Multivariate Normal Imputation Research Articles

Changes in the neighborhood food environment and walking time among older adults: A longitudinal Japan Gerontological Evaluation Study (JAGES) between 2016 and 2019

Objective Maintaining or increasing walking provides several health benefits to older adults. However, the mid-term evaluation of Health Japan 21 [second term] showed that older adults' daily steps did not meet the goal. Therefore, this study emphasized primordial prevention, which is different from previous preventive approaches and focuses on the relationship between the built environment and physical activities, including daily steps. This study investigated the relationship between changes in the number of food stores and walking time.Methods This longitudinal study utilized the self-administered mail survey data between 2016 and 2019 from the Japan Gerontological Evaluation Study (JAGES). Older adults aged ≥65 years and residing in 27 independent municipalities were recruited. The dependent variable was a change in the walking time at two-time points (increase or not). Our explanatory variable was the change in the number of food stores at two-time points, reported on a 5-point scale, including no store (reference), increased stores, store available, decreased stores, and I don't know. Equivalently, it was defined as the self-reported change in the number of food stores (stores that sell meats, fish, fruits, and vegetables) within the walking distance of participants' homes (within ～1 km) from 2016 to 2019. The covariates included demographic factors, health behavior factors, environmental factors, and health factors in 2016. We used Poisson regression analysis (5% significance level) to calculate the cumulative incidence rate ratio (CIRR) and 95% confidence interval (CI) for an increase in walking time compared to no increase in walking time. The multivariate normal imputation method supplemented missing data of the dependent variable, explanatory variable, and covariates. Additionally, respondents' answer of "other" for the covariates was supplemented.Results Three years later, 13,400 (20.4%) respondents had increased their walking time. Older adults who reported increased number of stores (5,311, 8.1%) had more walking time than those who reported no stores (6,577, 10.0%) (CIRR=1.12; 95% CI: 1.03-1.21).Conclusion Participants who reported an increase in the number of fresh food stores within the walking distance had 12% more walking time three years later. A built environment might be used to measure primordial prevention that increases the amount of walking in daily life. Our results may provide evidence for policymakers and stakeholders to consider healthy urban planning.

Tackling UCR's missing data problem: A multiple imputation approach

Purpose: This paper addresses concerns related to missing data in the UCR. We compare several methods using multiple imputation in an effort to improve the data. Methods: We develop a two-stage procedure for imputing missing values in the UCR. First, we use agencies' past reporting to impute missing values. Then, after merging in demographic data from the census, we use multiple imputation to fill in the remaining missing values. Several methods are considered, including multivariate normal imputation (MVNI) and multiple imputation by chained equations (MICE). Results: Methods are compared using a complete subset of the UCR with values systematically deleted. We find that a model using MICE with random forest prediction produces results that are comparable to the methods NACJD uses when preparing the county level UCR data. Conclusions: We recommend applying multiple imputation to the UCR rather than relying on the county level data published by NACJD. Not only are our results similar to NACJD's, but additionally, an approach using multiple imputation accounts for the uncertainty in imputed values, so that correct standard errors can be obtained in subsequent analyses.

Choosing Imputation Models

AbstractImputing missing values is an important preprocessing step in data analysis, but the literature offers little guidance on how to choose between imputation models. This letter suggests adopting the imputation model that generates a density of imputed values most similar to those of the observed values for an incomplete variable after balancing all other covariates. We recommend stable balancing weights as a practical approach to balance covariates whose distribution is expected to differ if the values are not missing completely at random. After balancing, discrepancy statistics can be used to compare the density of imputed and observed values. We illustrate the application of the suggested approach using simulated and real-world survey data from the American National Election Study, comparing popular imputation approaches including random forests, hot-deck, predictive mean matching, and multivariate normal imputation. An R package implementing the suggested approach accompanies this letter.

Multiple imputation of semi-continuous exposure variables that are categorized for analysis.

