%). Statistical analyses of the ‘hot deck’ imputed data included multilevel mixed-effects linear regression allowing for random effects at the study centre and GP practice within study centre level.Results:Regarding cardiovascular and metabolic diseases, multimorbidity progressed more rapidly in patients who reported less physical activity (ß = −0.28; 95% confidence interval = −0.35 to −0.20), had more tobacco-related pack years (0.15; 0.07–0.22) and consumed less alcohol (−0.21; −0.31 to −0.12) at baseline. Multimorbidity related to psychiatric and pain-related disorders progressed more rapidly if the patients had less perceived social support (−0.31; −0.55 to −0.07) and reported less physical activity (−0.08; −0.15 to −0.02) at baseline. Education and income only slightly modified the effects of these variables.Conclusion:Depending on the multimorbidity cluster, different strategies should be used for slowing down the progression of multimorbidity. Changing lifestyle and increasing social support are beneficial for the entire group of elderly multimorbid patients – regardless of their socio-economic status.Registration:ISRCTN89818205

How handling missing data may impact conclusions: A comparison of six different imputation methods for categorical questionnaire data.

Objectives:Missing data is a recurrent issue in many fields of medical research, particularly in questionnaires. The aim of this article is to describe and compare six conceptually different multiple imputation methods, alongside the commonly used complete case analysis, and to explore whether the choice of methodology for handling missing data might impact clinical conclusions drawn from a regression model when data are categorical.Methods:In addition to the commonly used complete case analysis, we tested the following six imputation methods: multiple imputation using expectation–maximization with bootstrapping, multiple imputation using multiple correspondence analysis, multiple imputation using latent class analysis, multiple hot deck imputation and multivariate imputation by chained equations with two different model specifications: logistic regression and random forests. The methods are tested on real data from a questionnaire-based study in the Norwegian opioid maintenance treatment programme.Results:All methods performed relatively well when the sample size was large (n = 1000). For a smaller sample size (n = 200), the regression estimates depend heavily on the level of missing. When the amount of missing was ⩾20%, in particular, complete case analysis, hot deck and random forests had biased estimates with too low coverage. Multiple imputation using multiple correspondence analysis had the best performance all over.Conclusion:The choice of missing handling methodology has a significant impact on the clinical interpretation of the accompanying statistical analyses. With missing data, the choice of whether to impute or not, and choice of imputation method, can influence clinical conclusion drawn from a regression model and should therefore be given sufficient consideration.

Geographic Imputation of Missing Activity Space Data from Ecological Momentary Assessment (EMA) GPS Positions.

This research presents a pilot study to develop and compare methods of geographic imputation for estimating the location of missing activity space data collected using geographic ecological momentary assessment (GEMA). As a demonstration, we use data from a previously published analysis of the effect of neighborhood disadvantage, captured at the U.S. Census Bureau tract level, on momentary psychological stress among a sample of 137 urban adolescents. We investigate the impact of listwise deletion on model results and test two geographic imputation techniques adapted for activity space data from hot deck and centroid imputation approaches. Our results indicate that listwise deletion can bias estimates of place effects on health, and that these impacts are mitigated by the use of geographic imputation, particularly regarding inflation of the standard errors. These geographic imputation techniques may be extended in future research by incorporating approaches from the non-spatial imputation literature as well as from conventional geographic imputation and spatial interpolation research that focus on non-activity space data.

Hot Deck Multiple Imputation for Handling Missing Accelerometer Data.

Missing data due to non-wear are common in accelerometer studies measuring physical activity and sedentary behavior. Accelerometer output are high-dimensional time-series data that are episodic and often highly skewed, presenting unique challenges for handling missing data. Common methods for missing accelerometry either are ad-hoc, require restrictive parametric assumptions, or do not appropriately impute bouts. This study developed a flexible hot deck multiple imputation (MI; i.e., "replacing" missing data with observed values) procedure to handle missing accelerometry. For each missing segment of accelerometry, "donor pools" contained observed segments from either the same or different participants, and 10 imputed segments were randomly drawn from the donor pool according to selection weights, where the donor pool and selection weight depended on variables associated with non-wear and/or accelerometer-based measures. A simulation study of 2,550 women compared hot deck MI to two standard methods in the field: available case (AC) analysis (i.e., analyzing all observed accelerometry with no restriction on wear time or number of days) and complete case (CC) analysis (i.e., analyzing only participants that wore the accelerometer for ≥10 hours for 4-7 days). This was repeated using accelerometry from the entire 24-hour day and daytime (10am- 8pm) only, and data were missing at random. For the entire 24-hour day, MI produced less bias and better 95% confidence interval (CI) coverage than AC and CC. For the daytime only, MI produced less bias and better 95% CI coverage than AC; CC produced similar bias and 95% CI coverage, but longer 95% CIs than MI.

