Imputation Model Research Articles

Attention-based generative adversarial networks for aquaponics environment time series data imputation

Environmental parameter data collected by sensors for monitoring the environment of agricultural facility operations are usually incomplete due to external environmental disturbances and device failures. And the missing of collected data is completely at random. In practice, missing data could create biased estimations and make multivariate time series predictions of environmental parameters difficult, leading to imprecise environmental control. A multivariate time series imputation model based on generative adversarial networks and multi-head attention (ATTN-GAN) is proposed in this work to reducing the negative consequence of missing data. ATTN-GAN can capture the temporal and spatial correlation of time series, and has a good capacity to learn data distribution. In the downstream experiments, we used ATTN-GAN and baseline models for data imputation, and predicted the imputed data, respectively. For the imputation of missing data, over the 20%, 50% and 80% missing rate, ATTN-GAN had the lowest RMSE, 0.1593, 0.2012 and 0.2688 respectively. For water temperature prediction, data processed with ATTN-GAN over MLP, LSTM, DA-RNN prediction methods had the lowest MSE, 0.6816, 0.8375 and 0.3736 respectively. Those results revealed that ATTN-GAN outperformed all baseline models in terms of data imputation accuracy. The data processed by ATTN-GAN is the best for time series prediction.

Phylosem: A fast and simple R package for phylogenetic inference and trait imputation using phylogenetic structural equation models.

Phylogenetic comparative methods (PCMs) can be used to study evolutionary relationships and trade-offs among species traits. Analysts using PCM may want to (1) include latent variables, (2) estimate complex trait interdependencies, (3) predict missing trait values, (4) condition predicted traits upon phylogenetic correlations and (5) estimate relationships as slope parameters that can be compared with alternative regression methods. The Comprehensive R Archive Network (CRAN) includes well-documented software for phylogenetic linear models (phylolm), phylogenetic path analysis (phylopath), phylogenetic trait imputation (Rphylopars) and structural equation models (sem), but none of these can simultaneously accomplish all five analytical goals. We therefore introduce a new package phylosem for phylogenetic structural equation models (PSEM) and summarize features and interface. We also describe new analytical options, where users can specify any combination of Ornstein-Uhlenbeck, Pagel's-δ and Pagel's-λ transformations for species covariance. For the first time, we show that PSEM exactly reproduces estimates (and standard errors) for simplified cases that are feasible in sem, phylopath, phylolm and Rphylopars and demonstrate the approach by replicating a well-known case study involving trade-offs in plant energy budgets.

Comparison of the performance of multiple imputation models in filling gaps in hourly and daily meteorological series from two locations in the state of São Paulo-Brazil

Comparison of the performance of multiple imputation models in filling gaps in hourly and daily meteorological series from two locations in the state of São Paulo-Brazil

Robust analyzes for longitudinal clinical trials with missing and non-normal continuous outcomes

Missing data are unavoidable in longitudinal clinical trials, and outcomes are not always normally distributed. In the presence of outliers or heavy-tailed distributions, the conventional multiple imputation with the mixed model with repeated measures analysis of the average treatment effect (ATE) based on the multivariate normal assumption may produce bias and power loss. Control-based imputation (CBI) is an approach for evaluating the treatment effect under the assumption that participants in both the test and control groups with missing outcome data have a similar outcome profile as those with an identical history in the control group. We develop a robust framework to handle non-normal outcomes under CBI without imposing any parametric modeling assumptions. Under the proposed framework, sequential weighted robust regressions are applied to protect the constructed imputation model against non-normality in the covariates and the response variables. Accompanied by the subsequent mean imputation and robust model analysis, the resulting ATE estimator has good theoretical properties in terms of consistency and asymptotic normality. Moreover, our proposed method guarantees the analysis model robustness of the ATE estimation in the sense that its asymptotic results remain intact even when the analysis model is misspecified. The superiority of the proposed robust method is demonstrated by comprehensive simulation studies and an AIDS clinical trial data application.

Logistic regression vs. predictive mean matching for imputing binary covariates.

