Continuous Response Variables Research Articles

Bayesian inference for multivariate probit model with latent envelope.

The response envelope model proposed by Cook etal. (2010) is an efficient method to estimate the regression coefficient under the context of the multivariate linear regression model. It improves estimation efficiency by identifying material and immaterial parts of responses and removing the immaterial variation. The response envelope model has been investigated only for continuous response variables. In this paper, we propose the multivariate probit model with latent envelope, in short, the probit envelope model, as a response envelope model for multivariate binary response variables. The probit envelope model takes into account relations between Gaussian latent variables of the multivariate probit model by using the idea of the response envelope model. We address the identifiability of the probit envelope model by employing the essential identifiability concept and suggest a Bayesian method for the parameter estimation. We illustrate the probit envelope model via simulation studies and real-data analysis. The simulation studies show that the probit envelope model has the potential to gain efficiency in estimation compared to the multivariate probit model. The real data analysis shows that the probit envelope model is useful for multi-label classification.

Comparison of the C5.0 Algorithm and the CART Algorithm in Stroke Classification

The C5.0 and CART algorithms are similar in terms of velocity and handling of categorical and numeric type data. However, these two algorithms are differences in terms the CART algorithm is binary and classifies categorical, numerical and continuous response variables resulting in classification and regression decision trees. Meanwhile, the C5.0 algorithm is non-binary and classifies categorical response variables resulting in a classification tree. This research aims to classify the Kaggle’s Stroke Prediction Dataset to find out the variables that most influence the risk of stroke, as well as to compare the results of the classification accuracy of the both algorithms. The results of the study showed that CART algorithm has a higher value of accuracy and precision, but its recall value is lower than C5.0. The accuracy value of each algorithm is 77.9% and 77.5%, presision is 89.5% and 83.2%, recall is 67% and 71.4%. Overrall, it can be concluded that there is no difference in classification between the two algorithm. Beside that, in the CART there were 3 variables that most influence on stroke risk, they are age, BMI, and average blood glucose levels. Meanwhile, in C5.0 only 2 variable that most influence, there are age and average blood glucose levels.

A framework for block-wise missing data in multi-omics.

High-throughput technologies have generated vast amounts of omic data. It is a consensus that the integration of diverse omics sources improves predictive models and biomarker discovery. However, managing multiple omics data poses challenges such as data heterogeneity, noise, high-dimensionality and missing data, especially in block-wise patterns. This study addresses the challenges of high dimensionality and block-wise missing data through a regularization and constrained-based approach. The methodology is implemented in the R package bwm for binary and continuous response variables, and applied to breast cancer and exposome multi-omics datasets, achieving strong performance even in scenarios with missing data present in all omics. In binary classification task, our proposed model achieves accuracy in the range of 86% to 92%, and F1 in the range of 68% to 79%. And, in regression task the correlation between true and predicted responses is in the range of 72% to 76%. However, there is a slight decline in performance metrics as the percentage of missing data increases. In scenarios where block-wise missing data affects multiple omics, the model performance actually surpasses that of scenarios where missing data is present in only one omics. One possible explanation for this might be that the other scenarios introduce a greater diversity of observation profiles, leading to a more robust model. Depending on the specific omics being studied, there is greater consistency in feature selection when comparing block-wise missing data scenarios.

Analyzing clustered continuous response variables with ordinal regression models.

Continuous response data are regularly transformed to meet regression modeling assumptions. However, approaches taken to identify the appropriate transformation can be ad hoc and can increase model uncertainty. Further, the resulting transformations often vary across studies leading to difficulties with synthesizing and interpreting results. When a continuous response variable is measured repeatedly within individuals or when continuous responses arise from clusters, analyses have the additional challenge caused by within-individual or within-cluster correlations. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered, continuous response data using generalized estimating equationsfor ordinal responses. With the proposed approach, estimates of marginal model parameters, cumulative distribution functions , expectations, and quantiles conditional on covariates can be obtained without pretransformation of the response data. While computational challenges arise with large numbers of distinct values of the continuous response variable, we propose feasible and computationally efficient approaches to fit CPMs under commonly used working correlation structures. We study finite sample operating characteristics of the estimators via simulation and illustrate their implementation with two data examples. One studies predictors of CD4:CD8 ratios in a cohort living with HIV, and the other investigates the association of a single nucleotide polymorphism and lung function decline in a cohort with early chronic obstructive pulmonarydisease.

