missMDA: A Package for Handling Missing Values in Multivariate Data Analysis

We present the R package missMDA which performs principal component methods on incomplete data sets, aiming to obtain scores, loadings and graphical representations despite missing values. Package methods include principal component analysis for continuous variables, multiple correspondence analysis for categorical variables, factorial analysis on mixed data for both continuous and categorical variables, and multiple factor analysis for multi-table data. Furthermore, missMDA can be used to perform single imputation to complete data involving continuous, categorical and mixed variables. A multiple imputation method is also available. In the principal component analysis framework, variability across different imputations is represented by confidence areas around the row and column positions on the graphical outputs. This allows assessment of the credibility of results obtained from incomplete data sets

The 2005 European e-Business Readiness Index

Assessment of the eEurope 2005 Action Plan Benchmarking Index “E-Business Readiness Composite Indicator” using data collected by National Statistical Institutes and harmonised by Eurostat, using surveys “ICT usage of enterprises”, with reference years 2003 and 2004. This report contains data from 26 countries as collected in 2004 and as reported by Eurostat in June 2005. Performed analyses include obustness analysis, uncertainty and sensitivity analysis for two categories of ICT (Adoption and Use), univariate analysis of basic indicators; principal component analysis and finally assessment of resulted country rankings and methodological notes.ICT, e-business, adoption, composite, indicator, eEurope, e-Europe, EU, multiple imputation imputation

Multiple imputation for continuous variables using a Bayesian principal component analysis

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the PCA model. Using a simulation study and real data sets, the method is compared to two classical approaches: multiple imputation based on joint modelling and on fully conditional modelling. Contrary to the others, the proposed method can be easily used on data sets where the number of individuals is less than the number of variables and when the variables are highly correlated. In addition, it provides unbiased point estimates of quantities of interest, such as an expectation, a regression coefficient or a correlation coefficient, with a smaller mean squared error. Furthermore, the widths of the confidence intervals built for the quantities of interest are often smaller whilst ensuring a valid coverage.Comment: 16 page

Multiple imputation and maximum likelihood principal component analysis of incomplete multivariate data from a study of the ageing of port

A multivariate data matrix containing a number of missing values was obtained from a study on the changes in colour and phenolic composition during the ageing of port. Two approaches were taken in the analysis of the data. The first involved the use of multiple imputation (MI) followed by principal components analysis (PCA). The second examined the use of maximum likelihood principal component analysis (MLPCA). The use of multiple imputation allows for missing value uncertainty to be incorporated into the analysis of the data. Initial estimates of missing values were firstly calculated using the Expectation Maximization algorithm (EM), followed by Data Augmentation (DA) in order to generate five imputed data matrices. Each complete data matrix was subsequently analysed by PCA, then averaging their principal component (PC) scores and loadings to give an estimation of errors. The first three PCs accounted for 93.3% of the explained variance. Changes to colour and monomeric anthocyanin composition were explained on PC1 (79.63% explained variance), phenolic composition and hue mainly on PC2 (8.61% explained variance) and phenolic composition and the formation of polymeric pigment on PC3 (5.04% explained variance). In MLPCA estimates of measurement uncertainty is incorporated in the decomposition step, with missing values being assigned large measurement uncertainties. PC scores on the first two PCs after multiple imputation and PCA (MI+PCA) were comparable to maximum likelihood scores on the first two PCs extracted by MLPCA

Use of data imputation tools to reconstruct incomplete air quality datasets:a case-study in Temuco, Chile

© 2018 Elsevier LtdMissing data from air quality datasets is a common problem, but is much more severe in small cities or localities. This poses a great challenge for environmental epidemiology as high exposures to pollutants worldwide occur in these settings and gaps in datasets hinder health studies that could later inform local and international policies. Here, we propose the use of imputation methods as a tool to reconstruct air quality datasets and have applied this approach to an air quality dataset in Temuco, a mid-size city in Chile as a case-study. We attempted to reconstruct the database comparing five approaches: mean imputation, conditional mean imputation, K-Nearest Neighbor imputation, multiple imputation and Bayesian Principal Component Analysis imputation. As a base for the imputation methods, linear regression models were fitted for PM2.5 against other air quality and meteorological variables. Methods were challenged against validation sets where data was removed arti