Multivariate imputation using chained equations (MICE) is a popular algorithm for imputing missing data that entails specifying multivariate models through conditional distributions. For imputing missing continuous variables, two common imputation methods are the use of parametric imputation using a linear model and predictive mean matching. When imputing missing binary variables, the default approach is parametric imputation using a logistic regression model. In the R implementation of MICE, the use of predictive mean matching can be substantially faster than using logistic regression as the imputation model for missing binary variables. However, there is a paucity of research into the statistical performance of predictive mean matching for imputing missing binary variables. Our objective was to compare the statistical performance of predictive mean matching with that of logistic regression for imputing missing binary variables. Monte Carlo simulations were used to compare the statistical performance of predictive mean matching with that of logistic regression for imputing missing binary outcomes when the analysis model of scientific interest was a multivariable logistic regression model. We varied the size of the analysis samples (N = 250, 500, 1,000, 5,000, and 10,000) and the prevalence of missing data (5%-50% in increments of 5%). In general, the statistical performance of predictive mean matching was virtually identical to that of logistic regression for imputing missing binary variables when the analysis model was a logistic regression model. This was true across a wide range of scenarios defined by sample size and the prevalence of missing data. In conclusion, predictive mean matching can be used to impute missing binary variables. The use of predictive mean matching to impute missing binary variables can result in a substantial reduction in computer processing time when conducting simulations of multiple imputation.

Epidemiological Modeling of the Impact of Public Health Policies on Hepatitis C: Protocol for a Gamification Tool Targeting Microelimination.

Hepatitis C is a disease with a strong social component, as its main transmission route is via blood, making it associated with lifestyle. Therefore, it is suitable to be worked on from the perspective of public health policy, which still has a lot of room to explore and improve, contrary to diagnoses and treatments, which are already very refined and effective. An interactive gamified policy tool, designated as Let's End HepC (LEHC), was created to understand the impact of policies related to hepatitis C on the disease's epidemiology on a yearly basis until 2030. To this end, an innovative epidemiological model was developed, integrating Markov chains to model the natural history of the disease and adaptive conjoint analysis to reflect the degree of application of each of the 24 public health policies included in the model. This double imputation model makes it possible to assess a set of indicators such as liver transplant, incidence, and deaths year by year until 2030 in different risk groups. Populations at a higher risk were integrated into the model to understand the specific epidemiological dynamics within the total population of each country and within segments that comprise people who have received blood products, prisoners, people who inject drugs, people infected through vertical transmission, and the remaining population. The model has already been applied to a group of countries, and studies in 5 of these countries have already been concluded, showing results very close to those obtained through other forms of evaluation. The LEHC model allows the simulation of different degrees of implementation of each policy and thus the verification of its epidemiological impact on each studied population. The gamification feature allows assessing the adequate fulfillment of the World Health Organization goals for the elimination of hepatitis C by 2030. LEHC supports health decision makers and people who practice patient advocacy in making decisions based on science, and because LEHC is democratically shared, it ends up contributing to the increase of citizenship in health. RR1-10.2196/38521.

Semantic understanding and prompt engineering for large-scale traffic data imputation

Intelligent Transportation Systems (ITS) face the formidable challenge of large-scale missing data, particularly in the imputation of traffic data. Existing studies have mainly relied on modeling network-level spatiotemporal correlations to address this issue. However, these methods often overlook the rich semantic information (e.g., road infrastructure, sensor location, etc.) inherent in road networks when capturing network-wide spatiotemporal correlations. We address this limitation by presenting the Graph Transformer-based Traffic Data Imputation (GT-TDI) model, which imputes missing values in extensive traffic data by leveraging spatiotemporal semantic understanding of road networks. The proposed model leverages semantic descriptions that capture the spatial and temporal dynamics of traffic across road networks, enhancing its capacity to infer comprehensive spatiotemporal relationships. Moreover, to augment the model’s capabilities, we employ a Large Language Model (LLM) and prompt engineering to enable natural and intuitive interactions with the traffic data imputation system, allowing users to query and request in plain language, without requiring expert knowledge or complex mathematical models. The proposed model, GT-TDI, utilizes Graph Neural Networks (GNN) and Transformer architectures to perform large-scale traffic data imputation using deficient observations, sensor social connectivity, and semantic descriptions as inputs. We evaluate the GT-TDI model on the PeMS freeway dataset and benchmark it against cutting-edge models. The experimental evidence demonstrates that GT-TDI surpasses the cutting-edge approaches in scenarios with intricate patterns and varying rates of missing data.

