Models For Multivariate Data Research Articles

Changing Educational Assessments in the Post‐COVID‐19 Era: From Assessment of Learning (AoL) to Assessment as Learning (AaL)

AbstractThe upgrade educational information technology triggered by COVID‐19 has shaped a new educational order and new educational forms. As a result, traditional educational measurement is now facing a systematic transformation, that is, from the Assessment of Learning (AoL) to Assessment for Learning (AfL), and finally to Assessment as Learning (AaL). By showing the initiative and the flexibility of large‐scale online learning during the COVID‐19 pandemic, this paper examines the evolution from AoL to AaL from four aspects: participants, test form, multivariate data for process‐based measurement, and measurement models for multivariate data. We propose multidisciplinary corporations in the field, which integrate education, psychology, and information technology into the theories and methods of educational measurement. Further, we emphasize that the validity, ethics, and fairness of the measurement should also be considered the critical issues. Researchers and practitioners of educational measurement must persist in pursuing the substantive significance of measurement and provide unique experience and guidance for the theoretical and practical development of educational assessment in this great revolution.

Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications

As major components of the random matrix theory, Gaussian random matrices have been playing an important role in many fields, because they are both unitary invariant and have independent entries and can be used as models for multivariate data or multivariate phenomena. Tail bounds for eigenvalues of Gaussian random matrices are one of the hot study problems. In this paper, we present tail and expectation bounds for the ℓ1 norm of Gaussian random matrices, respectively. Moreover, the tail and expectation bounds for the ℓ1 norm of the Gaussian Wigner matrix are calculated based on the resulting bounds. Compared with existing results, our results are more suitable for the high‐dimensional matrix case. Finally, we study the tail bounds for the parameter vector of some existing regularization algorithms.

Rapid authentication of coffee bean varieties of different forms by using a pocket-sized spectrometer and multivariate data modelling.

Coffee is the most consumed beverage and the second most valuable traded commodity in the world. In this current study, a pocket-sized spectrometer and multivariate analysis were used for rapid authentication of coffee varieties (Arabica and Robusta) in three states to check mislabelling (food fraud). Two main coffee varieties were collected from different locations in Africa. The samples were scanned in the 740-1070 nm wavelength and the spectral data were pre-treated with several methods: mean centering (MC), multiplicative scatter correction (MSC), first derivative (FD), second derivative (SD) and standard normal variate (SNV) independently while partial least squares discriminate analysis (PLS-DA), K-nearest neighbour (KNN) and support vector machine (SVM) were used to comparatively build the prediction models for coffee beans (raw, roasted and powdered). The performances of the models were evaluated by using accuracy and efficiency. Among the classification methods developed, the best results were obtained for the following: raw coffee bean SD-SVM had an accuracy of 0.92 and efficiency of 0.82. For roasted coffee beans, SD-KNN had an accuracy of 0.92 and efficiency of 0.87, while for roasted powdered coffee, FD-KNN showed an accuracy of 0.97 and efficiency of 0.97. These finding reveals that for a more accurate differentiation of coffee beans, the roasted powder offers the best results. The obtained results showed that a pocket-sized spectrometer coupled with chemometrics could be employed to provide accurate and rapid authentication of different categories of coffee bean varieties.

Type I multivariate zero-inflated COM-Poisson regression model.

In this paper, we present the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution, whose development is based on the extension of the Type I multivariate zero-inflated Poisson distribution. We developed important properties of the distribution and present a regression model. The AIC and BIC criteria are used to select the best fitted model. Two real data sets have been used to illustrate the proposed model. Moreover, we conclude by stating that the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution produces a better fitted model for multivariate count data with excess of zeros.

Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach

Commonly assumed for multivariate functional regression models are normality and structural dependence, which, however, may not hold in practice. To relax these restrictions, we propose a new semiparametric transformation latent process functional regression model for multivariate functional data. Our model does not require normality assumptions or any specific dependence structures among multivariate response curves or intra-individual variability across time. We propose a combined likelihood- and estimating equation-based method to estimate parameters, transformation functions and covariance structures. We establish theoretical properties, including n−consistency and asymptotic normality, for the proposed estimators. The utility of the method is illustrated via extensive simulations and analyses of an elderly cognitive evolution dataset, which yield a better fit than the other competing methods and some interesting findings.

UV Hyperspectral Imaging as Process Analytical Tool for the Characterization of Oxide Layers and Copper States on Direct Bonded Copper.

Hyperspectral imaging and reflectance spectroscopy in the range from 200–380 nm were used to rapidly detect and characterize copper oxidation states and their layer thicknesses on direct bonded copper in a non-destructive way. Single-point UV reflectance spectroscopy, as a well-established method, was utilized to compare the quality of the hyperspectral imaging results. For the laterally resolved measurements of the copper surfaces an UV hyperspectral imaging setup based on a pushbroom imager was used. Six different types of direct bonded copper were studied. Each type had a different oxide layer thickness and was analyzed by depth profiling using X-ray photoelectron spectroscopy. In total, 28 samples were measured to develop multivariate models to characterize and predict the oxide layer thicknesses. The principal component analysis models (PCA) enabled a general differentiation between the sample types on the first two PCs with 100.0% and 96% explained variance for UV spectroscopy and hyperspectral imaging, respectively. Partial least squares regression (PLS-R) models showed reliable performance with R2c = 0.94 and 0.94 and RMSEC = 1.64 nm and 1.76 nm, respectively. The developed in-line prototype system combined with multivariate data modeling shows high potential for further development of this technique towards real large-scale processes.

A joint model for multivariate longitudinal and survival data to discover the conversion to Alzheimer's disease.

Alzheimer's disease (AD) is an incurable and progressive disease that starts from mild cognitive impairment and deteriorates over time. Examining the effects of patients' longitudinal cognitive decline on time to conversion to AD and obtaining a reliable diagnostic model are therefore critical to the evaluation of AD prognosis and early treatment. Previous studies either assess patients' cognitive impairment through a single cognitive test or assume it changes linearly across time, thereby leading to an incomplete measure of cognitive decline or overlooking the subtle trajectory pattern of patients' cognitive impairment. This study develops a new joint model to address these shortcomings. First, a dynamic factor analysis model is adopted to characterize cognitive impairment through multiple cognitive measures in a comprehensive manner. Second, a spline-based random coefficient model is proposed to reveal possibly nonlinear trajectories of patients' cognitive decline. Finally, a proportional hazard model is considered to examine the effects of time-invariant markers and time-variant cognitive impairment on AD hazards. A Bayesian approach coupled with spline approximation techniques and MCMC methods is developed to conduct statistical inference. The application of the proposed method to the Alzheimer's Disease Neuroimaging Initiative study provides new insights into the prevention of AD and shows a high prediction capacity of the proposed method.

Event detection in temporal social networks using a higher-order network model.

Event detection is one of the most important areas of complex network research. It aims to identify abnormal points in time corresponding to social events. Traditional methods of event detection, based on first-order network models, are poor at describing the multivariate sequential interactions of components in complex systems and at accurately identifying anomalies in temporal social networks. In this article, we propose two valid approaches, based on a higher-order network model, namely, the recovery higher-order network algorithm and the innovation higher-order network algorithm, to help with event detection in temporal social networks. Given binary sequential data, we take advantage of chronological order to recover the multivariate sequential data first. Meanwhile, we develop new multivariate sequential data using logical sequence. Through the efficient modeling of multivariate sequential data using a higher-order network model, some common multivariate interaction patterns are obtained, which are used to determine the anomaly degree of a social event. Experiments in temporal social networks demonstrate the significant performance of our methods finally. We believe that our methods could provide a new perspective on the interplay between event detection and the application of higher-order network models to temporal networks.

Bayesian consensus clustering for multivariate longitudinal data.