Semi-continuous variables are characterized by a point mass at one value and a continuous range of values for remaining observations. An example is alcohol consumption quantity, with a spike of zeros representing non-drinkers and positive values for drinkers. If multiple imputation is used to handle missing values for semi-continuous variables, it is unclear how this should be implemented within the standard approaches of fully conditional specification (FCS) and multivariate normal imputation (MVNI). This question is brought into focus by the use of categorized versions of semi-continuous exposure variables in analyses (eg, no drinking, drinking below binge level, binge drinking, heavy binge drinking), raising the question of how best to achieve congeniality between imputation and analysis models. We performed a simulation study comparing nine approaches for imputing semi-continuous exposures requiring categorization for analysis. Three methods imputed the categories directly: ordinal logistic regression, and imputation of binary indicator variables representing the categories using MVNI (with two variants). Six methods (predictive mean matching, zero-inflated binomial imputation, and two-part imputation methods with variants in FCS and MVNI) imputed the semi-continuous variable, with categories derived after imputation. The ordinal and zero-inflated binomial methods had good performance across most scenarios, while MVNI methods requiring rounding after imputation did not perform well. There were mixed results for predictive mean matching and the two-part methods, depending on whether the estimands were proportions or regression coefficients. The results highlight the need to consider the parameter of interest when selecting an imputation procedure.

A comparison of multiple imputation strategies for handling missing data in multi-item scales: Guidance for longitudinal studies.

Medical research often involves using multi-item scales to assess individual characteristics, disease severity, and other health-related outcomes. It is common to observe missing data in the scale scores, due to missing data in one or more items that make up that score. Multiple imputation (MI) is a popular method for handling missing data. However, it is not clear how best to use MI in the context of scale scores, particularly when they are assessed at multiple waves of data collection resulting in large numbers of items. The aim of this article is to provide practical advice on how to impute missing values in a repeatedly measured multi-item scale using MI when inference on the scale score is of interest. We evaluated the performance of five MI strategies for imputing missing data at either the item or scale level using simulated data and a case study based on four waves of the Longitudinal Study of Australian Children (LSAC). MI was implemented using both multivariate normal imputation and fully conditional specification, with two rules for calculating the scale score. A complete case analysis was also performed for comparison. Based on our results, we caution against the use of a MI strategy that does not include the scale score in the imputation model(s) when the scale score is required for analysis.

Multiple imputation methods for handling missing values in longitudinal studies with sampling weights: Comparison of methods implemented in Stata.

Many analyses of longitudinal cohorts require incorporating sampling weights to account for unequal sampling probabilities of participants, as well as the use of multiple imputation (MI) for dealing with missing data. However, there is no guidance on how MI and sampling weights should be implemented together. We simulated a target population based on the Australian Bureau of Statistics Estimated Resident Population and drew 1000 random samples dependent on three design variables to mimic the Longitudinal Study of Australian Children. The target analysis was the weighted prevalence of overweight/obesity over childhood. We evaluated the performance of several MI approaches available in Stata, based on multivariate normal imputation (MVNI), fully conditional specification (FCS) and twofold FCS: a weighted imputation model, imputing missing data separately for each quintile sampling weight grouping, including the design stratum indicator in the imputation model, and using sampling weights as a covariate in the imputation model. Approaches based on available cases and inverse probability weighting (IPW), with time-varying weights, were also compared. We observed severe issues of convergence with FCS and twofold FCS. All MVNI-based approaches performed similarly, producing minimal bias and nominal coverage, except for when imputation was conducted separately for each quintile sampling weight group. IPW performed equally as well as MVNI-based approaches in terms of bias, however, was less precise. In similar longitudinal studies, we recommend using MVNI with the design stratum as a covariate in the imputation model. If this is unknown, including the sampling weight as a covariate is an appropriate alternative.