Application of Statistical Methods for Central Statistical Monitoring and Implementations on the German Multiple Sclerosis Registry

Monitoring of clinical trials is a fundamental process required by regulatory agencies. It assures the compliance of a center to the required regulations and the trial protocol. Traditionally, monitoring teams relied on extensive on-site visits and source data verification. However, this is costly, and the outcome is limited. Thus, central statistical monitoring (CSM) is an additional approach recently embraced by the International Council for Harmonisation (ICH) to detect problematic or erroneous data by using visualizations and statistical control measures. Existing implementations have been primarily focused on detecting inlier and outlier data. Other approaches include principal component analysis and distribution of the data. Here we focus on the utilization of comparisons of centers to the Grand mean for different model types and assumptions for common data types, such as binomial, ordinal, and continuous response variables. We implement the usage of multiple comparisons of single centers to the Grand mean of all centers. This approach is also available for various non-normal data types that are abundant in clinical trials. Further, using confidence intervals, an assessment of equivalence to the Grand mean can be applied. In a Monte Carlo simulation study, the applied statistical approaches have been investigated for their ability to control type I error and the assessment of their respective power for balanced and unbalanced designs which are common in registry data and clinical trials. Data from the German Multiple Sclerosis Registry (GMSR) including proportions of missing data, adverse events and disease severity scores were used to verify the results on Real-World-Data (RWD).

Finite-Mixture Continuous Logit Model: Formulation and Application for Shopping Start Time Choice of Non-Commuters

As a continuous generalization of the multinomial logit (MNL) model, the continuous logit (CL) model can be used for continuous response variables (e.g., departure time and activity duration). However, the existing CL model requires the calculation of numerical integrals to obtain the choice probabilities; it thus takes a long time to estimate the model parameters, particularly when the sample size is large. In this paper, we formulate the finite-mixture CL (FMCL) model as a new continuous choice model by combining the finite-mixture method and the CL model, in which the continuous distributional function of the finite mixture is embedded in the CL model. As a result, the individual choice probability can be obtained directly by computing the probability density of the continuous distribution function; this avoids calculation of the integral but still obeys the random utility maximization (RUM) principle. Simulation experiments are conducted to demonstrate the capability of the model. In an empirical study, the proposed model is applied for non-commuters’ shopping activity start time using the expectation-maximization (EM) algorithm based on Shanghai Household Travel Survey data. The results show that the FMCL model developed in this paper can greatly reduce the model estimation time (10,048 observations requiring only 3 min) of the CL model, and the model also has a more intuitive interpretation of model coefficients, directly reflecting variable effects on time-of-day choice. These two advantages can greatly enhance the practical value of the proposed modeling method.

History, neighborhood, and proximity as factors of land-use change: A dynamic spatial regression model

Spatio-temporal land-use change (LUC) modeling provides vital information about land development dynamics. However, accounting for such dynamics faces methodological challenges. This research introduces a Dynamic Spatial Panel Data (DSPD) modeling framework for LUC, incorporating spatial and temporal dependencies. A continuous response variable is introduced to take advantage of traditional spatial regression models. The DSPD model is applied to balanced spatial panel data at the block-group level covering Florida between 2010 and 2019 and incorporating both new and previously used proxy variables. The urban growth impacts of site-specific, proximity, neighborhood, socio-economic, and transportation factors are investigated. This study contributes to the literature by providing extensive insights into spatial autocorrelation, spillover, heterogeneity, and temporal lag effects in urban growth. Also, the study reveals the importance of mobility and mortgage financing in land development. The proposed modeling framework achieves high accuracy. The dynamic structure of this model provides an opportunity to predict future urban growth without the need for a land development scenario. Such predictions provide insights about future land development to practitioners and policymakers.

