Missing data is an inevitable aspect of every empirical research. Researchers developed several techniques to handle missing data to avoid information loss and biases. Over the past 50 years, these methods have become more and more efficient and also more complex. Building on previous review studies, this paper aims to analyze what kind of missing data handling methods are used among various scientific disciplines. For the analysis, we used nearly 50.000 scientific articles that were published between 1999 and 2016. JSTOR provided the data in text format. Furthermore, we utilized a text-mining approach to extract the necessary information from our corpus. Our results show that the usage of advanced missing data handling methods such as Multiple Imputation or Full Information Maximum Likelihood estimation is steadily growing in the examination period. Additionally, simpler methods, like listwise and pairwise deletion, are still in widespread use.

The monitoring of surface-water quality followed by water-quality modeling and analysis is essential for generating effective strategies in water resource management. However, water-quality studies are limited by the lack of complete and reliable data sets on surface-water-quality variables. These deficiencies are particularly noticeable in developing countries.

This work focuses on surface-water-quality data from Santa Lucía Chico river (Uruguay), a mixed lotic and lentic river system. Data collected at six monitoring stations are publicly available at https://www.dinama.gub.uy/oan/datos-abiertos/calidad-agua/. The high temporal and spatial variability that characterizes water-quality variables and the high rate of missing values (between 50% and 70%) raises significant challenges.

To deal with missing values, we applied several statistical and machine-learning imputation methods. The competing algorithms implemented belonged to both univariate and multivariate imputation methods (inverse distance weighting (IDW), Random Forest Regressor (RFR), Ridge (R), Bayesian Ridge (BR), AdaBoost (AB), Huber Regressor (HR), Support Vector Regressor (SVR), and K-nearest neighbors Regressor (KNNR)).

IDW outperformed the others, achieving a very good performance (NSE greater than 0.8) in most cases.

In this dataset, we include the original and imputed values for the following variables:

• Water temperature (Tw)

• Dissolved oxygen (DO)

• Electrical conductivity (EC)

• pH

• Turbidity (Turb)

• Nitrite (NO2-)

• Nitrate (NO3-)

• Total Nitrogen (TN)

Each variable is identified as [STATION] VARIABLE FULL NAME (VARIABLE SHORT NAME) [UNIT METRIC].

More details about the study area, the original datasets, and the methodology adopted can be found in our paper https://www.mdpi.com/2071-1050/13/11/6318.

If you use this dataset in your work, please cite our paper:
Rodríguez, R.; Pastorini, M.; Etcheverry, L.; Chreties, C.; Fossati, M.; Castro, A.; Gorgoglione, A. Water-Quality Data Imputation with a High Percentage of Missing Values: A Machine Learning Approach. Sustainability 2021, 13, 6318. https://doi.org/10.3390/su13116318