In clinical and epidemiological studies, there is a growing interest in studying the heterogeneity among patients based on longitudinal characteristics to identify subtypes of the study population. Compared to clustering a single longitudinal marker, simultaneously clustering multiple longitudinal markers allow additional information to be incorporated into the clustering process, which reveals co-existing longitudinal patterns and generates deeper biological insight. In the current study, we propose a Bayesian consensus clustering (BCC) model for multivariate longitudinal data. Instead of arriving at a single overall clustering, the proposed model allows each marker to follow marker-specific local clustering and these local clusterings are aggregated to find a global (consensus) clustering. To estimate the posterior distribution of model parameters, a Gibbs sampling algorithm is proposed. We apply our proposed model to the primary biliary cirrhosis study to identify patient subtypes that may be associated with their prognosis. We also perform simulation studies to compare the clustering performance between the proposed model and existing models under several scenarios. The results demonstrate that the proposed BCC model serves as a useful tool for clustering multivariate longitudinal data.

Penalized mediation models for multivariate data.

Statistical methods to integrate multiple layers of data, from exposures to intermediate traits to outcome variables, are needed to guide interpretation of complex data sets for which variables are likely contributing in a causal pathway from exposure to outcome. Statistical mediation analysis based on structural equation models provide a general modeling framework, yet they can be difficult to apply to high-dimensional data and they are not automated to select the best fitting model. To overcome these limitations, we developed novel algorithms and software to simultaneously evaluate multiple exposure variables, multiple intermediate traits, and multiple outcome variables. Our penalized mediation models are computationally efficient and simulations demonstrate that they produce reliable results for large data sets. Application of our methods to a study of vascular disease demonstrates their utility to identify novel direct effects of single-nucleotide polymorphisms (SNPs) on coronary heart disease and peripheral artery disease, while disentangling the effects of SNPs on the intermediate risk factors including lipids, cigarette smoking, systolic blood pressure, and type 2 diabetes.

A Latent Class Model for Multivariate Binary Data Subject to Missingness

When researchers are interested in measuring social phenomena that cannot be measured using a single variable, the appropriate statistical tool to be used is a latent variable model. A number of manifest variables is used to define the latent phenomenon. The manifest variables may be incomplete due to different forms of non-response that may or may not be random. In such cases, especially when the missingness is nonignorable, it is inevitable to include a missingness mechanism in the model to obtain valid estimates for parameters. In social surveys, categorical items can be considered the most common type of variable. We thus propose a latent class model where two categorical latent variables are defined; one represents the latent phenomenon of interest, and another represents a respondent’s propensity to respond to survey items. All manifest items are considered to be categorical. The proposed model incorporates a missingness mechanism that accounts for forms of missingness that may not be random by allowing the latent response propensity class to depend on the latent phenomenon under consideration, given a set of covariates. The Expectation-Maximization (EM) algorithm is used for estimating the proposed model. The proposed model is used to analyze data from 2014 Egyptian Demographic and Health Survey (EDHS14). Missing data is artificially created in order to study results under the three types of missingness: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR).

Semiparametric analysis of multivariate panel count data with nonlinear interactions.

Multivariate panel count data frequently arise in follow up studies involving several related types of recurrent events. For univariate panel count data, several varying coefficient models have been developed. However, varying coefficient models for multivariate panel count data remain to be studied. In this paper, we propose a varying coefficient mean model for multivariate panel count data to describe the possible nonlinear interact effects between the covariates and the local logarithm partial likelihood procedure is considered to estimate the unknown covariate effects. Furthermore, a Breslow-type estimator is constructed for the baseline mean functions. The consistency and asymptotic normality of the proposed estimators are established under some mild conditions. The utility of the proposed approach is evaluated by some numerical simulations and an application to a dataset of skin cancer study.

