Score Statistics Research Articles

Influence diagnostics on a reparameterized t-Student spatial linear model

In this paper, we consider a spatial linear model under the multivariate Student’s t-distribution with finite second moment. This distribution, which contains the normal distribution, offers a more flexible framework for modelling spatial data. We use a reparameterized version of the multivariate Student’s t-distribution, so that the scale matrix corresponds to the covariance matrix of the spatial data. The main goal of this work is to develop influence measures to detect presence of influential observations and possible outliers, based on the likelihood displacement and on the score statistics. A heteroskedastic model is considered as a perturbation scheme to the covariance matrix of t-Student spatial linear model. Identifiability issues and robustness aspects of the maximum likelihood estimators are also discussed. The results are illustrated using a soybean yield real data and a simulation study.

Novel score test to increase power in association test by integrating external controls.

Recent advances in genotyping and sequencing technologies have enabled genetic association studies to leverage high-quality genotyped data to identify variants accounting for a substantial portion of disease risk. The usage of external controls, whose genomes have already been genotyped and are publicly available, could be a cost-effective approach to increase the power of association testing. There has been recent effort to integrate external controls while adjusting for possible batch effects, such as the integrating External Controls into Association Test (iECAT). The original iECAT test, however, cannot adjust for covariates such as age, gender, and so forth. Hence, based on the insight of iECAT, we propose a novel score-based test that allows for covariate adjustment and constructs a shrinkage score statistic that is a weighted sum of the score statistics using exclusively internal samples and uses both internal and external control samples. We assess the existence of batch effect at a variant by comparing control samples of internal and external sources. We show by simulation studies that our method has increased power over the original iECAT while controlling for type I error rates. We present the application of our method to the association studies of age-related macular degeneration (AMD) utilizing data from the International AMD Genomics Consortiumand Michigan Genomics Initiative. Through the incorporation of the score test approach, we extend the use of iECAT to adjust for covariates and improve power, further honing the statistical methods needed to identify disease-causing variants within the human genome.

An extended regularized adjusted plus-minus analysis for lineup management in basketball using play-by-play data

AbstractIn this work we analyse basketball play-by-play data in order to evaluate the efficiency of different five-man lineups employed by teams. Starting from the adjusted plus-minus framework, we present a model-based strategy for the analysis of the result of partial match outcomes, extending the current literature in two main directions. The first extension replaces the classical response variable (scored points) with a comprehensive score that combines a set of box score statistics. This allows various aspects of the game to be separated. The second extension focuses on entire lineups rather than individual players, using a suitable extended model specification. The model fitting procedure is Bayesian and provides the necessary regularization. An advantage of this approach is the use of posterior distributions to rank players and lineups, providing an effective tool for team managers. For the empirical analysis, we use the 2018/2019 regular season of the Turkish Airlines Euroleague Championship, with play-by-play and box scores for 240 matches, which are made available by the league website. The results of the model fitting can be used for several investigations as, for instance, the comparative analysis of the effects of single players and the estimation of total and synergic effects of lineups monitoring. Moreover, the behaviour of players and lineups during the season, updating the estimation results after each gameday, can represent a rather useful tool.

: A score statistic for spatiotemporal change point detection

We present an efficient score statistic, called the statistic, to detect the emergence of a spatially and temporally correlated signal from either fixed-sample or sequential data. The signal may cause a mean shift and/or a change in the covariance structure. The score statistic can capture both the spatial and temporal structures of the change and hence is particularly powerful in detecting weak signals. The score statistic is computationally efficient and statistically powerful. Our main theoretical contribution is accurate analytical approximations to the false alarm rate of the detection procedures, which can be used to calibrate the threshold analytically. Numerical experiments on simulated and real data, as well as a case study of water quality monitoring using sensor networks, demonstrate the good performance of our procedure.

Forecasting stock market in high and low volatility periods: a modified multifractal volatility approach

We propose a new multifractal volatility measure (MVA) and accordingly construct new types of multifractal volatility models. We compare these models to some alternatives, and consider long memory features, the benefits of leverage effects, and the presence of jumps. The analysis is applied to the multifractal volatility and realized volatility series of three representative indices, adopting six loss functions as guidance for the model selection. The forecast performance is evaluated and tested using model confident set (MCS) in both high- and low-volatility periods, as well as based on robustness checks on the continuous rank probability score statistics. The results show satisfactory performances for the new multifractal volatility models. Specifically, we find that our new multifractal volatility model significantly improves the one-day-ahead volatility forecasts in the high-volatility period. While in the low-volatility periods, the out-of-sample test results highlight the superiority of the traditional multifractal volatility models in the accuracy of volatility forecasting. These findings will be helpful for market volatility prediction and investment strategies.