1. NCCTG Lung cancer datasetSurvival in patients with advanced lung cancer from the North Central Cancer Treatment Group. Performance scores rate how well the patient can perform usual daily activities.2.CNV measurements of CNV of GBM This dataset records the information about copy number variation of Glioblastoma (GBM).Abstract:In biology and medicine, conservative patient and data collection malpractice can lead to missing or incorrect values in patient registries, which can affect both diagnosis and prognosis. Insufficient or biased patient information significantly impedes the sensitivity and accuracy of predicting cancer survival. In bioinformatics, making a best guess of the missing values and identifying the incorrect values are collectively called “imputation”. Existing imputation methods work by establishing a model based on the data mechanism of the missing values. Existing imputation methods work well under two assumptions: 1) the data is missing completely at random, and 2) the percentage of missing values is not high. These are not cases found in biomedical datasets, such as the Cancer Genome Atlas Glioblastoma Copy-Number Variant dataset (TCGA: 108 columns), or the North Central Cancer Treatment Group Lung Cancer (NCCTG) dataset (NCCTG: 9 columns). We tested six existing imputation methods, but only two of them worked with these datasets: The Last Observation Carried Forward (LOCF) and K-nearest Algorithm (KNN). Predictive Mean Matching (PMM) and Classification and Regression Trees (CART) worked only with the NCCTG lung cancer dataset with fewer columns, except when the dataset contains 45% missing data. The quality of the imputed values using existing methods is bad because they do not meet the two assumptions.In our study, we propose a Restricted Boltzmann Machine (RBM)-based imputation method to cope with low randomness and the high percentage of the missing values. RBM is an undirected, probabilistic and parameterized two-layer neural network model, which is often used for extracting abstract information from data, especially for high-dimensional data with unknown or non-standard distributions. In our benchmarks, we applied our method to two cancer datasets: 1) NCCTG, and 2) TCGA. The running time, root mean squared error (RMSE) of the different methods were gauged. The benchmarks for the NCCTG dataset show that our method performs better than other methods when there is 5% missing data in the dataset, with 4.64 RMSE lower than the best KNN. For the TCGA dataset, our method achieved 0.78 RMSE lower than the best KNN.In addition to imputation, RBM can achieve simultaneous predictions. We compared the RBM model with four traditional prediction methods. The running time and area under the curve (AUC) were measured to evaluate the performance. Our RBM-based approach outperformed traditional methods. Specifically, the AUC was up to 19.8% higher than the multivariate logistic regression model in the NCCTG lung cancer dataset, and the AUC was higher than the Cox proportional hazard regression model, with 28.1% in the TCGA dataset.Apart from imputation and prediction, RBM models can detect outliers in one pass by allowing the reconstruction of all the inputs in the visible layer with in a single backward pass. Our results show that RBM models have achieved higher precision and recall on detecting outliers than other methods.

Replication and simulation reproduction materials for the article "The MIDAS Touch: Accurate and Scalable Missing-Data Imputation with Deep Learning." Please see the README file for a summary of the contents and the Replication Guide for a more detailed description. Article abstract: Principled methods for analyzing missing values, based chiefly on multiple imputation, have become increasingly popular yet can struggle to handle the kinds of large and complex data that are also becoming common. We propose an accurate, fast, and scalable approach to multiple imputation, which we call MIDAS (Multiple Imputation with Denoising Autoencoders). MIDAS employs a class of unsupervised neural networks known as denoising autoencoders, which are designed to reduce dimensionality by corrupting and attempting to reconstruct a subset of data. We repurpose denoising autoencoders for multiple imputation by treating missing values as an additional portion of corrupted data and drawing imputations from a model trained to minimize the reconstruction error on the originally observed portion. Systematic tests on simulated as well as real social science data, together with an applied example involving a large-scale electoral survey, illustrate MIDAS's accuracy and efficiency across a range of settings. We provide open-source software for implementing MIDAS.

Multiple imputation (MI) is effectively used to deal with missing data when the missing mechanism is missing at random. However, MI may not be effective when the missing mechanism is not missing at random (NMAR). In such cases, additional information is required to obtain an appropriate imputation. Pham et al. (2019) proposed the calibrated-δ adjustment method, which is a multiple imputation method using population information. It provides appropriate imputation in two NMAR settings. However, the calibrated-δ adjustment method has two problems. First, it can be used only when one variable has missing values. Second, the theoretical properties of the variance estimator have not been provided. This article proposes a multiple imputation method using population information that can be applied when several variables have missing values. The proposed method is proven to include the calibrated-δ adjustment method. It is shown that the proposed method provides a consistent estimator for the parameter of the imputation model in an NMAR situation. The asymptotic variance of the estimator obtained by the proposed method and its estimator are also given.

Missing values are a notable challenge when analyzing mass spectrometry-based proteomics data. While the field is still actively debating the best practices, the challenge increased with the emergence of mass spectrometry-based single-cell proteomics and the dramatic increase in missing values. A popular approach to deal with missing values is to perform imputation. Imputation has several drawbacks for which alternatives exist, but currently, imputation is still a practical solution widely adopted in single-cell proteomics data analysis. This perspective discusses the advantages and drawbacks of imputation. We also highlight 5 main challenges linked to missing value management in single-cell proteomics. Future developments should aim to solve these challenges, whether it is through imputation or data modeling. The perspective concludes with recommendations for reporting missing values, for reporting methods that deal with missing values, and for proper encoding of missing values.