Cancer survivors not participating in observational patient-reported outcome studies have a lower survival compared to participants: the population-based PROFILES registry

PurposeThe ‘Patient Reported Outcomes Following Initial treatment and Long-term Evaluation of Survivorship’ (PROFILES) registry collects patient-reported outcomes (PROs) from short- and long-term cancer survivors in the Netherlands, in a population-based setting. The aim of this analysis is to assess the generalizability of observational PRO research among cancer survivors by comparing socio-demographic and clinical characteristics, and survival of participants and non-participants in cancer survivors invited for questionnaire research through the PROFILES registry.MethodsBetween 2008 and 2015, cancer survivors with different cancer diagnoses (N = 14,011) were invited to participate in PROFILES registry studies, of whom 69% (N = 9684) participated. Socio-demographic and clinical characteristics and survival data, collected through the Netherlands Cancer Registry, were associated with participation versus non-participation in multivariable logistic regression analyses and cox proportional hazard regression models, respectively.ResultsParticipants had a significantly better survival compared to non-participants (HR = 1.47, P < .01). Participation was associated with male gender, being 60–70 years old, high socio-economic status, receiving any treatment, receiving radiotherapy, having no comorbidities, and a cancer diagnosis 2–3 years before invitation. Sensitivity analysis demonstrates that the health-related quality of life (HRQoL) might be up to 1.3 points lower (scale 0–100) using hot deck imputation compared to non-imputed participant data.ConclusionsCancer survivors not participating in observational PROs research significantly differ from participants, with respect to socio-demographic and clinical characteristics, and survival. Their HRQoL scores may be systematically lower compared to participants. Therefore, even in PRO studies with relatively high participation rates, observed outcomes may represent the healthier patient with better outcomes.

Estimating the causal effect of treatment regimes for organ transplantation.

Patients awaiting cadaveric organ transplantation face a difficult decision if offered a low-quality organ: accept the organ or remain on the waiting list and hope a better organ is offered in the future. A dynamic treatment regime (DTR) for transplantation is a rule that determines whether a patient should decline an offered organ. Existing methods can estimate the effect of DTRs on survival outcomes, but these were developed for applications where treatment is abundantly available. For transplantation, organ availability is limited, and existing methods can only estimate the effect of a DTR assuming a single patient follows the DTR. We show for transplantation that the effect of a DTR depends on whether other patients follow the DTR. To estimate the anticipated survival if the entire population awaiting transplantation were to adopt a DTR, we develop a novel inverse probability weighted estimator (IPCW) which re-weights patients based on the probability of following their transplant history in the counterfactual world in which all patients follow the DTR of interest. We estimate this counterfactual probability using hot deck imputation to fill in data that is not observed for patients who are artificially censored by IPCW once they no longer follow the DTR of interest. We show via simulation that our proposed method has good finite-sample properties, and we apply our method to a lung transplantation observational registry.

Multiple Imputation by Predictive Mean Matching When Sample Size Is Small

Abstract. Predictive mean matching (PMM) is a state-of-the-art hot deck multiple imputation (MI) procedure. The quality of its results depends, inter alia, on the availability of suitable donor cases. Applying PMM in small sample scenarios often found in psychological or medical research could be problematic, as there might not be many (or any) suitable donor cases in the data set. So far, there has not been any systematic research that examined the performance of PMM, when sample size is small. The present study evaluated PMM in various multiple regression scenarios, where sample size, missing data percentages, the size of the regression coefficients, and PMM’s donor selection strategy were systematically varied. Results show that PMM could be used in most scenarios, however results depended on the donor selection strategy: overall, PMM using either automatic distance-aided selection of donors ( Gaffert, Meinfelder, &amp; Bosch, 2016 ) or using the nearest neighbor produced the best results.

Labour income inequality in Mexico: Puzzles solved and unsolved

We analyse the evolution and proximate determinants of labour income inequality in Mexico between 1989 and 2017. Labour income inequality increased between 1989 and 1994 and declined between 1994 and 2006. What happened after 2006 is subject to uncertainty. The national labour force survey shows a steady decline and the income expenditure survey suggests that inequality increased. We correct for high and rising item (labour income) non-response and underrepresentation of high-wage earners through a ‘hot deck’ imputation method and post-survey weight adjustments. We obtain the new weights for formal workers from tabulations recently released by the Mexican social security administration. For informal workers, we correct using the hot deck imputation method. With corrected data, inequality no longer declines between 2006 and 2017.