Multiple-Model-based Robust Estimation of Causal Treatment Effect on a Binary Outcome with Integrated Information from Secondary Outcomes

– An assessment of the causal treatment effect in the development and progression of certain diseases is important in clinical trials and biomedical studies. However, it is not possible to infer a causal relationship when the treatment assignment is imbalanced and confounded by other mechanisms. Specifically, when the treatment assignment is not randomized and the primary outcome is binary, a conventional logistic regression may not be valid to elucidate any causal inference. Moreover, exclusively capturing all confounders is extremely difficult and even impossible in large-scale observational studies. We propose a multiple-model-based robust (MultiMR) estimator for estimating the causal effect with a binary outcome, where multiple propensity score models and conditional mean imputation models are used to ensure estimation robustness. Furthermore, we propose an enhanced MultiMR (eMultiMR) estimator that reduces the estimation variability of MultiMR estimates by incorporating secondary outcomes that are highly correlated with the primary binary outcome. The resulting estimates are less sensitive to model mis-specification compared to those based on state-of-the-art doubly-robust methods. These estimates are verified through both theoretical and numerical assessments. The utility of (e)MultiMR estimation is illustrated using the Uniform Data Set (UDS) from the National Alzheimer’s Coordinating Center with the objective of detecting the causal effect of the short-term use of antihypertensive medications on the development of dementia or mild cognitive impairment. The proposed method has been implemented in an R package and is available at https://github.com/chencxxy28/eMultiMR.

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 confidence-valid 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.

Multiple imputation of missing data under missing at random: including a collider as an auxiliary variable in the imputation model can induce bias.

Epidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). In MI, in addition to those required for the substantive analysis, imputation models often include other variables ("auxiliary variables"). Auxiliary variables that predict the partially observed variables can reduce the standard error (SE) of the MI estimator and, if they also predict the probability that data are missing, reduce bias due to data being missing not at random. However, guidance for choosing auxiliary variables is lacking. We examine the consequences of a poorly chosen auxiliary variable: if it shares a common cause with the partially observed variable and the probability that it is missing (i.e., it is a "collider"), its inclusion can induce bias in the MI estimator and may increase the SE. We quantify, both algebraically and by simulation, the magnitude of bias and SE when either the exposure or outcome is incomplete. When the substantive analysis outcome is partially observed, the bias can be substantial, relative to the magnitude of the exposure coefficient. In settings in which a complete records analysis is valid, the bias is smaller when the exposure is partially observed. However, bias can be larger if the outcome also causes missingness in the exposure. When using MI, it is important to examine, through a combination of data exploration and considering plausible casual diagrams and missingness mechanisms, whether potential auxiliary variables are colliders.

Racial differences in patient-reported outcomes among men treated with radical prostatectomy for prostate cancer.

Real-world data on racial differences in the side effects of radical prostatectomy on quality of life (QoL) are lacking. We aimed to evaluate differences in patient-reported outcome measure (PROM) among non-Hispanic Black (NHB) and non-Hispanic White (NHW) men using the Expanded Prostate Cancer Index Composite for Clinical Practice (EPIC-CP) questionnaire to measure health-related QoL after radical prostatectomy. We retrospectively assessed prospectively collected PROMs using EPIC-CP scores at a tertiary care center between 2015 and 2021 for men with prostate cancer undergoing radical prostatectomy. The primary endpoint was the overall QoL score for NHB and NHW men, with a total score of 60 and higher scores indicating worse QoL. An imputed mixed linear regression model was used to examine the effect of covariates on the change in overall QoL score following surgery. A pairwise comparison was used to estimate the mean QoL scores before surgery as well as up to 24 months after surgery. Our cohort consisted of 2229 men who answered at least one EPIC-CP questionnaire before or after surgery, of which 110 (4.94%) were NHB and 2119 (95.07%) were NHW men. The QoL scores differed for NHB and NHW at baseline (2.34, 95% confidence interval [CI] 0.36-4.31, p = 0.02), 3 months (4.36, 95% CI 2.29-6.42, p < 0.01), 6 months (3.26, 95% CI 1.10-5.43, p < 0.01), and 12 months after surgery (2.48, 95% CI 0.19-4.77, p = 0.03) with NHB having worse scores. There was no difference in QoL between NHB and NHW men 24 months after surgery. A significant difference in QoL between NHB and NHW men was reported before surgery, 3, 6, and 12 months after surgery, with NHB having worse QoL scores. However, there was no long-term difference in reported QoL. Our findings inform strategies that can be implemented to mitigate racial differences in short-term outcomes.