Consistent estimation of a joint model for multivariate longitudinal and survival data with latent variables

The investigation of the relationship between a time-to-event outcome and time-dependent risk factors is often of great interest in longitudinal studies. However, the time-dependent risk factors may not be directly observed or simply measured by a single variable. Instead, they are latent and should be characterized by several observed variables from different aspects. In this article, we consider a novel joint modeling framework to examine the effects of latent time-dependent risk factors on the hazard of interest. A factor analysis model is used to depict the dependence between time-dependent latent variables and multivariate longitudinal observed variables, and a proportional hazard model is adopted for linking latent time-dependent factors to the hazard of interest. We develop a hybrid procedure that combines an asymptotically distribution-free generalized least square approach and a conditional score method. Theoretical results are provided on the consistency and asymptotic normality of parameter estimators. The method is evaluated through simulation studies and applied to a dataset about Alzheimer’s disease.

Random effect models for multivariate mixed data: A Parafac-based finite mixture approach

We discuss a flexible regression model for multivariate mixed responses. Dependence between outcomes is introduced via the joint distribution of discrete outcome- and individual-specific random effects that represent potential unobserved heterogeneity in each outcome profile. A different number of locations can be used for each margin, and the association structure is described by a tensor that can be further simplified by using the Parafac model. A case study illustrates the proposal.

Exploring relationship between sustainability and firm performance in travel and tourism industry: a global evidence

PurposeThe study aims to investigate the relationship between aggregate and individual dimensions of sustainability and financial and stock market performances of the firms in the travel and tourism industry (TTI) across different geographies.Design/methodology/approachThe sample under study consists of 146 firms belonging to TTI that have consistently obtained environmental, social and governance (ESG) rating over the period 2011–2017 as a part of Thomson Reuters Asset 4 ESG database. An empirical multivariate panel data model is developed to analyse the impact of sustainability (ESG) on firm profitability and market value within three tourism-related industries (transportation, hotel and leisure).FindingsThe study extends the existing literature by investigating the impact of each of the vital dimensions of sustainability performance – ESG – and examines how each dimension would affect financial performance and market value among firms within three tourism-related industries (transportation, hotel and leisure). Among the three tourism industries, hotel industry is observed to have the highest ESG compliance, followed by the transportation industry. Based on the agency and stakeholder theory, the authors hypothesized all ESG components to have significant positive effect on the financial and stock market performance; however, the results reveal that each dimension has different impact on financial performance and market value of firms in the tourism industry.Research limitations/implicationsThe study could help firms in the travel and tourism industries to understand which of the dimension of ESG activities is significantly important for their financial and stock market performance.Originality/valueThe unique contribution of this study is that it considers wider definition of the term “Sustainability” and examines the relationship between financial and stock market performances of the firms and each component of ESG. This is one of the few studies at the global level that provides much needed evidence in the area of sustainability performance by the travel and tourism firms.

Metrological properties of neuropsychological tests for measuring cognitive change in individuals with prodromal Alzheimer’s disease

Objectives In Alzheimer’s Disease (AD) research, choosing appropriate method for measuring change in cognitive function over time can be challenging. The aim for this study was to examine the sensitivity of four neuropsychological tests used to measure cognition during the transition from mild cognitive impairment (MCI) to AD, and the impacts of associated covariates. Methods We enrolled 223 patients with MCI who progressed to AD and had completed multiple follow-up assessments in the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. We constructed nonlinear mixed model for multivariate longitudinal data assuming that multiple neuropsychological tests would exhibit nonlinear transformation of a common factor in the latent cognitive process underlying the progression from MCI to AD. Results The Clinical Dementia Rating-Sum of the Boxes (CDR-SB) and Alzheimer’s Disease Assessment Scale (11 items; ADAS-11) were more sensitive to cognitive changes in individuals with higher cognitive function, the Functional Activities Questionnaire (FAQ) was more sensitive to cognitive changes in individuals with middle cognitive function, and the Mini-Mental State Examination (MMSE) was more sensitive to cognitive changes in individuals with lower cognitive function. Gender (p = 0.0139) and educational level (p = 0.0094) had varying effects on different tests, such that men performed better on the FAQ and CDR-SB, and individuals with higher educational level tended to perform better on the FAQ and MMSE. Conclusions When choosing appropriate neuropsychological tests in cognitive measurements, the cognitive functional level of the patient as well as the impacts of covariates should be considered.