Linking Differences in Eating Behavior with Appetitive Hormones in Women

Abstract Objectives Examine and compare the hormones related to satiety in women identified as 1) restrained + disinhibited eaters, 2) restrained, non-disinhibited eaters, or 3) unrestrained, non-disinhibited eaters. We hypothesized restrained eaters with disinhibition would have a different pattern of appetitive hormones involved in food intake regulation. Methods 178 women from a cross-sectional study completed the three factor eating questionnaire (TFEQ), and were classified as restrained + disinhibited eaters (RD, n = 38), restrained, non-disinhibited eaters (R, n = 52), or unrestrained, non-disinhibited eaters (LL, n = 88). Women fasted for 12 h prior to baseline blood collection, and postprandial blood was collected after a meal challenge at 30 min, 3 h, and 6 h. Data were evaluated for outliers and missingness, and transformed and imputed using multivariate normal imputation. Differences in glucose, insulin and ghrelin were analyzed using a linear mixed model comparing groups. Time to peak and nadir for glucose, insulin and ghrelin were calculated from response curves. Chi square tests of proportions were used to determine whether the distribution of participants in the three groups were different in their times to peak and nadir. Results There were no significant differences between groups in ghrelin or insulin concentrations over time. However, overall glucose levels in RD were significantly lower than R and LL groups (P = 0.05 and P = 0.03, respectively). Chi-squared tests indicated that a greater proportion of women in the RD group reached peak glucose at 3 h, compared to women in R and LL with peak glucose occurring at 30 min (P = 0.04). Glucose nadir displayed a bimodal distribution in R, with more women at baseline and 3 h compared to RD and LL (P = 0.05). Ghrelin nadir was reached at 3 h for more participants in RD and LL, but occurred later at 6 h in more participants in R (P = 0.04). Conclusions Dietary restraint and disinhibition are associated with circulating glucose and ghrelin concentrations; however, prospective research is needed to determine if there is a causal relationship. Funding Sources USDA CRIS 2032-51530-022, 2032-51530-025, and 2032-51530-026-00-D, and a grant from Arla Foods Inc.

Missing data in longitudinal studies: Comparison of multiple imputation methods in a real clinical setting.

Missing data represent a challenge in longitudinal studies. The aim of the study is to compare the performance of the multivariate normal imputation and the fully conditional specification methods, using real data set with missing data partially completed 2 years later. The data used came from an ongoing randomized controlled trial with 5-year follow-up. At a certain time, we observed a number of patients with missing data and a number of patients whose data were unobserved because they were not yet eligible for a given follow-up. Both unobserved and missing data were imputed. The imputed unobserved data were compared with the corresponding real information obtained 2 years later. Both imputation methods showed similar performance on the accuracy measures and produced minimally biased estimates. Despite the large number of repeated measures with intermittent missing data and the non-normal multivariate distribution of data, both methods performed well and was not possible to determine which was better.

A closer examination of three small-sample approximations to the multiple-imputation degrees of freedom, erratum

Incomplete data is a common complication in applied research. In this study, we use simulation to compare two approaches to the multiple imputation of a continuous predictor: multiple imputation through chained equations and multivariate normal imputation. This study extends earlier work by being the first to 1) compare the small-sample approximations to the multiple-imputation degrees of freedom proposed by Barnard and Rubin (1999, Biometrika 86: 948- 955); Lipsitz, Parzen, and Zhao (2002, Journal of Statistical Computation and Simulation 72: 309-318); and Reiter (2007, Biometrika 94: 502-508) and 2) ask if the sampling distribution of the t statistics is in fact a Student's t distribution with the specified degrees of freedom. In addition to varying the imputation method, we varied the number of imputa- tions (m =5 , 10, 20, 100) that were averaged over 500,000 replications to obtain the combined estimates and standard errors for a linear model that regressed the log price of a home on its age (years) and size (square feet) in a sample of 25 ob- servations. Six age values were randomly set equal to missing for each replication. As assessed by the absolute percentage and relative percentage bias, the two ap- proaches performed similarly. The absolute bias of the regression coefficients for age and size was roughly −0.1% across the levels of m for both approaches; the ab- solute bias for the constant was 0.6% for the chained-equations approach and 1.0% for the multivariate normal model. The absolute biases of the standard errors for age, size, and the constant were 0.2%, 0.3%, and 1.2%, respectively. In general, the relative percentage bias was slightly smaller for the chained-equations approach. Graphical and numerical inspection of the empirical sampling distributions for the three t statistics suggested that the area from the shoulder to the tail was reasonably well approximated by a t distribution and that the small-sample ap- proximations to the multiple-imputation degrees of freedom proposed by Barnard and Rubin and by Reiter performed satisfactorily.