Fossil-based estimates of diversity and evolutionary dynamics mainly rely on the study of morphological variation. Unfortunately, organism remains are often altered by post-mortem taphonomic processes such as weathering or distortion. Such a loss of information often prevents quantitative multivariate description and statistically controlled comparisons of extinct species based on morphometric data. A common way to deal with missing data involves imputation methods that directly fill the missing cases with model estimates. Over the last several years, several empirically determined thresholds for the maximum acceptable proportion of missing values have been proposed in the literature, whereas other studies showed that this limit actually depends on several properties of the study dataset and of the selected imputation method, and is by no way generalizable. We evaluate the relative performances of seven multiple imputation techniques through a simulation-based analysis under three distinct patterns of missing data distribution. Overall, Fully Conditional Specification and Expectation-Maximization algorithms provide the best compromises between imputation accuracy and coverage probability. Multiple imputation (MI) techniques appear remarkably robust to the violation of basic assumptions such as the occurrence of taxonomically or anatomically biased patterns of missing data distribution, making differences in simulation results between the three patterns of missing data distribution much smaller than differences between the individual MI techniques. Based on these results, rather than proposing a new (set of) threshold value(s), we develop an approach combining the use of multiple imputations with procrustean superimposition of principal component analysis results, in order to directly visualize the effect of individual missing data imputation on an ordinated space. We provide an R function for users to implement the proposed procedure.

Missing values in proteomic data sets have real consequences on downstream data analysis and reproducibility. Although several imputation methods exist to handle missing values, no single imputation method is best suited for a diverse range of data sets, and no clear strategy exists for evaluating imputation methods for clinical DIA-MS data sets, especially at different levels of protein quantification. To navigate through the different imputation strategies available in the literature, we have established a strategy to assess imputation methods on clinical label-free DIA-MS data sets. We used three DIA-MS data sets with real missing values to evaluate eight imputation methods with multiple parameters at different levels of protein quantification: a dilution series data set, a small pilot data set, and a clinical proteomic data set comparing paired tumor and stroma tissue. We found that imputation methods based on local structures within the data, like local least-squares (LLS) and random forest (RF), worked well in our dilution series data set, whereas imputation methods based on global structures within the data, like BPCA, performed well in the other two data sets. We also found that imputation at the most basic protein quantification levelfragment levelimproved accuracy and the number of proteins quantified. With this analytical framework, we quickly and cost-effectively evaluated different imputation methods using two smaller complementary data sets to narrow down to the larger proteomic data set’s most accurate methods. This acquisition strategy allowed us to provide reproducible evidence of the accuracy of the imputation method, even in the absence of a ground truth. Overall, this study indicates that the most suitable imputation method relies on the overall structure of the data set and provides an example of an analytic framework that may assist in identifying the most appropriate imputation strategies for the differential analysis of proteins.

How to deal w_ missing input data

This repository contains the models, configs, and results files for the paper Gauch et al., "How to deal w_ missing input data".

The corresponding analysis code is available on GitHub: https://github.com/gauchm/missing-inputs.

Contents of this repository

missing-inputs.ipynb -- Jupyter notebook to reproduce figures from the paper.

results/ -- Folder with model weights, configs, and predictions used in missing-inputs.ipynb.

patches/ -- Contains patches for local modifications to reproduce experiments from the paper.

Required setup

Clone neuralhydrology: git clone https://github.com/neuralhydrology/neuralhydrology.git.

Install an editable version of neuralhydrology: cd neuralhydrology && pip install -e ..

Download the following data:

the CAMELS US dataset (CAMELS time series meteorology, observed flow, meta data, version 1.2) from NCAR into some data directory (has to match data_dir in the config files).

the extended Maurer and NLDAS forcings set available on HydroShare: Maurer, NLDAS.

the models, results, and config files from this paper avaliable on this Zenodo repository.

Note that to reproduce the experiments, local modifications to NeuralHydrology are necessary. To do so, apply the patches in the patches/ directory: git apply patches/experiment-N.patch.