The impact of methods to handle missing data on the estimated prevalence of dementia and mild cognitive impairment in a cross-sectional study including non-responders

ObjectiveAlthough several statistical methods for adjusting for missing data have been developed and are widely applied in research, few studies have investigated these methods in adjusting for missingness in datasets that aim to estimate the prevalence of dementia. We attempted to develop a more feasible approach for handling missingness in a cross-sectional study among elderly. MethodsFive methods of estimating prevalence, including stratified weighting (SW), inverse-probability weighting (IPW), hot deck imputation (HDI), ordinal logistic regression (OLR) and multiple imputation (MI), were applied to handle the missing data yielded by a dataset that include 2231 non-responders. ResultsCompared with the results of the complete case analysis, the differences in the prevalence rates of dementia and mild cognitive impairment (MCI) calculated by the prevalence-estimating methods after adjusting for non-responders were less than 7% and 6%, respectively. In contrast to the results of other methods, the estimated prevalence of dementia and MCI calculated by MI increased when more predictive factors were included, and the lowest rate of missing data was achieved using MI. Using the participants’ ages, the cognitive screening sores and activity of daily life sores as predictive variables when correcting for missingness induced relatively larger effects on the estimated dementia prevalence. ConclusionsWhen adjusting for missingness while estimating the prevalence of dementia in cross-sectional studies, a simple method, such as SW, is recommended when limited information is available, whereas MI is the preferred method when additional information is available. Further simulation studies are needed to determine the optimal approach.

패널자료에서의 항목무응답 대체 방법 비교

설문조사를 실시할 때 응답자가 설문조사의 일부 문항에 대하여 응답하지 않는 경우 항목무응답이 발생한다. 무응답이 발생한 자료를 제외하고 완전하게 응답된 자료 만에 근거한 분석은 분석 결과에 편의가 발생할 수 있으므로, 이를 채워 넣어 완전한 형태의 자료로 분석하기 위해서 무응답 대체가 흔히 사용되고 있으며 여러 가지 무응답 대체 기법들을 비교하는 연구들도 많이 존재한다. 패널조사 연구는 연구 대상 패널에 대하여 정해진 시간에 따라 반복적으로 동일한 설문 문항에 대하여 응답을 조사하여 시간에 따른 변화를 살펴보는 조사 방법을 나타낸다. 패널조사 자료의 항목 무응답을 대체할 때 이전 시점의 응답 자료가 존재한다면 이를 포함하여 대체를 실시하는 것이 바람직한 것으로 여겨져 왔으나 이에 관한 직접적인 연구는 찾기 힘들다. 따라서 본 연구에서는 패널자료에서 이전 시점의 정보를 고려하지 않고 대체를 실시하는 방법과 이전 시점의 정보를 활용하여 대체하는 방법들 중에서 어느 대체 방법이 보다 적절한 대체를 제공하는지 살펴보았다. 특히 이전 시점의 응답 정보를 이용하는 방법인 비대체, 선형혼합모형을 이용한 대체와 선형혼합모형에 근거한 베이지안 대체 방법을 고려하였고, 이를 이전 시점의 정보를 고려하지 않는 대체 방법들 중 흔히 사용되는 평균대체, 핫덱대체 방법과 비교하였다. 모의실험 결과 선형혼합모형에 근거한 베이지 안 대체 방법이 다른 대체 방법에 비해 무응답 비율이 높아지더라도 편의도 작으며 평균에 관한 95% 신뢰구간의 포함률도 높게 나타나서 가장 좋은 대체 방법으로 확인되었다. When conducting a survey, item nonresponse occurs if the respondent does not respond to some items. Since analysis based only on completely observed data may cause biased results, imputation is often conducted to analyze data in its complete form. The panel study is a survey method that examines changes of responses over time. In panel studies, there has been a preference for using information from response values of previous waves when the imputation of item nonresponses is performed; however, limited research has been conducted to support this preference. Therefore, this study compares the performance of imputation methods according to whether or not information from previous waves is utilized in the panel study. Among imputation methods that utilize information from previous responses, we consider ratio imputation, imputation based on the linear mixed model, and imputation based on the Bayesian linear mixed model approach. We compare the results from these methods against the results of methods that do not use information from previous responses, such as mean imputation and hot deck imputation. Simulation results show that imputation based on the Bayesian linear mixed model performs best and yields small biases and high coverage rates of the 95% confidence interval even at higher nonresponse rates.