TaxaHFE: a machine learning approach to collapse microbiome datasets using taxonomic structure.

Biologists increasingly turn to machine learning models not just to predict, but to explain. Feature reduction is a common approach to improve both the performance and interpretability of models. However, some biological datasets, such as microbiome data, are inherently organized in a taxonomy, but these hierarchical relationships are not leveraged during feature reduction. We sought to design a feature engineering algorithm to exploit relationships in hierarchically organized biological data. We designed an algorithm, called TaxaHFE, to collapse information-poor features into their higher taxonomic levels. We applied TaxaHFE to six previously published datasets and found, on average, a 90% reduction in the number of features (SD = 5.1%) compared to using the most complete taxonomy. Using machine learning to compare the most resolved taxonomic level (i.e. species) against TaxaHFE-preprocessed features, models based on TaxaHFE features achieved an average increase of 3.47% in receiver operator curve area under the curve. Compared to other hierarchical feature engineering implementations, TaxaHFE introduces the novel ability to consider both categorical and continuous response variables to inform the feature set collapse. Importantly, we find TaxaHFE's ability to reduce hierarchically organized features to a more information-rich subset increases the interpretability of models. TaxaHFE is available as a Docker image and as R code at https://github.com/aoliver44/taxaHFE.

Rethinking Habitat Occupancy Modeling and the Role of Diel Activity in an Anthropogenic World

AbstractCurrent methods to model species habitat use through space and diel time are limited. Development of such models is critical when considering rapidly changing habitats where species are forced to adapt to anthropogenic change, often by shifting their diel activity across space. We use an occupancy modeling framework to specify the multistate diel occupancy model (MSDOM), which can evaluate species diel activity against continuous response variables that may impact diel activity within and across seasons or years. We used two case studies, fosas in Madagascar and coyotes in Chicago, Illinois, to conceptualize the application of this model and to quantify the impacts of human activity on species spatial use in diel time. We found support that both species varied their habitat use by diel states-in and across years and by human disturbance. Our results exemplify the importance of understanding animal diel activity patterns and how human disturbance can lead to temporal habitat loss. The MSDOM will allow more focused attention in ecology and evolution studies on the importance of the short temporal scale of diel time in animal-habitat relationships and lead to improved habitat conservation and management.

Mixed-effect models with trees

Tree-based regression models are a class of statistical models for predicting continuous response variables when the shape of the regression function is unknown. They naturally take into account both non-linearities and interactions. However, they struggle with linear and quasi-linear effects and assume iid data. This article proposes two new algorithms for jointly estimating an interpretable predictive mixed-effect model with two components: a linear part, capturing the main effects, and a non-parametric component consisting of three trees for capturing non-linearities and interactions among individual-level predictors, among cluster-level predictors or cross-level. The first proposed algorithm focuses on prediction. The second one is an extension which implements a post-selection inference strategy to provide valid inference. The performance of the two algorithms is validated via Monte Carlo studies. An application on INVALSI data illustrates the potentiality of the proposed approach.

Faktor-Faktor yang Memengaruhi Keberhasilan Studi Mahasiswa IPB Jalur Ketua OSIS dengan Metode Pohon Regresi