Abstract: Given the methodological sophistication of the debate over the “political resource curse”—the purported negative relationship between natural resource wealth (in particular oil wealth) and democracy—it is surprising that scholars have not paid more attention to the basic statistical issue of how to deal with missing data. This article highlights the problems caused by the most common strategy for analyzing missing data in the political resource curse literature—listwise deletion—and investigates how addressing such problems through the best-practice technique of multiple imputation affects empirical results. I find that multiple imputation causes the results of a number of influential recent studies to converge on a key common finding: A political resource curse does exist, but only since the widespread nationalization of petroleum industries in the 1970s. This striking finding suggests that much of the controversy over the political resource curse has been caused by a neglect of missing-data issues.

Penalized regression methods are used in many biomedical applications for variable selection and simultaneous coefficient estimation. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors. This article considers a general class of penalized objective functions which, by construction, force selection of the same variables across imputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as “stacked” and “grouped” objective functions. Building on existing work, we (i) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for continuous and binary outcome data, (ii) incorporate adaptive shrinkage penalties, (iii) compare these methods through simulation, and (iv) develop an R package miselect. Simulations demonstrate that the “stacked” approaches are more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Biorepository aiming to identify the association between environmental pollutants and ALS risk. Supplementary materials for this article are available online.

Modern high-dimensional statistical inference often faces the problem of missing data. In recent decades, many studies have focused on this topic and provided strategies including complete-sample analysis and imputation procedures. However, complete-sample analysis discards information of incomplete samples, while imputation procedures have accumulative errors from each single imputation. In this paper, we propose a new method, Sample-wise COmbined missing effect Model with penalization (SCOM), to deal with missing data occurring in predictors. Instead of imputing the predictors, SCOM estimates the combined effect caused by all missing data for each incomplete sample. SCOM makes full use of all available data. It is robust with respect to various missing mechanisms. Theoretical studies show the oracle inequality for the proposed estimator, and the consistency of variable selection and combined missing effect selection. Simulation studies and an application to the Residential Building Data also illustrate the effectiveness of the proposed SCOM.

Multivariate data are typically represented by a rectangular matrix (table) in which the rows are the objects (cases) and the columns are the variables (measurements). When there are many variables one often reduces the dimension by principal component analysis (PCA), which in its basic form is not robust to outliers. Much research has focused on handling rowwise outliers, that is, rows that deviate from the majority of the rows in the data (e.g., they might belong to a different population). In recent years also cellwise outliers are receiving attention. These are suspicious cells (entries) that can occur anywhere in the table. Even a relatively small proportion of outlying cells can contaminate over half the rows, which causes rowwise robust methods to break down. In this article, a new PCA method is constructed which combines the strengths of two existing robust methods to be robust against both cellwise and rowwise outliers. At the same time, the algorithm can cope with missing values. As of yet it is the only PCA method that can deal with all three problems simultaneously. Its name MacroPCA stands for PCA allowing for Missingness And Cellwise & Rowwise Outliers. Several simulations and real datasets illustrate its robustness. New residual maps are introduced, which help to determine which variables are responsible for the outlying behavior. The method is well-suited for online process control.

Applications of modern methods for analyzing data with missing values, based primarily on multiple imputation, have in the last half-decade become common in American politics and political behavior. Scholars in these fields have thus increasingly avoided the biases and inefficiencies caused by ad hoc methods like listwise deletion and best guess imputation. However, researchers in much of comparative politics and international relations, and others with similar data, have been unable to do the same because the best available imputation methods work poorly with the time-series cross-section data structures common in these fields. We attempt to rectify this situation. First, we build a multiple i mputation model that allows smooth time trends, shifts across cross-sectional units, and correlations over time and space, resulting in far more accurate imputations. Second, we build nonignorable missingness models by enabling analysts to incorporate knowledge from area studies experts via priors on individual missing cell values, rather than on difficult-to-interpret model parameters. Third, since these tasks could not be accomplished within existing imputation algorithms, in that they cannot handle as many variables as needed even in the simpler cross-sectional data for which they were designed, we also develop a new algorithm that substantially expands the range of computationally feasible data types and sizes for which multiple imputation can be used. These developments also made it possible to implement the methods introduced here in freely available open source software that is considerably more reliable than existing strategies. These developments also made it possible to implement the methods introduced here in freely available open source software, Amelia II: A Program for Missing Data, that is considerably more reliable than existing strategies. See also: Missing Data