Multiple imputation in the presence of an incomplete binary variable created from an underlying continuous variable.

Multiple imputation (MI) is used to handle missing at random (MAR) data. Despite warnings from statisticians, continuous variables are often recoded into binary variables. With MI it is important that the imputation and analysis models are compatible; variables should be imputed in the same form they appear in the analysis model. With an encoded binary variable more accurate imputations may be obtained by imputing the underlying continuous variable. We conducted a simulation study to explore how best to impute a binary variable that was created from an underlying continuous variable. We generated a completely observed continuous outcome associated with an incomplete binary covariate that is a categorized version of an underlying continuous covariate, and an auxiliary variable associated with the underlying continuous covariate. We simulated data with several sample sizes, and set 25% and 50% of data in the covariate to MAR dependent on the outcome and the auxiliary variable. We compared the performance of five different imputation methods: (a) Imputation of the binary variable using logistic regression; (b) imputation of the continuous variable using linear regression, then categorizing into the binary variable; (c, d) imputation of both the continuous and binary variables using fully conditional specification (FCS) and multivariate normal imputation; (e) substantive-model compatible (SMC) FCS. Bias and standard errors were large when the continuous variable only was imputed. The other methods performed adequately. Imputation of both the binary and continuous variables using FCS often encountered mathematical difficulties. We recommend the SMC-FCS method as it performed best in our simulation studies.

Data Mining Effective for Casing-Failure Prediction and Prevention

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 19311, “Data-Mining Approaches for Casing-Failure Prediction and Prevention,” by Christine Noshi, SPE, Samuel Noynaert, SPE, and Jerome Schubert, SPE, Texas A&M University, prepared for the 2019 International Petroleum Technology Conference, Beijing, 26–28 March. The paper has not been peer reviewed. Copyright 2019 International Petroleum Technology Conference. Reproduced by permission. Recent casing failures in the Granite Wash play in the western Anadarko Basin have sparked deep concerns for operators in North Texas and Oklahoma. Hydrostatic tests made in the field show that current API standards do not assure adequate joint and bursting strength to meet deep-well requirements. This paper is part of an ongoing effort to minimize the likelihood of failure using data-mining and machine-learning algorithms. Introduction Casing failure has long presented a challenge to the industry. The combined effects of design, dynamic borehole conditions, metallurgy, and handling have been challenging to quantify and predict accurately. Additionally, most casing-string challenges have been handled reactively instead of proactively; the total number of failures have been underreported and overlooked. The authors focus on the effects of poor cement as a primary factor; this translates into the absence of cement in a case study presented in the complete paper. Additional factors are the pumping of corrosive acids and poor standardized casing design that does not account for varied formations along with cyclical temperatures. Casing with partial cementation and sheaths with voids can contribute to excessive buckling-related collapse and tensile failures. Large pressure loadings, along with significant change in temperature, contribute to significant stresses in the intercasing annuli. In fragmentally cemented casing, tensile loading can show a great discrepancy between compression and high tension, with instances of failures in both the outer and inner strings. Additionally, cement thickening by downward flow could lack uniformity and could be prone to channeling. Air entrapment might occur, establishing bridges that hinder the process. Some authors in the literature related cementing failures with hole enlargements and washouts in long cement depths. The lack of cement support in those significant intervals exposed the casing to movement during drillpipe rotation, which triggered wear and ultimate buckling. Methodology The data were descriptively visualized using methods such as box plots, mosaic plots, and trellis charts, while predictive techniques included artificial neural networks (ANNs) and boosted-ensemble trees. A statistical software package was used along with Python coding to implement the models and choose the most-significant factors contributing to failure. Data-preprocessing techniques were implemented. The process began with data cleaning to account for missing data, re-move the bias incurred by noise, and remove outliers. For missing values, multivariate normal imputation on the basis of all samples belonging to the same class was used. Then, several parameters from different databases were integrated. Data transformation involved standardizing the data by the subtraction of the mean value and the subsequent division by standard deviation from each feature. Categorical variables were converted to numerical values because models such as neural nets, regression, and nearest-neighbor involve only numeric inputs. The compiled data set comprised 78 wells. Caution should be taken when assessing its statistical significance.