The success of IPB student's study can be seen from the achievement index obtained at the end of each semester. Meanwhile, the success rate of one's study is generally influenced by two factors, internal factors and external factors. Internal factors consist of intelligence (intellectual), physical, attitudes, interests, talents, and motivations, while external factors consist of family circumstances, school conditions, and the community environment. Therefore, this study uses the analysis method of classification and regression trees (CART) to find out what factors influenced the success of the Student Council (OSIS) university students.
 Regression tree it is one of the methods of classification and regression trees (CART) to perform classification analysis on both categorical and continuous response variables. Continuous response variables will produce a regression tree or hierarchical data group that starts at the root and ends with a relatively homogeneous small group. The response variable used in this study is the Achievement Index of first semester students. The results obtained from the analysis showed that there are several different variables in each class in influencing the success of the student council (OSIS) university students, but if we look further, there are two variables that are the same in influencing the success of the student council (OSIS) university students, which are variables from high school province and student study programs.
 This study uses secondary data from 493 IPB students track the chairman of the student council of the year 2018-2020 which is still active until now. Furthermore, the analysis of the regression tree is performed against four different models, for each of the force and the overall force by adjusting the variables available. The formation of tree regression performed 10 repetitions and the results of regression trees is taken from a tree which has the approximate value of the smallest risk. Then, the final results obtained from the analysis showed that there are several different variables in each class in influencing the success of the student council (OSIS) university students, but if we look further, there are two variables that are the same in influencing the success of the student council (OSIS) university students, which are variables from high school province and student study programs.

Misclassification Analysis of Elementary School Accreditation Data in Ambon City Using Multivariate Adaptive Regression Spline

Many classification methods have been developed, one of which is the Multivariate Adaptive Regression Spline (MARS) method. MARS is one of the classification methods in the form of a combination of Recursive Partitioning Regression (RPR) and the spline method that is able to process high-dimensional and large-sized data and process data with continuous or binary response variables. The purpose of this study was to measure the misclassification of elementary school accreditation in Ambon city using the MARS method. This study uses accreditation data with the results of eight components of accreditation in elementary schools that have accreditation A (group 1) and accreditation B (group 2) in Ambon city. To evaluate the classification method used the APER classification error measure. The best classification result from the MARS method is when using a combination of BF=32, MI=3, MO=1 because it produces a minimum Generalized Cross Validation (GCV) of 0.066 and information is obtained that the correct classification data is 181 and the misclassified data is 10. Based on the results of the analysis, the size of the APER classification error is 5.23%, which can be said that the MARS method is good or statistically significant for classifying elementary schools in Ambon City based on their accreditation rating.

Model-free feature screening for ultrahigh dimensional data via a Pearson chi-square based index

For ultrahigh dimensional data, we propose a model-free marginal feature screening procedure, which can handle continuous, categorical and discrete response variables, based on the integral Pearson chi-square (IPC) index. The IPC index can be regarded as an extension of the AD index studied by He et al. [A modified mean-variance feature-screening procedure for ultrahigh-dimensional discriminant analysis. Comput Stat Data Anal. 2019;137:155–169]. When the response variable is categorical, we extend He et al.'s work to the case of allowing a diverging number of response categories. However, the IPC index is difficult to estimate when the response is continuous. Thus we modify it and define the fused IPC index using the slice-and-fuse technique. Our feature screening procedure ranking the IPC or fused IPC index is robust to heavy-tailed features and outliers. The sure screening properties and the ranking consistency properties are established for both categorical and continuous responses under mild conditions. The finite sample performance of the proposed procedure is demonstrated through various numerical simulations and two real data applications.

Longitudinal Joint Modelling of Binary and Continuous Outcomes: A Comparison of Bridge and Normal Distributions


 Background: Longitudinal joint models consider the variation caused by repeated measurements over time as well as the association among the response variables. In the case of combining binary and continuous response variables using generalized linear mixed models, integrating over a normally distributed random intercept in the binary logistic regression sub-model does not yield to a closed form. In this paper, we assessed the impact of assuming a Bridge distribution for the random intercept in the binary logistic regression submodel and compared the results to that of normal distribution.
 Method: The response variables are combined through correlated random intercepts. The random intercept in the continuous outcome submodel follows a normal distribution. The random intercept in the binary outcome submodel follows a normal or Bridge distribution. The estimations were carried out using a likelihood-based approach in direct and conditional joint modeling approaches. To illustrate the performance of the models, a simulation study was conducted
 Results: Based on the simulation results and regardless of the joint modeling approach, the models with a Bridge distribution for the random intercept of the binary outcome resulted in a slightly more accurate estimations and better performance.
 Conclusion: In addition to the fact that assuming a bridge distribution for the random intercept in binary logistic regression yields to the same interpretation of parameter estimates in marginal and conditional forms, our study revealed that even if the random intercept of binary logistic regression is normally distributed, assuming a Bridge distribution in the model will result in more accurate results. 