High-dimensional Imputation for the Social Sciences: a Comparison of State-of-the-art Methods

Including a large number of predictors in the imputation model underlying a multiple imputation (MI) procedure is one of the most challenging tasks imputers face. A variety of high-dimensional MI techniques can help, but there has been limited research on their relative performance. In this study, we investigated a wide range of extant high-dimensional MI techniques that can handle a large number of predictors in the imputation models and general missing data patterns. We assessed the relative performance of seven high-dimensional MI methods with a Monte Carlo simulation study and a resampling study based on real survey data. The performance of the methods was defined by the degree to which they facilitate unbiased and confidencevalid estimates of the parameters of complete data analysis models. We found that using lasso penalty or forward selection to select the predictors used in the MI model and using principal component analysis to reduce the dimensionality of auxiliary data produce the best results

Accounting for Calibration Uncertainties in X-ray Analysis: Effective Areas in Spectral Fitting

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties.Comment: 61 pages double spaced, 8 figures, accepted for publication in Ap

Algorithmic Techniques in Gene Expression Processing. From Imputation to Visualization

The amount of biological data has grown exponentially in recent decades. Modern biotechnologies, such as microarrays and next-generation sequencing, are capable to produce massive amounts of biomedical data in a single experiment. As the amount of the data is rapidly growing there is an urgent need for reliable computational methods for analyzing and visualizing it. This thesis addresses this need by studying how to efficiently and reliably analyze and visualize high-dimensional data, especially that obtained from gene expression microarray experiments. First, we will study the ways to improve the quality of microarray data by replacing (imputing) the missing data entries with the estimated values for these entries. Missing value imputation is a method which is commonly used to make the original incomplete data complete, thus making it easier to be analyzed with statistical and computational methods. Our novel approach was to use curated external biological information as a guide for the missing value imputation. Secondly, we studied the effect of missing value imputation on the downstream data analysis methods like clustering. We compared multiple recent imputation algorithms against 8 publicly available microarray data sets. It was observed that the missing value imputation indeed is a rational way to improve the quality of biological data. The research revealed differences between the clustering results obtained with different imputation methods. On most data sets, the simple and fast k-NN imputation was good enough, but there were also needs for more advanced imputation methods, such as Bayesian Principal Component Algorithm (BPCA). Finally, we studied the visualization of biological network data. Biological interaction networks are examples of the outcome of multiple biological experiments such as using the gene microarray techniques. Such networks are typically very large and highly connected, thus there is a need for fast algorithms for producing visually pleasant layouts. A computationally efficient way to produce layouts of large biological interaction networks was developed. The algorithm uses multilevel optimization within the regular force directed graph layout algorithm.Siirretty Doriast

Evaluation of multiple-imputation procedures for three-mode component models

Three-mode analysis is a generalization of principal component analysis to three-mode data. While two-mode data consist of cases that are measured on several variables, three-mode data consist of cases that are measured on several variables at several occasions. As any other statistical technique, the results of three-mode analysis may be influenced by missing data. Three-mode software packages generally use the expectation–maximization (EM) algorithm for dealing with missing data. However, there are situations in which the EM algorithm is expected to break down. Alternatively, multiple imputation may be used for dealing with missing data. In this study we investigated the influence of eight different multiple-imputation methods on the results of three-mode analysis, more specifically, a Tucker2 analysis, and compared the results with those of the EM algorithm. Results of the simulations show that multilevel imputation with the mode with the most levels nested within cases and the mode with the least levels represented as variables gives the best results for a Tucker2 analysis. Thus, this may be a good alternative for the EM algorithm in handling missing data in a Tucker2 analysis.Development Psychopathology in context: famil