Electronic health records (EHRs) have been widely adopted in recent years, but often include a high proportion of missing data, which can create difficulties in implementing machine learning and other tools of personalized medicine. Completed datasets are preferred for a number of analysis methods, and successful imputation of missing EHR data can improve interpretation and increase our power to predict health outcomes. However, use of the most popular imputation methods mainly require scripting skills, and are implemented using various packages and syntax. Thus, the implementation of a full suite of methods is generally out of reach to all except experienced data scientists. Moreover, imputation is often considered as a separate exercise from exploratory data analysis, but should be considered as art of the data exploration process. We have created a new graphical tool, ImputEHR, that is based on a Python base and allows implementation of a range of simple and sophisticated (e.g., gradient-boosted tree-based and neural network) data imputation approaches. In addition to imputation, the tool enables data exploration for informed decision-making, as well as implementing machine learning prediction tools for response data selected by the user. Although the approach works for any missing data problem, the tool is primarily motivated by problems encountered for EHR and other biomedical data. We illustrate the tool using multiple real datasets, providing performance measures of imputation and downstream predictive analysis.

The data set corresponds the data presented in the data paper : “How to use scale invariant properties of imperviousness in urban areas to handle missing data ?“ which has been submitted to Water Resources Research ” (https://agupubs.onlinelibrary.wiley.com/journal/19447973).

It corresponds to :

- the rainfall data collected on 2019-06-02 with 5 min and 30 s time steps by a disdrometer installed on the roof of Ecole des Ponts ParisTech building.

- land use distribution for the Jouy-en-Josas catchment (1 = forest, 2= road, 3=Grass, 4=building, 5=Gully, 6=missing data), with pixel size of 10 m and 2 m.

More details can be found in the file and in the paper.

Dozens of missing epochs in the monthly gravity product of the satellite mission Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) mission greatly inhibit the complete analysis and full utilization of the data. Despite previous attempts to handle this problem, a general all-purpose gap-filling solution is still lacking. Here we propose a non-parametric, data-adaptive and easy-to-implement approach - composed of the Singular Spectrum Analysis (SSA) gap-filling technique, cross-validation, and spectral testing for significant components - to produce reasonable gap-filling results in the form of spherical harmonic coefficients (SHCs). We demonstrate that this approach is adept at inferring missing data from long-term and oscillatory changes extracted from available observations. A comparison in the spectral domain reveals that the gap-filling result resembles the product of GRACE missions below spherical harmonic degree 30 very well. As the degree increases above 30, the amplitude per degree of the gap-filling result decreases more rapidly than that of GRACE/GRACE-FO SHCs, showing effective suppression of noise. As a result, our approach can reduce noise in the oceans without sacrificing resolutions on land. The gap filling dataset is stored in the “SSA_filing/" folder. Each file represents a monthly result in the form of spherical harmonics. The data format follows the convention of the site ftp://isdcftp.gfz-potsdam.de/grace/. Low degree corrections (degree-1, C20, C30) have been made. The code to generate the dataset is located in the “code_share/“ folder, with an example for C30. The model-based Greenland mass balance result for data validation (results given in the paper) is provided in the "Greenland_SMB-D.txt” file.

The integration of proteomic datasets, generated by non-cooperating laboratories using different LC-MS/MS setups can overcome limitations in statistically underpowered sample cohorts but has not been demonstrated to this day. In proteomics, differences in sample preservation and preparation strategies, chromatography and mass spectrometry approaches and the used quantification strategy distort protein abundance distributions in integrated datasets. The Removal of these technical batch effects requires setup-specific normalization and strategies that can deal with missing at random (MAR) and missing not at random (MNAR) type values at a time. Algorithms for batch effect removal, such as the ComBat-algorithm, commonly used for other omics types, disregard proteins with MNAR missing values and reduce the informational yield and the effect size for combined datasets significantly. Here, we present a strategy for data harmonization across different tissue preservation techniques, LC-MS/MS instrumentation setups and quantification approaches. To enable batch effect removal without the need for data reduction or error-prone imputation we developed an extension to the ComBat algorithm, ´ComBat HarmonizR, that performs data harmonization with appropriate handling of MAR and MNAR missing values by matrix dissection The ComBat HarmonizR based strategy enables the combined analysis of independently generated proteomic datasets for the first time. Furthermore, we found ComBat HarmonizR to be superior for removing batch effects between different Tandem Mass Tag (TMT)-plexes, compared to commonly used internal reference scaling (iRS). Due to the matrix dissection approach without the need of data imputation, the HarmonizR algorithm can be applied to any type of -omics data while assuring minimal data loss