Comparison of mixed model based approaches for correcting for population substructure with application to extreme phenotype sampling

BackgroundMixed models are used to correct for confounding due to population stratification and hidden relatedness in genome-wide association studies. This class of models includes linear mixed models and generalized linear mixed models. Existing mixed model approaches to correct for population substructure have been previously investigated with both continuous and case-control response variables. However, they have not been investigated in the context of extreme phenotype sampling (EPS), where genetic covariates are only collected on samples having extreme response variable values. In this work, we compare the performance of existing binary trait mixed model approaches (GMMAT, LEAP and CARAT) on EPS data. Since linear mixed models are commonly used even with binary traits, we also evaluate the performance of a popular linear mixed model implementation (GEMMA).ResultsWe used simulation studies to estimate the type I error rate and power of all approaches assuming a population with substructure. Our simulation results show that for a common candidate variant, both LEAP and GMMAT control the type I error rate while CARAT’s rate remains inflated. We applied all methods to a real dataset from a Québec, Canada, case-control study that is known to have population substructure. We observe similar type I error control with the analysis on the Québec dataset. For rare variants, the false positive rate remains inflated even after correction with mixed model approaches. For methods that control the type I error rate, the estimated power is comparable.ConclusionsThe methods compared in this study differ in their type I error control. Therefore, when data are from an EPS study, care should be taken to ensure that the models underlying the methodology are suitable to the sampling strategy and to the minor allele frequency of the candidate SNPs.

A New Deep Learning Calibration Method Enhances Genome-Based Prediction of Continuous Crop Traits.

Genomic selection (GS) has the potential to revolutionize predictive plant breeding. A reference population is phenotyped and genotyped to train a statistical model that is used to perform genome-enabled predictions of new individuals that were only genotyped. In this vein, deep neural networks, are a type of machine learning model and have been widely adopted for use in GS studies, as they are not parametric methods, making them more adept at capturing nonlinear patterns. However, the training process for deep neural networks is very challenging due to the numerous hyper-parameters that need to be tuned, especially when imperfect tuning can result in biased predictions. In this paper we propose a simple method for calibrating (adjusting) the prediction of continuous response variables resulting from deep learning applications. We evaluated the proposed deep learning calibration method (DL_M2) using four crop breeding data sets and its performance was compared with the standard deep learning method (DL_M1), as well as the standard genomic Best Linear Unbiased Predictor (GBLUP). While the GBLUP was the most accurate model overall, the proposed deep learning calibration method (DL_M2) helped increase the genome-enabled prediction performance in all data sets when compared with the traditional DL method (DL_M1). Taken together, we provide evidence for extending the use of the proposed calibration method to evaluate its potential and consistency for predicting performance in the context of GS applied to plant breeding.

Rice farm income diversification in Ghana and implications on household consumption expenditure

PurposeThis study investigates implications of crop and income diversifications on consumption expenditure (welfare) of rice-producing households in Ghana. It further compares diversification by three rice production systems: two-season rain-fed, two-season irrigated and one-season rain-fed rice production.Design/methodology/approachPrimary data were sourced from 225 rice farmers. Margalef index and three-stage least-squares were employed.FindingsMajority of rice-farming households in Ghana diversify livelihoods. The extent of livelihood diversification differs among two-season rain-fed, two-season irrigated and one-season rain-fed rice-producing households. Credit, distance to district capitals, production purpose and number of farming seasons influence crop and income diversifications, and consumption expenditure of rice-producing households. While crop diversification reduces consumption expenditure, income diversification increases it. Crop and income diversifications positively influence each other. Consumption expenditure reduces crop diversification but increases income diversification.Practical implicationsPolicy should be directed towards the promotion of more livelihood activities to boost rice farmers' welfare. There should be awareness creation and training programmes to enable rice farmers realize different economic activities within and outside the agricultural value chain.Originality/valueCrop and income diversifications were measured as continuous response variables, unlike previous studies that used a binary response variable. The authors established a synergy among crop and income diversifications, and consumption expenditure (welfare). The authors further compared crop and income diversifications by three rice production systems: two-season rain-fed, two-season irrigated and one-season rain-fed rice production systems.