Multiple imputation methods for handling missing values in a longitudinal categorical variable with restrictions on transitions over time: a simulation study

BackgroundLongitudinal categorical variables are sometimes restricted in terms of how individuals transition between categories over time. For example, with a time-dependent measure of smoking categorised as never-smoker, ex-smoker, and current-smoker, current-smokers or ex-smokers cannot transition to a never-smoker at a subsequent wave. These longitudinal variables often contain missing values, however, there is little guidance on whether these restrictions need to be accommodated when using multiple imputation methods. Multiply imputing such missing values, ignoring the restrictions, could lead to implausible transitions.MethodsWe designed a simulation study based on the Longitudinal Study of Australian Children, where the target analysis was the association between (incomplete) maternal smoking and childhood obesity. We set varying proportions of data on maternal smoking to missing completely at random or missing at random. We compared the performance of fully conditional specification with multinomial and ordinal logistic imputation, and predictive mean matching, two-fold fully conditional specification, indicator based imputation under multivariate normal imputation with projected distance-based rounding, and continuous imputation under multivariate normal imputation with calibration, where each of these multiple imputation methods were applied, accounting for the restrictions using a semi-deterministic imputation procedure.ResultsOverall, we observed reduced bias when applying multiple imputation methods with restrictions, and fully conditional specification with predictive mean matching performed the best. Applying fully conditional specification and two-fold fully conditional specification for imputing nominal variables based on multinomial logistic regression had severe convergence issues. Both imputation methods under multivariate normal imputation produced biased estimates when restrictions were not accommodated, however, we observed substantial reductions in bias when restrictions were applied with continuous imputation under multivariate normal imputation with calibration.ConclusionIn a similar longitudinal setting we recommend the use of fully conditional specification with predictive mean matching, with restrictions applied during the imputation stage.

A comparison of multiple imputation methods for missing data in longitudinal studies

BackgroundMultiple imputation (MI) is now widely used to handle missing data in longitudinal studies. Several MI techniques have been proposed to impute incomplete longitudinal covariates, including standard fully conditional specification (FCS-Standard) and joint multivariate normal imputation (JM-MVN), which treat repeated measurements as distinct variables, and various extensions based on generalized linear mixed models. Although these MI approaches have been implemented in various software packages, there has not been a comprehensive evaluation of the relative performance of these methods in the context of longitudinal data.MethodUsing both empirical data and a simulation study based on data from the six waves of the Longitudinal Study of Australian Children (N = 4661), we investigated the performance of a wide range of MI methods available in standard software packages for investigating the association between child body mass index (BMI) and quality of life using both a linear regression and a linear mixed-effects model.ResultsIn this paper, we have identified and compared 12 different MI methods for imputing missing data in longitudinal studies. Analysis of simulated data under missing at random (MAR) mechanisms showed that the generally available MI methods provided less biased estimates with better coverage for the linear regression model and around half of these methods performed well for the estimation of regression parameters for a linear mixed model with random intercept. With the observed data, we observed an inverse association between child BMI and quality of life, with available data as well as multiple imputation.ConclusionBoth FCS-Standard and JM-MVN performed well for the estimation of regression parameters in both analysis models. More complex methods that explicitly reflect the longitudinal structure for these analysis models may only be needed in specific circumstances such as irregularly spaced data.