A Bayesian adjusted plus-minus analysis for the esport Dota 2

Abstract Analytics and professional sports have become linked over the past several years, but little attention has been paid to the growing field of esports within the sports analytics community. We seek to apply an Adjusted Plus Minus (APM) model, an accepted analytic approach used in traditional sports like hockey and basketball, to one particular esports game: Defense of the Ancients 2 (Dota 2). As with traditional sports, we show how APM metrics developed with Bayesian hierarchical regression can be used to quantify individual player contributions to their teams and, ultimately, use this player-level information to predict game outcomes. In particular, we first provide evidence that gold can be used as a continuous proxy for wins to evaluate a team’s performance, and then use a Bayesian APM model to estimate how players contribute to their team’s gold differential. We demonstrate that this APM model outperforms models based on common team-level statistics (often referred to as “box score statistics”). Beyond the specifics of our modeling approach, this paper serves as an example of the potential utility of applying analytical methodologies from traditional sports analytics to esports.

Analysis of the External Assessment of Educational Achievements in Kazakhstan in 2019

Due to the transition to market-oriented relations, the number of universities in Kazakhstan has increased,which has led to competition at regional and national levels in higher education. To ensure thecompetitiveness of an educational institution in the market of educational services, universities developand offer new educational programs that determine the level of professional training, offer a new pricingpolicy, and introduce various innovations in the organization of education. In the article the authorsreviewed the indicators of the results of the external assessment of educational achievements (EAEA) ofHigher education for 2019. Statistical data is presented in the context of directions and disciplines basedon the results of the EAEA in 2019. A quantitative analysis was performed. A comparative analysis is alsopresented in the disciplines “Information and communication technologies” and “Foreign language (English)”,statistics of the average score in the context of directions. According to the results of EAEA you cansee the strengths and weaknesses of the level of knowledge of students and evaluate the effectiveness ofthe educational process through comparative analysis of fields, professions, disciplines among universities.The results of the EAEA allow carrying out the state monitoring, which is used to assess the qualityof education provided by the country’s universities, and determine the ratingKey words: quality of education, monitoring the quality of education, external assessment of educationalachievements, analysis.

Multiple QTL Mapping in Autopolyploids: A Random-Effect Model Approach with Application in a Hexaploid Sweetpotato Full-Sib Population.

In developing countries, the sweetpotato, Ipomoea batatas (L.) Lam. [Formula: see text], is an important autopolyploid species, both socially and economically. However, quantitative trait loci (QTL) mapping has remained limited due to its genetic complexity. Current fixed-effect models can fit only a single QTL and are generally hard to interpret. Here, we report the use of a random-effect model approach to map multiple QTL based on score statistics in a sweetpotato biparental population ('Beauregard' × 'Tanzania') with 315 full-sibs. Phenotypic data were collected for eight yield component traits in six environments in Peru, and jointly adjusted means were obtained using mixed-effect models. An integrated linkage map consisting of 30,684 markers distributed along 15 linkage groups (LGs) was used to obtain the genotype conditional probabilities of putative QTL at every centiMorgan position. Multiple interval mapping was performed using our R package QTLpoly and detected a total of 13 QTL, ranging from none to four QTL per trait, which explained up to 55% of the total variance. Some regions, such as those on LGs 3 and 15, were consistently detected among root number and yield traits, and provided a basis for candidate gene search. In addition, some QTL were found to affect commercial and noncommercial root traits distinctly. Further best linear unbiased predictions were decomposed into additive allele effects and were used to compute multiple QTL-based breeding values for selection. Together with quantitative genotyping and its appropriate usage in linkage analyses, this QTL mapping methodology will facilitate the use of genomic tools in sweetpotato breeding as well as in other autopolyploids.