Weighted pivot coordinates for partial least squares‐based marker discovery in high‐throughput compositional data

AbstractHigh‐throughput data representing large mixtures of chemical or biological signals are ordinarily produced in the molecular sciences. Given a number of samples, partial least squares (PLS) regression is a well‐established statistical method to investigate associations between them and any continuous response variables of interest. However, technical artifacts generally make the raw signals not directly comparable between samples. Thus, data normalization is required before any meaningful scientific information can be drawn. This often allows to characterize the processed signals as compositional data where the relevant information is contained in the pairwise log‐ratios between the components of the mixture. The (log‐ratio) pivot coordinate approach facilitates the aggregation into single variables of the pairwise log‐ratios of a component to all the remaining components. This simplifies interpretability and the investigation of their relative importance but, particularly in a high‐dimensional context, the aggregated log‐ratios can easily mix up information from different underlaying processes. In this context, we propose a weighting strategy for the construction of pivot coordinates for PLS regression which draws on the correlation between response variable and pairwise log‐ratios. Using real and simulated data sets, we demonstrate that this proposal enhances the discovery of biological markers in high‐throughput compositional data.

Handling missing values in trait data

AbstractAimTrait data are widely used in ecological and evolutionary phylogenetic comparative studies, but often values are not available for all species of interest. Traditionally, researchers have excluded species without data from analyses, but estimation of missing values using imputation has been proposed as a better approach. However, imputation methods have largely been designed for randomly missing data, whereas trait data are often not missing at random (e.g., more data for bigger species). Here, we evaluate the performance of approaches for handling missing values when considering biased datasets.LocationAny.Time periodAny.Major taxa studiedAny.MethodsWe simulated continuous traits and separate response variables to test the performance of nine imputation methods and complete‐case analysis (excluding missing values from the dataset) under biased missing data scenarios. We characterized performance by estimating the error in imputed trait values (deviation from the true value) and inferred trait–response relationships (deviation from the true relationship between a trait and response).ResultsGenerally, Rphylopars imputation produced the most accurate estimate of missing values and best preserved the response–trait slope. However, estimates of missing data were still inaccurate, even with only 5% of values missing. Under severe biases, errors were high with every approach. Imputation was not always the best option, with complete‐case analysis frequently outperforming Mice imputation and, to a lesser degree, BHPMF imputation. Mice, a popular approach, performed poorly when the response variable was excluded from the imputation model.Main conclusionsImputation can handle missing data effectively in some conditions but is not always the best solution. None of the methods we tested could deal effectively with severe biases, which can be common in trait datasets. We recommend rigorous data checking for biases before and after imputation and propose variables that can assist researchers working with incomplete datasets to detect data biases and minimize errors.

On a new mixture-based regression model: simulation and application to data with high censoring

In this paper, we derive a new continuous-discrete mixture regression model which is useful for describing highly censored data. This mixture model employs the Birnbaum-Saunders distribution for the continuous response variable of interest, whereas the Bernoulli distribution is used for the point mass of the censoring observations. We estimate the corresponding parameters with the maximum likelihood method. Numerical evaluation of the model is performed by means of Monte Carlo simulations and of an illustration with real data. The results show the good performance of the proposed model, making it an addition to the tool-kit of biometricians, medical doctors, applied statisticians, and data scientists.