Filling time-series gaps using image techniques: Multidimensional context autoencoder approach for building energy data imputation

Building energy prediction and management has become increasingly important in recent decades, driven by the growth of Internet of Things (IoT) devices and the availability of more energy data. However, energy data is often collected from multiple sources and can be incomplete or inconsistent, which can hinder accurate predictions and management of energy systems and limit the usefulness of the data for decision-making and research. To address this issue, past studies have focused on imputing missing gaps in energy data, including random and continuous gaps. One of the main challenges in this area is the lack of validation on a benchmark dataset with various building and meter types, making it difficult to accurately evaluate the performance of different imputation methods. Another challenge is the lack of application of state-of-the-art imputation methods for missing gaps in energy data. Contemporary image-inpainting methods, such as Partial Convolution (PConv), have been widely used in the computer vision domain and have demonstrated their effectiveness in dealing with complex missing patterns. Given that energy data often exhibits regular daily or weekly patterns, such methods could be leveraged to exploit the regularity of the data to learn underlying patterns and generate more accurate predictions for missing values. To study whether energy data imputation can benefit from the image-based deep learning method, this study compared PConv, Convolutional neural networks (CNNs), and weekly persistence method using one of the biggest publicly available whole building energy datasets, consisting of 1479 power meters worldwide, as the benchmark. The results show that, compared to the CNN with the raw time series (1D-CNN) and the weekly persistence method, neural network models with reshaped energy data with two dimensions reduced the Mean Squared Error (MSE) by 10% to 30%. The advanced deep learning method, Partial convolution (PConv), has further reduced the MSE by 20%–30% than 2D-CNN and stands out among all models. Based on these results, this study demonstrates the potential applicability of time-series imaging in imputing energy data. The proposed imputation model has also been tested on a benchmark dataset with a range of meter types and sources, demonstrating its generalizability to include additional accessible energy datasets. This offers a scalable and effective solution for filling in missing energy data in both academic and industrial contexts.

Robust imputation method with context-aware voting ensemble model for management of water-quality data.

Water-quality monitoring and management are crucial for ensuring the safety and sustainability of water resources. However, missing data is a frequent problem in water-quality datasets, which can result in biased results in hydrological modeling and data analysis. While classic statistical methods and emerging machine/deep learning methods have been applied for imputing missing values, most existing studies perform well in specific missing scenarios, but not in universal scenarios. Therefore, existing imputation methods often fail to robustly impute missing values across various scenarios. To address the problem, we propose an imputation method that uses a context-aware voting-ensemble model to dynamically select optimal weights to integrate various imputation models across different missingness scenarios. For first identify the attributes of missingness scenarios that influence imputation accuracy. Then after introducing missing values in collected data according to the missingness scenarios, we measure the accuracy of various imputation models across the missingness scenarios. Weights of imputation models are optimized by estimating non-linear functions with regression model that can capture relationships between missingness scenarios and imputation accuracies of models. The final imputed value of the ensemble model for a missing scenario can be determined by multiplying each imputation model's weight by its imputed value, then summing the products. The method inherits the advantages of state-of-art imputation models, including the ability to learn long-term dependencies in time series, as well as the flexibility of using a dynamic weighting strategy to process various missingness scenarios. To validate the superiority of our method, we evaluate on real-world water-quality data from a river in South Korea. The proposed method achieves higher accuracy and lower variation of imputed values than baseline models across various missingness scenarios. Furthermore, we showed the applicability of our method to various hydrological environment by validating our method on industrial water quality dataset. This study highlights the potential value of the ensemble model with dynamic weighting in robust imputation of water-quality data.

