Model-based Imputation Research Articles

Imputation of missing values for compositional data using classical and robust methods

New imputation algorithms for estimating missing values in compositional data are introduced. A first proposal uses the k -nearest neighbor procedure based on the Aitchison distance, a distance measure especially designed for compositional data. It is important to adjust the estimated missing values to the overall size of the compositional parts of the neighbors. As a second proposal an iterative model-based imputation technique is introduced which initially starts from the result of the proposed k -nearest neighbor procedure. The method is based on iterative regressions, thereby accounting for the whole multivariate data information. The regressions have to be performed in a transformed space, and depending on the data quality classical or robust regression techniques can be employed. The proposed methods are tested on a real and on simulated data sets. The results show that the proposed methods outperform standard imputation methods. In the presence of outliers, the model-based method with robust regressions is preferable.

AN EMPIRICAL COMPARISON OF TECHNIQUES FOR HANDLING INCOMPLETE DATA USING DECISION TREES

Increasing the awareness of how incomplete data affects learning and classification accuracy has led to increasing numbers of missing data techniques. This article investigates the robustness and accuracy of seven popular techniques for tolerating incomplete training and test data for different patterns of missing data—different proportions and mechanisms of missing data on resulting tree-based models. The seven missing data techniques were compared by artificially simulating different proportions, patterns, and mechanisms of missing data using 21 complete datasets (i.e., with no missing values) obtained from the University of California, Irvine repository of machine-learning databases (Blake and Merz, 1998). A four-way repeated measures design was employed to analyze the data. The simulation results suggest important differences. All methods have their strengths and weaknesses. However, listwise deletion is substantially inferior to the other six techniques, while multiple imputation, that utilizes the expectation maximization algorithm, represents a superior approach to handling incomplete data. Decision tree single imputation and surrogate variables splitting are more severely impacted by missing values distributed among all attributes compared to when they are only on a single attribute. Otherwise, the imputation—versus model-based imputation procedures gave—reasonably good results although some discrepancies remained. Different techniques for addressing missing values when using decision trees can give substantially diverse results, and must be carefully considered to protect against biases and spurious findings. Multiple imputation should always be used, especially if the data contain many missing values. If few values are missing, any of the missing data techniques might be considered. The choice of technique should be guided by the proportion, pattern, and mechanisms of missing data, especially the latter two. However, the use of older techniques like listwise deletion and mean or mode single imputation is no longer justifiable given the accessibility and ease of use of more advanced techniques, such as multiple imputation and supervised learning imputation.

Model-Based Imputation Approach for Data Analysis in the Presence of Non-detects

A model-based multiple imputation approach for analyzing sample data with non-detects is proposed. The imputation approach involves randomly generating observations below the detection limit using the detected sample values and then analyzing the data using complete sample techniques, along with suitable adjustments to account for the imputation. The method is described for the normal case and is illustrated for making inferences for constructing prediction limits, tolerance limits, for setting an upper bound for an exceedance probability and for interval estimation of a log-normal mean. Two imputation approaches are investigated in the paper: one uses approximate maximum likelihood estimates (MLEs) of the parameters and a second approach uses simple ad hoc estimates that were developed for the specific purpose of imputations. The accuracy of the approaches is verified using Monte Carlo simulation. Simulation studies show that both approaches are very satisfactory for small to moderately large sample sizes, but only the MLE-based approach is satisfactory for large sample sizes. The MLE-based approach can be calibrated to perform very well for large samples. Applicability of the method to the log-normal distribution and the gamma distribution (via a cube root transformation) is outlined. Simulation studies also show that the imputation approach works well for constructing tolerance limits and prediction limits for a gamma distribution. The approach is illustrated using a few practical examples.

Robust Model-Based Inference for Incomplete Data via Penalized Spline Propensity Prediction

Parametric model-based regression imputation is commonly applied to missing-data problems, but is sensitive to misspecification of the imputation model. Little and An (2004) proposed a semiparametric approach called penalized spline propensity prediction (PSPP), where the variable with missing values is modeled by a penalized spline (P-Spline) of the response propensity score, which is logit of the estimated probability of being missing given the observed variables. Variables other than the response propensity are included parametrically in the imputation model. However they only considered point estimation based on single imputation with PSPP. We consider here three approaches to standard errors estimation incorporating the uncertainty due to non response: (a) standard errors based on the asymptotic variance of the PSPP estimator, ignoring sampling error in estimating the response propensity; (b) standard errors based on the bootstrap method; and (c) multiple imputation-based standard errors using draws from the joint posterior predictive distribution of missing values under the PSPP model. Simulation studies suggest that the bootstrap and multiple imputation approaches yield good inferences under a range of simulation conditions, with multiple imputation showing some evidence of closer to nominal confidence interval coverage when the sample size is small.

Impact of Missing Data on Person—Model Fit and Person Trait Estimation

The purpose of this research was to examine the effects of missing data on person—model fit and person trait estimation in tests with dichotomous items. Under the missing-completely-at-random framework, four missing data treatment techniques were investigated including pairwise deletion, coding missing responses as incorrect, hotdeck imputation, and model-based imputation. Person traits were estimated using the two-parameter item response model. Overall, missing data increased the difficulty in assessing person—model fit for both model-fitting and model-misfitting persons. The higher the proportion of missing data, the larger the number of persons incorrectly diagnosed. Among the four techniques, the pairwise deletion method performed best in recovering person—model fit and person trait level. Treating missing responses as incorrect caused the examinees with missing data to not fit the measurement model, thus invalidating the person trait estimates.