Calibrated Hot Deck Imputation for Numerical Data Under Edit Restrictions

We develop a nonparametric imputation method for item nonresponse based on the well-known hot deck approach. The proposed imputation method is developed for imputing numerical data that ensure that all record-level edit rules are satisfied and previously estimated or known totals are exactly preserved. We propose a sequential hot deck imputation approach that takes into account survey weights. Original survey weights are not changed; rather the imputations themselves are calibrated so that weighted estimates will equal known or estimated population totals. Edit rules are preserved by integrating the sequential hot deck imputation with Fourier-Motzkin elimination, which defines the range of feasible values that can be used for imputation such that all record-level edits will be satisfied. We apply the proposed imputation method under different scenarios of random and nearest-neighbor hot deck on two data sets: an annual structural business survey and a synthetically generated data set with a large proportion of missing data. We compare the proposed imputation methods to standard imputation methods based on a set of evaluation measures.

The HCUP SID Imputation Project: Improving Statistical Inferences for Health Disparities Research by Imputing Missing Race Data.

To identify the most appropriate imputation method for missing data in the HCUP State Inpatient Databases (SID) and assess the impact of different missing data methods on racial disparities research. HCUP SID. A novel simulation study compared four imputation methods (random draw, hot deck, joint multiple imputation [MI], conditional MI) for missing values for multiple variables, including race, gender, admission source, median household income, and total charges. The simulation was built on real data from the SID to retain their hierarchical data structures and missing data patterns. Additional predictive information from the U.S. Census and American Hospital Association (AHA) database was incorporated into the imputation. Conditional MI prediction was equivalent or superior to the best performing alternatives for all missing data structures and substantially outperformed each of the alternatives in various scenarios. Conditional MI substantially improved statistical inferences for racial health disparities research with the SID.

Using multiple imputation to address the inconsistent distribution of a controlling variable when modeling an infrequent outcome.

Temporal changes in methods for collecting longitudinal data can generate inconsistent distributions of affected variables, but effects on parameter estimates have not been well described. We examined differences in Apgar scores of infants born in 2000-2006 to women with ovulatory dysfunction (risk) or tubal obstruction (reference) who underwent assisted reproductive technology (ART), using Florida, Massachusetts, and Michigan birth certificate data linked to the Centers for Disease Control and Prevention's National ART Surveillance System database. Florida had inconsistent information on induction of labor (a control variable) from a 2004 change in birth certificate format. Because we wanted to control for bias that may be introduced by the inconsistent distribution of labor induction in analysis, we used multiple imputation data in analysis. We used Cox-Iannacchione weighted sequential hot deck method to conduct multiple imputation for the labor induction values in Florida data collected before this change, and missing values in Florida data collected after the change and overall Massachusetts and Michigan data. The adjusted odds ratios for low Apgar score were 1.94 (95% confidence interval [CI] 1.32-2.85) using imputed induction of labor and 1.83 (95% CI 1.20-2.80) using not imputed induction of labor. Compared with the estimate from multiple imputation, the estimate obtained using not imputed induction of labor was biased towards the null with inflated standard errors, but the magnitude of differences was small.

Research and implementation of animations evaluation system

A scientific and systematical evaluation of animations will be able to reflect the integrated strength of animations. Based on the popularity of animations in the market and the quality of animations, and following the principles of index selection, we propose an animations evaluation system (AES) by using multiple social research methods. We establish and analyze a mathematical model based on analytic hierarchy process and fuzzy comprehensive evaluation. We then treat the missing data of the market repercussion index and the professional evaluation index by using hot deck imputation and mean imputation. Finally, with sample test to the data extracted from Chinese market, experimental results show that AES and the mathematical model is feasible and the missing data treatment is reasonable. Furthermore, we prove that social values and artistic values of animations, which are both part and parcel of the integrated strength of animations, can be objectively reflected by AES.

Imputation Methods for Longitudinal Data: A Comparative Study

Longitudinal studies play an important role in scientific researches. The defining characteristic of the longitudinal studies is that observations are collected from each subject repeatedly over time, or under different conditions. Missing values are common in longitudinal studies. The presence of missing values is always a fundamental challenge since it produces potential bias, even in well controlled conditions. Three different missing data mechanisms are defined; missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). Several imputation methods have been developed in literature to handle missing values in longitudinal data. The most commonly used imputation methods include complete case analysis (CCA), mean imputation (Mean), last observation carried forward (LOCF), hot deck (HOT), regression imputation (Regress), K-nearest neighbor (KNN), The expectation maximization (EM) algorithm, and multiple imputation (MI). In this article, a comparative study is conducted to investigate the efficiency of these eight imputation methods under different missing data mechanisms. The comparison is conducted through simulation study. It is concluded that the MI method is the most effective method as it has the least standard errors. The EM algorithm has the largest relative bias. The different methods are also compared via real data application.