Groundwater Level Prediction with Deep Learning Methods

The development of civilization and the preservation of environmental ecosystems are strongly dependent on water resources. Typically, an insufficient supply of surface water resources for domestic, industrial, and agricultural needs is supplemented with groundwater resources. However, groundwater is a natural resource that must accumulate over many years and cannot be recovered after a short period of recharge. Therefore, the long-term management of groundwater resources is an important issue for sustainable development. The accurate prediction of groundwater levels is the first step in evaluating total water resources and their allocation. However, in the process of data collection, data may be lost due to various factors. Filling in missing data is a main problem that any research field must address. It is well known that to maintain data integrity, one effective approach is missing value imputation (MVI). In addition, it has been demonstrated that machine learning may be a better tool. Therefore, the main purpose of this study was to utilize a generative adversarial network (GAN) that consists of a generative model and a discriminative model for imputation. Although the GAN could not capture the groundwater level endpoints in every section, the overall simulation performance was still excellent to some extent. Our results show that the GAN can improve the accuracy of water resource evaluations. In the current study, two interdisciplinary deep learning methods, univariate and Seq2val (sequence-to-value), were used for groundwater level estimation. In addition to addressing the significance of the parameter conditions, the advantages and disadvantages of these two models in hydrological simulations were also discussed and compared. Regarding parameter selection, the simulation results for univariate analysis were better than those for Seq2val analysis. Finally, univariate was employed to examine the limits of the models in long-term water level simulations. Our results suggest that the accuracy of CNNs is better, while LSTM is better for the simulation of multistep prediction. Therefore, the interdisciplinary deep learning approach may be beneficial for providing a better evaluation of water resources.

GraphCpG: imputation of single-cell methylomes based on locus-aware neighboring subgraphs.

Single-cell DNA methylation sequencing can assay DNA methylation at single-cell resolution. However, incomplete coverage compromises related downstream analyses, outlining the importance of imputation techniques. With a rising number of cell samples in recent large datasets, scalable and efficient imputation models are critical to addressing the sparsity for genome-wide analyses. We proposed a novel graph-based deep learning approach to impute methylation matrices based on locus-aware neighboring subgraphs with locus-aware encoding orienting on one cell type. Merely using the CpGs methylation matrix, the obtained GraphCpG outperforms previous methods on datasets containing more than hundreds of cells and achieves competitive performance on smaller datasets, with subgraphs of predicted sites visualized by retrievable bipartite graphs. Besides better imputation performance with increasing cell number, it significantly reduces computation time and demonstrates improvement in downstream analysis. The source code is freely available at https://github.com/yuzhong-deng/graphcpg.git.

Dual-branch cross-dimensional self-attention-based imputation model for multivariate time series

In real-world scenarios, partial information losses of multivariate time series degrade the time series analysis. Hence, the time series imputation technique has been adopted to compensate for the missing values. Existing methods focus on investigating temporal correlations, cross-variable correlations, and bidirectional dynamics of time series, and most of these methods rely on recurrent neural networks (RNNs) to capture temporal dependency. However, the RNN-based models suffer from the common problems of slow speed and high complexity when dealing with long-term dependency. While some self-attention-based models without any recurrent structures can tackle long-term dependency with parallel computing, they do not fully learn and utilize correlations across the temporal and cross-variable dimensions. To address the limitations of existing methods, we propose a novel so-called dual-branch cross-dimensional self-attention-based imputation (DCSAI) model for multivariate time series, which is capable of performing global and auxiliary cross-dimensional analyses when imputing the missing values. In particular, this model contains masked multi-head self-attention-based encoders aligned with auxiliary generators to obtain global and auxiliary correlations in two dimensions, and these correlations are then combined into one final representation through three weighted combinations. Extensive experiments are presented to show that our model performs better than other state-of-the-art benchmarkers on three real-world public datasets under various missing rates. Furthermore, ablation study results demonstrate the efficacy of each component of the model.