Strategies for handling missing data in longitudinal studies with questionnaires

ABSTRACTMissing data methods, maximum likelihood estimation (MLE) and multiple imputation (MI), for longitudinal questionnaire data were investigated via simulation. Predictive mean matching (PMM) was applied at both item and scale levels, logistic regression at item level and multivariate normal imputation at scale level. We investigated a hybrid approach which is combination of MLE and MI, i.e. scales from the imputed data are eliminated if all underlying items were originally missing. Bias and mean square error (MSE) for parameter estimates were examined. ML seemed to provide occasionally the best results in terms of bias, but hardly ever on MSE. All imputation methods at the scale level and logistic regression at item level hardly ever showed the best performance. The hybrid approach is similar or better than its original MI. The PMM-hybrid approach at item level demonstrated the best MSE for most settings and in some cases also the smallest bias.

Early Infant Feeding of Formula or Solid Foods and Risk of Childhood Overweight or Obesity in a Socioeconomically Disadvantaged Region of Australia: A Longitudinal Cohort Analysis.

In southwestern Sydney the timing of introduction of formula and solids may be associated with risk of childhood overweight or obesity, and this may vary by age at breastfeeding cessation during first year. We included 346 infants from southwestern Sydney using the longitudinal study for Australian children (LSAC), who at baseline were singleton, full term, and normal weight births. The outcome risk of overweight or obesity was measured at every two-year interval of children aged 0 or 1 year at baseline until they reached age 10 or 11, defined by body mass index (BMI) ≥ 85th percentile, using the Centre for Disease Control and Prevention growth charts. Age at introduction to formula or solids was dichotomized at four months. We used mixed effects logistic regression for performing all analyses with and without adjusting for mother’s BMI, age during pregnancy, and social disadvantage index. Missing data were estimated using multivariate normal imputation having 25 imputations. The odds of overweight or obesity were significantly higher among infants introduced to formula or solids at ≤4 months compared to those introduced at >4 months in both unadjusted (odds ratio = 2.3262, p = 0.023) and adjusted (odds ratio = 1.9543, p = 0.0475) analyses. The odds of overweight or obesity when age at formula or solids introduction was held fixed at ≤4 months, increased significantly (odds ratio = 2.0856, p = 0.0215) for children stopping breastfeeding at age ≤4 months compared to >4 months. Thus, increasing the prevalence of breast-feeding without any formula or solids to 4–6 months in southwest Sydney should be a worthwhile public health measure.

Missing Data in Longitudinal Surveys: A Comparison of Performance of Modern Techniques

Using a simulation study, the performance of complete case analysis, full information maximum likelihood, multivariate normal imputation, multiple imputation by chained equations and two-fold fully conditional specification to handle missing data were compared in longitudinal surveys with continuous and binary outcomes, missing covariates, and an interaction term.

A comparison of multiple imputation methods for handling missing values in longitudinal data in the presence of a time-varying covariate with a non-linear association with time: a simulation study