Asymptotic properties of a spatial autoregressive stochastic frontier model

This paper considers asymptotic properties of a spatial autoregressive stochastic frontier model. Relying on the asymptotic theory for nonlinear spatial NED processes, we prove the consistency and asymptotic distribution of the maximum likelihood estimator under regularity conditions. When inefficiency exists, all parameter estimators have the $$\sqrt{n}$$ -rate of convergence and are asymptotically normal. However, when there is no inefficiency, only some parameter estimators have the $$\sqrt{n}$$ -rate of convergence, and the rest have slower convergence rates. We also investigate a corrected two stage least squares estimator that is computationally simple, and derive the asymptotic distributions of the score and likelihood ratio test statistics that test for the existence of inefficiency.

Identifying High-risk Areas of Foot-and-mouth Disease Outbreak Using a Spatiotemporal Score Statistic: A Case of South Korea

The objective of this study is to identify high-risk areas of foot-and-mouth disease (FMD) in South Korea using nationwide data collected for the disease cases that occurred during the period from December 2014 to April 2015. High-risk areas of FMD occurrence are defined as local clusters or hot spots, where the frequency of disease occurrence is higher than expected. An issue in the FMD detection study is in identifying a spatial pattern deviated significantly from the expected value under the null hypothesis that no spatial process is investigated. While identifying geographic clusters is challenging to reveal the causes of disease outbreak, it is most useful to detect and monitor potential areas of risk occurrence and suggest a further in-depth investigation. This study extended a traditional score statistic (SC) that has limited to identify the spatial pattern by proposing a spatiotemporal score statistic (STSC) that incorporates a temporal component into the SC approach. STSC, a local spatial statistic, was utilized to detect clusters around the known foci with a latent period. This study demonstrated STSC could better exploit the advantage of the original SC and improve the cluster detection due to the latent time component. The empirical results of STSC are expected to provide more useful policy implications with agencies in charge of preventing and controlling the spread of epidemics when deciding where to concentrate the limited resources available.

Robust Inference in the Capital Asset Pricing Model Using the Multivariate t-distribution

In this paper, we consider asset pricing models under the multivariate t-distribution with finite second moment. Such a distribution, which contains the normal distribution, offers a more flexible framework for modeling asset returns. The main objective of this work is to develop statistical inference tools, such as parameter estimation and linear hypothesis tests in asset pricing models, with an emphasis on the Capital Asset Pricing Model (CAPM). An extension of the CAPM, the Multifactor Asset Pricing Model (MAPM), is also discussed. A simple algorithm to estimate the model parameters, including the kurtosis parameter, is implemented. Analytical expressions for the Score function and Fisher information matrix are provided. For linear hypothesis tests, the four most widely used tests (likelihood-ratio, Wald, score, and gradient statistics) are considered. In order to test the mean-variance efficiency, explicit expressions for these four statistical tests are also presented. The results are illustrated using two real data sets: the Chilean Stock Market data set and another from the New York Stock Exchange. The asset pricing model under the multivariate t-distribution presents a good fit, clearly better than the asset pricing model under the assumption of normality, in both data sets.

RETIREMENT CHALLENGES AND ADJUSTMENT STRATEGIES OF RETIRED LOCAL GOVERNMENT CIVIL SERVANTS IN BENUE STATE, NIGERIA

This study investigated the retirement challenges and adjustment strategies of retired Local Government Civil Servants in Benue stage, Nigeria. To guide the study, two research questions and two hypotheses were formulated. The survey research design was adopted for the study. The population was the entire 5678 retired Local Government Civil Servants from Benue state Local Government Service Commission. Purposive sampling technique was used to select 384 retirees as respondents for the study while simple random sampling was used to select the Local Government Area for the study. The researcher used an instrument titled: Retirement Challenges and Adjustment Strategies Questionnaire (RCASQ) for the study. Data was collected through the administration of questionnaire. The demographic data and research questions were analyzed by the use of descriptive statistics of mean score, the hypotheses were tested by the use of t-test statistics. The results indicated that retired local government civil servants experience challenges in socio-economic, physical and psychological areas. It was also revealed that the adjustment strategies do not significantly differ in terms of gender. The study, therefore, recommended that there should be proper orientation and pre-retirement vocational training for retirees’ efficient, workable pension schemes. It should also cover post-retirement follow up programme for retirees.