Neural network imputation: An experience with the national resources inventory survey

Imputation is needed in almost all major surveys. Imputation tools are often adopted according to the convenience and the contexts of the surveys. Traditional hot-deck imputation needs extensive knowledge of the survey variables. Explicit model-based imputation needs a valid model for every survey variable. In large-scale national surveys, different groups of people with different backgrounds work on different stages of surveys and often the statistical estimation group has little or insufficient communication with the other groups. In such situations, it is difficult to use hot-deck imputation. On the other hand, because of the complex nature of the survey, finding a suitable model for every survey variable may not be easy and thus a nonparametric method— such as neural network imputation—may be attractive. One such large-scale national survey is the U.S. Department of Agriculture’s National Resources Inventory Survey (NRI). By design, the survey has missing values. The missing values are imputed using a donor-based method. This article develops a neural network imputation model and compares its performance with that of the existing imputation method. The end result looks promising.

A new multipoint method for genome-wide association studies by imputation of genotypes

Genome-wide association studies are set to become the method of choice for uncovering the genetic basis of human diseases. A central challenge in this area is the development of powerful multipoint methods that can detect causal variants that have not been directly genotyped. We propose a coherent analysis framework that treats the problem as one involving missing or uncertain genotypes. Central to our approach is a model-based imputation method for inferring genotypes at observed or unobserved SNPs, leading to improved power over existing methods for multipoint association mapping. Using real genome-wide association study data, we show that our approach (i) is accurate and well calibrated, (ii) provides detailed views of associated regions that facilitate follow-up studies and (iii) can be used to validate and correct data at genotyped markers. A notable future use of our method will be to boost power by combining data from genome-wide scans that use different SNP sets.

Tukey's gh Distribution for Multiple Imputation

Tukey proposed a class of distributions, the g-and-h family (gh family), based on a transformation of a standard normal variable to accommodate different skewness and elongation in the distribution of variables arising in practical applications. It is easy to draw values from this distribution even though it is hard to explicitly state the probability density function. Given this flexibility, the gh family may be extremely useful in creating multiple imputations for missing data. This article demonstrates how this family, as well as its generalizations, can be used in the multiple imputation analysis of incomplete data. The focus of this article is on a scalar variable with missing values. In the absence of any additional information, data are missing completely at random, and hence the correct analysis is the complete-case analysis. Thus, the application of the gh multiple imputation to the scalar cases affords comparison with the correct analysis and with other model-based multiple imputation methods. Comparisons are made using simulated datasets and the data from a survey of adolescents ascertaining driving after drinking alcohol.

Ergänzung fehlender Daten in Umfragen / Imputation of Missing Data in Surveys

Zusammenfassung Gerade bei Umfragen mit sog. sensitiven Variablen, wie etwa dem Einkommen, ist bekannt, daß z. B. die Bezieher sehr hoher Einkommen eher zur Verweigerung der Beantwortung von Einkommensfragen neigen als andere. Einfaches Vernachlässigen der unvollständigen Datensätze für die statistische Analyse würde jedoch bei systematischen und insbesondere bei den sog. nicht zufälligen, verzerrenden Antwortausfällen zu einer Stichprobe führen, die nicht mehr als repräsentativ für die interessierende Grundgesamtheit betrachtet werden könnte. Verstärkt werden daher Methoden zur Ergänzung der fehlenden Daten, sog. Imputationstechniken, publiziert, in statistischer Standardsoftware zur Verfügung gestellt und in der Praxis eingesetzt. Diese Arbeit gibt zunächst ein Uberblick über gängige ad hoc und neuere modellbasierte Ergänzungstechniken, wobei die meisten dieser Verfahren eine gewisse Zufälligkeit in den Datenausfällen voraussetzen. Mit Hilfe einer Simulationsstudie wird anschließend der Einsatz verschiedener Verfahren zur Ergänzung systematisch fehlender Daten veranschaulicht und diskutiert. An normalverteilten Daten werden die Eigenschaften der üblichen Schätzfunktionen für Mittelwerte, Varianzen und Korrelationen untersucht, wenn verschiedene Ausfallmechanismen den Datenverlust steuern und Werte mit Hilfe unterschiedlicher Verfahren ergänzt werden. Es zeigt sich deutlich, wie wenig verzerrende Ausfälle durch die Ergänzung von Werten „geheilt" werden können.

Do expenditures explain income? A study of variables for income imputation

Income data in the U.S. Consumer Expenditure Survey are subject to nonresponse. Model-based imputation is being explored to diminish missing data problems. Since income is an important variable in predicting expenditures, might expenditures be useful in predicting incomes? Incomes from wages and salaries and self-employme\1t are modeled. These results are compared to regressions on demographic characteristics alone. Although each expenditure category adds to the predictive power of the model, total expenditures adds the most.

A comparison of analytic methods for non-random missingness of outcome data

Missing outcome values occur frequently in survey data and are rarely missing randomly. Depending on the pattern of missingness, the choice of analytic method has implications for accuracy of the estimated outcome distribution as well as multivariate models. Data from a study of patterns of care in disabled elders were used to evaluate several common methods when missingness of the outcome was non-random. Results from single and multiple model-based imputation were compared with results from complete-case analysis and mean imputation. By ignoring nonrespondents' covariate information, the latter two methods yielded biased estimates of population means. Mean imputation and single model-based imputation underestimated standard errors by treating imputed values as if they were observed. Mean imputation also distorted the relationship between the outcome and predictors. Multiple model-based imputation provided an easily implemented method of adjustment for non-random non-response in both univariate and multivariate analyses.