Revisiting the Thorny Issue of Missing Values in Single-Cell Proteomics.

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.

Differences in Use of Clinical Decision Support Tools and Implementation of Aspirin, Blood Pressure Control, Cholesterol Management, and Smoking Cessation Quality Metrics in Small Practices by Race and Sex

Practice-level evidence is needed to clarify the value of population-based clinical decision support (CDS) tools in reducing racial and sex disparities in cardiovascular care. To evaluate the association between CDS tools and racial and sex disparities in the aspirin use, blood pressure control, cholesterol management, and smoking cessation (ABCS) care quality metrics among smaller primary care practices. This cross-sectional study used practice-level data from the Agency for Healthcare Research and Quality-funded EvidenceNOW initiative. The national initiative from May 1, 2015, to April 30, 2021, spanned 12 US states and focused on improving cardiovascular preventive care by providing quality improvement support to smaller primary care practices. A total of 576 primary care practices in EvidenceNOW submitted both survey data and electronic health record (EHR)-derived ABCS data stratified by race and sex. Practice-level estimates of disparities between Black and White patients and between male and female patients were calculated as the difference in proportions of eligible patients within each practice meeting ABCS care quality metrics. The association between CDS tools (EHR prompts, standing orders, and clinical registries) and disparities was evaluated by multiply imputed multivariable models for each CDS tool, adjusted for practice rurality, ownership, and size. Across the 576 practices included in the analysis, 219 (38.0%) had patient panels that were more than half White and 327 (56.8%) had panels that were more than half women. The proportion of White compared with Black patients meeting metrics for blood pressure (difference, 5.16% [95% CI, 4.29%-6.02%]; P < .001) and cholesterol management (difference, 1.49% [95% CI, 0.04%-2.93%] P = .04) was higher; the proportion of men meeting metrics for aspirin use (difference, 4.36% [95% CI, 3.34%-5.38%]; P < .001) and cholesterol management (difference, 3.88% [95% CI, 3.14%-4.63%]; P < .001) was higher compared with women. Conversely, the proportion of women meeting practice blood pressure control (difference, -1.80% [95% CI, -2.32% to -1.28%]; P < .001) and smoking cessation counseling (difference, -1.67% [95% CI, -2.38% to -0.95%]; P < .001) metrics was higher compared with men. Use of CDS tools was not associated with differences in race or sex disparities except for the smoking metric. Practices using CDS tools showed a higher proportion of men meeting the smoking counseling metric than women (coefficient, 3.82 [95% CI, 0.95-6.68]; P = .009). The findings of this cross-sectional study suggest that practices using CDS tools had small disparities that were not statistically significant, but CDS tools were not associated with reductions in disparities. More research is needed on effective practice-level interventions to mitigate disparities.

Solving the many-variables problem in MICE with principal component regression.

Multiple Imputation (MI) is one of the most popular approaches to addressing missing values in questionnaires and surveys. MI with multivariate imputation by chained equations (MICE) allows flexible imputation of many types of data. In MICE, for each variable under imputation, the imputer needs to specify which variables should act as predictors in the imputation model. The selection of these predictors is a difficult, but fundamental, step in the MI procedure, especially when there are many variables in a data set. In this project, we explore the use of principal component regression (PCR) as a univariate imputation method in the MICE algorithm to automatically address the many-variables problem that arises when imputing large social science data. We compare different implementations of PCR-based MICE with a correlation-thresholding strategy through two Monte Carlo simulation studies and a case study. We find the use of PCR on a variable-by-variable basis to perform best and that it can perform closely to expertly designed imputation procedures.

Comparative assessment of univariate and multivariate imputation models for varying lengths of missing rainfall data in a humid tropical region: a case study of Kozhikode, Kerala, India

Comparative assessment of univariate and multivariate imputation models for varying lengths of missing rainfall data in a humid tropical region: a case study of Kozhikode, Kerala, India