Filtering the Intensity of Public Concern from Social Media Count Data with Jumps

Abstract Count time series obtained from online social media data, such as Twitter, have drawn increasing interest among academics and market analysts over the past decade. Transforming Web activity records into counts yields time series with peculiar features, including the coexistence of smooth paths and sudden jumps, as well as cross-sectional and temporal dependence. Using Twitter posts about country risks for the United Kingdom and the United States, this paper proposes an innovative state space model for multivariate count data with jumps. We use the proposed model to assess the impact of public concerns in these countries on market systems. To do so, public concerns inferred from Twitter data are unpacked into country-specific persistent terms, risk social amplification events and co-movements of the country series. The identified components are then used to investigate the existence and magnitude of country-risk spillovers and social amplification effects on the volatility of financial markets.

Sequential Truncation of R-Vine Copula Mixture Model for High-Dimensional Datasets

Uncovering hidden mixture dependencies among variables has been investigated in the literature using mixture R-vine copula models. They provide considerable flexibility for modeling multivariate data. As the dimensions increase, the number of the model parameters that need to be estimated is increased dramatically, which comes along with massive computational times and efforts. This situation becomes even much more complex and complicated in the regular vine copula mixture models. Incorporating the truncation method with a mixture of regular vine models will reduce the computation difficulty for the mixture-based models. In this paper, the tree-by-tree estimation mixture model is joined with the truncation method to reduce computational time and the number of parameters that need to be estimated in the mixture vine copula models. A simulation study and real data applications illustrated the performance of the method. In addition, the real data applications show the effect of the mixture components on the truncation level.

Dependence modeling of multivariate longitudinal hybrid insurance data with dropout

Financial services industries, such as insurance, increasingly use data from their broad cross-section of customers and follow these customers over time. In other areas such as medicine, engineering, and communication systems, it is well known that following subjects over time may result in biased data, for example, the so-called ”dropout effect”. This paper introduces techniques to address dropout commonly encountered in the insurance domain. Specifically, in the insurance context, multivariate claims outcomes may be related to a customer’s dropout or decision to lapse a policy. Insurance claims outcomes are also naturally a hybrid with both discrete and continuous components, which adds complexity to model calibration. Decision makers in the insurance industry will find our work provides helpful guidance in integrating customer loyalty, especially with bundled coverages. This paper introduces a generalized method of moments technique to estimate dependence parameters where associations are represented using copulas. This is especially useful for large data sets. The paper describes how the joint model provides new information that insurers can use to better manage their portfolios of risks. An application to a Spanish insurer data set is presented.

DSubSign: Classification of Instance-Feature Data Using Discriminative Subgraphs as Class Signatures

Applications like customer identification from their peculiar purchase patterns require class-wise discriminative feature subsets called as class signatures for classification. If the classifiers like KNN, SVM, etc. which require to work with a complete feature set, are applied to such applications, then the entire feature set may introduce errors in the classification. Decision tree classifier generates class-wise prominent feature subsets and hence, can be employed for such applications. However, all of these classifiers fail to model the relationship between features present in vector data. Thus, we propose to model the features and their interrelationships as graphs. Graphs occur naturally in protein molecules, chemical compounds, etc. for which several graph classifiers exist. However, multivariate data do not exhibit the graphs naturally. Thus, the proposed work focuses on (1) modeling multivariate data as graphs and (2) obtaining class-wise prominent subgraph signatures which are then used to train classifiers like SVM for decision making. The proposed method dSubSign can also classify multivariate data with missing values without performing imputation or case deletion. The performance analysis of both real-world and synthetic datasets shows that the accuracy of dSubSign is either higher or comparable to other existing methods.