BackgroundMissing data is a common problem in epidemiological studies, and is particularly prominent in longitudinal data, which involve multiple waves of data collection. Traditional multiple imputation (MI) methods (fully conditional specification (FCS) and multivariate normal imputation (MVNI)) treat repeated measurements of the same time-dependent variable as just another ‘distinct’ variable for imputation and therefore do not make the most of the longitudinal structure of the data. Only a few studies have explored extensions to the standard approaches to account for the temporal structure of longitudinal data. One suggestion is the two-fold fully conditional specification (two-fold FCS) algorithm, which restricts the imputation of a time-dependent variable to time blocks where the imputation model includes measurements taken at the specified and adjacent times. To date, no study has investigated the performance of two-fold FCS and standard MI methods for handling missing data in a time-varying covariate with a non-linear trajectory over time – a commonly encountered scenario in epidemiological studies.MethodsWe simulated 1000 datasets of 5000 individuals based on the Longitudinal Study of Australian Children (LSAC). Three missing data mechanisms: missing completely at random (MCAR), and a weak and a strong missing at random (MAR) scenarios were used to impose missingness on body mass index (BMI) for age z-scores; a continuous time-varying exposure variable with a non-linear trajectory over time. We evaluated the performance of FCS, MVNI, and two-fold FCS for handling up to 50% of missing data when assessing the association between childhood obesity and sleep problems.ResultsThe standard two-fold FCS produced slightly more biased and less precise estimates than FCS and MVNI. We observed slight improvements in bias and precision when using a time window width of two for the two-fold FCS algorithm compared to the standard width of one.ConclusionWe recommend the use of FCS or MVNI in a similar longitudinal setting, and when encountering convergence issues due to a large number of time points or variables with missing values, the two-fold FCS with exploration of a suitable time window.

Using dynamic Bayesian networks to model technical risk management efficiency

AbstractThe objective of this paper is to present a mathematical model helping decision makers achieve optimum efficiency in risk management of product development. The optimum we are seeking considers qualitative data derived from expert opinions and quantitative information on project characteristics. The mathematical model proposed here aims at integrating data from these sources to identify opportunities for decreasing product risk. Reduction of overall product risk, before product release to production, is an indicator of the efficiency of the risk management intervention. Acceptable risk targets vary according to industry type, organization characteristics, regulations, etc. In general, the risk management process consists of identification of risks, analysis of risks, risk control, and feedback. Here, we propose a mathematical approach to risk management by using dynamic Bayesian networks for evaluation of product risks during the development period. The properties of the model are assessed by using 2 validation methods: k‐fold cross validation and leave‐one‐out techniques. Mathematical imputation methods, like multivariate normal imputation, are invoked to deal with missing data. In addition, sensitivity analysis is performed to assess the uncertainty embedded in the parameters derived from the dynamic Bayesian network.Decision makers should consider the overall risk in product development estimated by this mathematical model. It may help to determine whether to release a product for Beta testing or to conduct additional activities to reduce the overall risk level before customer shipment. In addition, the model may be used for prediction purposes as it provides an estimate of the expected risk at time t + 1 based on the level of risk at time t.

Multiple imputation of unordered categorical missing data: A comparison of the multivariate normal imputation and multiple imputation by chained equations

Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of them may negatively affect the inferences drawn. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to deal with missing data. The former assumes a normal distribution of the variables in the imputation model and the latter fills in missing values taking into account the distributional form of the variables to be imputed. This study examines the performance of these methods when data are missing at random on unordered categorical variables treated as predictors in the regression models. First, a survey data set with no missing values is used to generate a data set with missing at random observations on unordered categorical variables. Then, the two methods are separately used to impute the missing values of the generated data set. Their performance is compared in terms of bias and standard errors of the estimates from the regression models that determine the association between the woman’s contraceptive methods use status and her marital status, controlling for the region of origin. The baseline data used is the 2007 Demographic and Health Survey (DHS) data set from the Democratic Republic of Congo. The findings indicate that although the MVNI relies on the statistical parametric theory, it produces more accurate estimates than MICE for nonordered categorical variables.

Multiple imputation for ordinal longitudinal data with monotone missing data patterns

ABSTRACTMissing data often complicate the analysis of scientific data. Multiple imputation is a general purpose technique for analysis of datasets with missing values. The approach is applicable to a variety of missing data patterns but often complicated by some restrictions like the type of variables to be imputed and the mechanism underlying the missing data. In this paper, the authors compare the performance of two multiple imputation methods, namely fully conditional specification and multivariate normal imputation in the presence of ordinal outcomes with monotone missing data patterns. Through a simulation study and an empirical example, the authors show that the two methods are indeed comparable meaning any of the two may be used when faced with scenarios, at least, as the ones presented here.