EQual Rubric Evaluation of the Association of American Medical Colleges’ Core Entrustable Professional Activities for Entering Residency

To have subject matter experts evaluate the Core Entrustable Professional Activities for Entering Residency (Core EPAs) with the EQual rubric to determine if revisions were required and, if applicable, how to focus revision efforts. Ten entrustable professional activity (EPA) experts were invited to evaluate the 13 Core EPAs. Experts had a 6-month window (December 2018-May 2019) to complete the evaluation, which contained the complete EQual rubric and 3 additional prompts, one of which-"Do you think this EPA requires revision?"-was limited to a "yes/no" response. Descriptive statistics for overall and domain-specific EQual rubric scores for each of the 13 Core EPAs were calculated. Free-text responses to why and/or how a Core EPA should be revised were summarized for any Core EPA that scored below a cutoff or for which the majority of experts recommended revision. Six experts completed the evaluation. Most Core EPAs' (9/13) overall score was above the cutoff, indicating that they align with the key domains of the EPA construct. The remaining 4 Core EPAs (2, 7, 9, and 13) scored below the overall cutoff, suggesting that they may require revision. A majority of experts felt that Core EPAs 6, 7, 9, and 13 required revision. With regard to domain-specific scores, Core EPAs 2, 3, 7, 9, and 13 were below the discrete units of work cutoff; Core EPAs 7, 9, and 13 were below the entrustable, essential, and important tasks of the profession of medicine cutoff; and Core EPA 9 was below the curricular role cutoff. The Core EPAs represent a promising initial framework of EPAs for undergraduate medical education. Some Core EPAs might benefit from revision. The process of improving the Core EPAs must continue if they are to standardize outcomes for medical school graduates.

An Improved Sample Size Calculation Method for Score Tests in Generalized Linear Models

Self and Mauritsen developed a sample size determination procedure for score tests in generalized linear models under contiguous alternatives. Its performance may deteriorate when the effect size is large. We propose a modification of the Self–Mauritsen method by taking into account of the variance of the score statistic under both the null and alternative hypotheses, and extend the method to noninferiority trials. The modified approach is employed to calculate the sample size for the logistic regression and negative binomial regression in superiority and noninferiority trials. We further explain why the formulae recently derived by Zhu and Lakkis tend to underestimate the required sample size for the negative binomial regression. Numerical examples are used to demonstrate the accuracy of the proposed method.

On hypothesis testing inference in location-scale models under model misspecification

The likelihood ratio, Wald, score and gradient test statistics can result in misleading conclusions when the assumed parametric model to the data at hand is not correctly specified. To overcome this issue, robust versions of these test statistics have been proposed in the statistic literature under model misspecification. In this paper, we address the issue of performing hypothesis testing inference in location-scale models under model misspecification. Monte Carlo simulation experiments are carried out to verify the performance of the robust test statistics, as well as usual test statistics (i.e. non-robust), in the class of location-scale models under model misspecification. The simulation results reveal that the robust tests we propose are more reliable than the usual tests since they lead to an accurate inference. An empirical application to real data is considered for illustrative purposes.

Confidence intervals of the difference between areas under two ROC curves in matched-pair experiments.

In a matched-pair study, when outcomes of two diagnostic tests are ordinal/continuous, the difference between two correlated areas under ROC curves (AUCs) is usually used to compare the overall discriminatory ability of two diagnostic tests. This article considers confidence interval (CI) construction problems of difference between two correlated AUCs in a matched-pair experiment, and proposes 13 hybrid CIs based on variance estimates recovery with the maximum likelihood estimation, Delong's statistic, Wilson score statistic (WS) and WS with continuity correction, the modified Wald statistic (MW) and MW with continuity correction and Agresti-Coull statistic, and three Bootstrap-resampling-based CIs. For comparison, we present traditional parametric and nonparametric CIs. Simulation studies are conducted to assess the performance of the proposed CIs in terms of empirical coverage probabilities, empirical interval widths, and ratios of the mesial noncoverage probabilities to the noncoverage probabilities. Two examples from clinical studies are illustrated by the proposed methodologies. Empirical results evidence that the hybrid Agresti-Coull CI with the empirical estimation (EAC) behaved most satisfactorily because its coverage probability was quite close to the prespecified confidence level with short interval width. Hence, we recommend the usage of the EAC CI in applications.

Statistical Method Based on Bayes-Type Empirical Score Test for Assessing Genetic Association with Multilocus Genotype Data.