Missing data is a prevalent problem that requires attention, as most data analysis techniques are unable to handle it. This is particularly critical in Multi-Label Classification (MLC), where only a few studies have investigated missing data in this application domain. MLC differs from Single-Label Classification (SLC) by allowing an instance to be associated with multiple classes. Movie classification is a didactic example since it can be “drama” and “bibliography” simultaneously. One of the most usual missing data treatment methods is data imputation, which seeks plausible values to fill in the missing ones. In this scenario, we propose a novel imputation method based on a multi-objective genetic algorithm for optimizing multiple data imputations called Multiple Imputation of Multi-label Classification data with a genetic algorithm, or simply EvoImp. We applied the proposed method in multi-label learning and evaluated its performance using six synthetic databases, considering various missing values distribution scenarios. The method was compared with other state-of-the-art imputation strategies, such as K-Means Imputation (KMI) and weighted K-Nearest Neighbors Imputation (WKNNI). The results proved that the proposed method outperformed the baseline in all the scenarios by achieving the best evaluation measures considering the Exact Match, Accuracy, and Hamming Loss. The superior results were constant in different dataset domains and sizes, demonstrating the EvoImp robustness. Thus, EvoImp represents a feasible solution to missing data treatment for multi-label learning.

The dataset is provided in a single .xlsx file named "eucalyptus_growth_environment_data_V2.xlsx" and consists of fifteen sheets:

Codebook: This sheet details the index, values, and descriptions for each field within the dataset, providing a comprehensive guide to understanding the data structure.

ALL NODES: Contains measurements from all devices, totalling 102,916 data points. This sheet aggregates the data across all nodes.

GWD1 to GWD10: These subset sheets include measurements from individual nodes, labelled according to the abbreviation “Generic Wireless Dendrometer” followed by device IDs 1 through 10. Each sheet corresponds to a specific node, representing measurements from ten trees (or nodes).

Metadata: Provides detailed metadata for each node, including species, initial diameter, location, measurement frequency, battery specifications, and irrigation status. This information is essential for identifying and differentiating the nodes and their specific attributes.

Missing Data Intervals: Details gaps in the data stream, including start and end dates and times when data was not uploaded. It includes information on the total duration of each missing interval and the number of missing data points.

Missing Intervals Distribution: Offers a summary of missing data intervals and their distribution, providing insight into data gaps and reasons for missing data.

All nodes utilize LoRaWAN for data transmission. Please note that intermittent data gaps may occur due to connectivity issues between the gateway and the nodes, as well as maintenance activities or experimental procedures.

Software considerations: The provided R code named “Simple_Dendro_Imputation_and_Analysis.R” is a comprehensive analysis workflow that processes and analyses Eucalyptus growth and environmental data from the "eucalyptus_growth_environment_data_V2.xlsx" dataset. The script begins by loading necessary libraries, setting the working directory, and reading the data from the specified Excel sheet. It then combines date and time information into a unified DateTime format and performs data type conversions for relevant columns. The analysis focuses on a specified device, allowing for the selection of neighbouring devices for imputation of missing data. A loop checks for gaps in the time series and fills in missing intervals based on a defined threshold, followed by a function that imputes missing values using the average from nearby devices. Outliers are identified and managed through linear interpolation. The code further calculates vapor pressure metrics and applies temperature corrections to the dendrometer data. Finally, it saves the cleaned and processed data into a new Excel file while conducting dendrometer analysis using the dendRoAnalyst package, which includes visualizations and calculations of daily growth metrics and correlations with environmental factors such as vapour pressure deficit (VPD).