Simultaneous testing of multiple genetic variants for association is widely recognized as a valuable complementary approach to single-marker tests. As such, principal component regression (PCR) has been found to have competitive power. We focus on exploring a robust test for an unknown genetic mode of all SNPs, an unknown Hardy-Weinberg equilibrium (HWE) in a population, and a large number of all SNPs. First, we propose a new global test by means of the use of codominant codes for all markers and PCR. The new global test is built on an empirical Bayes-type score statistic for testing marginal associations with each single marker. The new global test gains power by robustly exploiting the Hardy-Weinberg equilibrium in the control population and effectively using linkage disequilibrium among test markers. The new global test reduces to PCR when the genotype for each marker is coded as the number of minor alleles. This connection lends insight into the power of the new global test relative to PCR and some other popular multimarker test methods. Second, we propose a robust test method based on the new global test and the ordinary PCR test built on a prospective score statistic for testing marginal associations with each single marker when the genotype for each marker is coded as the number of minor alleles by taking the minimum p value of these two tests. Finally, through extensive simulation studies and analysis of the association between pancreatic cancer and some genes of interest, we show that the proposed robust test method has desirable power and can often identify association signals that may be missed by existing methods.

Spatial Characteristics and Factors of Truck Accidents

Identifying the causes of truck accidents is very important for efficient traffic safety policies. Thus, previous studies have dealt with human factors, vehicle factors, and environmental factors (road, weather). However, according to a recent research, the spatial characteristics of truck accidents must be considered when analyzing the causes of traffic accidents. Therefore, this study has intended to analyze the spatial characteristics of truck accidents and to derive the spatial factors that would affect traffic accidents. To meet the objectives, this study employed Getis-Ord Gi* Hotspot analysis and Local Score statistics, and set three hypotheses as follows: First, truck accidents show local clustering distribution; Second, individual factories significantly affect truck accidents more than the planned factories; and, Third, the old factories significantly affect truck accidents more than the non-old factories. As a result of testing the hypotheses, this study has found that truck accidents tend to cluster locally, and factories negatively affect truck accidents. Especially, old individual location factories very negatively affect truck accidents.

Quantifying the Predictive Accuracy of a Polygenic Risk Score for Predicting Incident Cancer Cases : Application to the CARTaGENE Cohort.

With the increasing use of polygenic risk scores (PRS) there is a need for adapted methods to evaluate the predictivity of these tools. In this work, we propose a new pseudo-R2 criterion to evaluate PRS predictive accuracy for time-to-event data. This new criterion is related to the score statistic derived under a two-component mixture model. It evaluates the effect of the PRS on both the propensity to experience the event and on the dynamic of the event among the susceptible subjects. Simulation results show that our index has good properties. We compared our index to other implemented pseudo-R2 for survival data. Along with our index, two other indices have comparable good behavior when the PRS has a non-null propensity effect, and our index is the only one to detect when the PRS has only a dynamic effect. We evaluated the 5-year predictivity of an 18-single-nucleotide-polymorphism PRS for incident breast cancer cases on the CARTaGENE cohort using several pseudo-R2 indices. We report that our index, which summarizes both a propensity and a dynamic effect, had the highest predictive accuracy. In conclusion, our proposed pseudo-R2 is easy to implement and well suited to evaluate PRS for predicting incident events in cohort studies.

Students’ knowledge and process skills in learning grade-8 chemistry

Determining the knowledge and skills of students are identified as aspects in enhancing the students’ academic performance in sciences. Using the research instrument composed of test items and process skills checklist, data were gathered from 332 grade 8 students from the seven (7) public high schools in the Division of Santiago City, Philippines to assess their knowledge and science process skills in learning grade 8-Chemistry. Standard score (z-score) and descriptive statistics were used to analyzed the data. It was revealed that the student-respondents’ knowledge belongs to “developing proficiency level” while their process skills were rated as poor in their grade 8-Chemistry subject. In using the z-scores, most of the respondents are partially proficient in their scientific knowledge and skills. Based from the result, specific topics in grade 8 chemistry that needs an intervention material were identified. These intervention materials will be subjected to validation and further assessment. In improving the level of process skills and knowledge, students are encouraged to participate in different chemistry activities and for the teachers to elevate their science instruction and students’ academic performances.