Violation Of Normality Assumption Research Articles

The selection of statistical models for reporting count outcomes and intervention effects in brief alcohol intervention trials: A review and recommendations.

Understanding the efficacy and relative effectiveness of a brief alcohol intervention (BAI) relies on obtaining a credible intervention effect estimate. Outcomes in BAI trials are often count variables, such as the number of drinks consumed, which may be overdispersed (i.e., greater variability than expected based on a given model) and zero-inflated (i.e., greater probability of zeros than expected based on a given model). Ignoring such distribution characteristics can lead to biased estimates and invalid statistical conclusions. In this critical review, we identified and reviewed 64 articles that reported count outcomes from a systematic review of BAI trials for adolescents and young adults from 2013 to 2018. Given many statistical models to choose from when analyzing count outcomes, we reviewed the models used and reporting practices in the BAI trial literature. A majority (61.3%) of analyses with count outcomes used linear models despite violations of normality assumptions; 75.6% of outcome variables demonstrated clear overdispersion. We provide an overview of available count models (Poisson, negative binomial, zero-inflated or hurdle, and marginalized zero-inflated Poisson regression) and formulate practical guidelines for reporting outcomes of BAIs. We provide a visual step-by-step decision guide for selecting appropriate statistical models and reporting results for count outcomes. We list accessible resources to help researchers select an appropriate model with which to analyze their data. Recent advances in count distribution-based models hold promise for evaluating count outcomes to gauge the efficacy and effectiveness of BAIs and identify critical covariates in alcohol epidemiologic research. We recommend that researchers report the distributional properties of count outcomes, such as the proportion of zero counts, and select an appropriate statistical analysis for count outcomes using the provided decision tree. By following these recommendations, future research may yield more accurate, transparent, and reproducible results.

Applying Structural Equation Modelling to Understand the Implementation of Social Distancing in the Professional Lives of Healthcare Workers.

This study, based on the normalization process theory (NPT), explores the implementation of nonpharmaceutical interventions (NPIs)-specifically social distancing (SD)-in the professional lives of healthcare workers in three Pakistani hospitals. We collected and analysed health workers' data using partial least squares structural equation modelling (PLS-SEM) and assessed the policy implications of the results. Violations of normality assumptions in the quantitative data and the need for scores of independent variables for follow-up analysis guided the researchers to adopt a structural equation modelling process that involved a stepwise evaluation process for convergent validity, individual item validity, discriminant validity, the structural model relationship, and overall model fitness. Theoretical constructs coherence, cognitive participation, collective action, and reflexive monitoring were found to influence the normalization of SD. The results show that SD was normalized in the professional lives of healthcare workers through strong collective action (resources required) and reflexive monitoring (appraisal) but weak cognitive participation (actors' engagement) and coherence (sense-making). Low and middle-income countries (LMICs) should work more on actors' sense-making and engagement in dealing with healthcare crises that require SD. The research findings can aid policy institutions in better understanding the loopholes in the implementation process and making better policies.

Robustified extreme learning machine regression with applications in outlier-blended wind-speed forecasting

Wind energy is a core sustainable source of electric power, and accurate wind-speed forecasting is pivotal to enhancing the power stability, efficiency, and utilization. The existing forecasting methods are still limited by the influence of outliers and the modelling difficulties caused by complex features in wind speed series. This paper proposes a new wind speed forecasting system based on a designed adaptive robust extreme learning machine (ARELM) model and signal decomposition algorithms. Firstly, the ARELM is designed to sufficiently lessen the violation of normality assumptions and contamination by outliers. ARELM takes an adaptive scaled Huber’s loss as its objective function, which can limit the influence of outliers and adaptively determine an appropriate mixture distribution of normal distribution and Laplace distribution at the same time. Secondly, the empirical mode decomposition (EMD) method and its improved methods (EEMD, CEEMD and CEEMDAN) are introduced to our wind-speed forecasting system, where the low-frequent sub-series are modelled by basic ELM and the high-frequent ones are modelled by ARELM. This can decompose the modelling complex wind speed series into modelling several simple sub-series and reduce the difficulty of modelling. Experimental results show that our combined forecasting system, ELM-ARELM, obtains up to 78% improvement in forecasting performance comparing with the methods using general Huber’s loss and other comparison methods, which show the superiority of the adaptive scaled Huber’s loss. The error indexes (MAE and RMSE) by the proposed system, which are (0.25, 0.34), (0.32, 0.45) and (0.38, 0.53) for 5 min head, 15 min ahead and 25 min ahead experiments respectively, demonstrate the effectiveness of decomposition methods on improving accuracy of wind speed prediction.

Semi-Nonparametric Generalized Autoregressive Conditional Heteroscedasticity Model with Application to Bitcoin Volatility Estimation

This study raises the problem of modeling conditional volatility under the random shocks’ normality assumption violation. To obtain more accurate esti ma tes of GARCH process parameters and conditional volatilities, we propose two semi-nonparametric GARCH models. The implementation of the proposed methods is based on an adaptation of the [Gallant, Nychka, 1987] semi-nonparametric method to the family of GARCH models. The approach provides a flexible estimation procedure by approximating the unknown density of random shocks both using po­lynomials (PGN-GARCH) and splines (SPL-GARCH). To study the properties of the obtained estimators and compare them with alternatives, we conducted an ana­lysis of simulated data considering forms of distributions other than normal. As a result, statistical evidence was found in favor of the significant advantage of the proposed methods over the classical GARCH model and some other counterparts introduced earlier in the literature. Further, the proposed PGN-GARCH and SPL-GARCH models were applied to study Bitcoin conditional volatility dynamics. Du­ring the analysis, we found statistical evidence that Bitcoin distribution of shocks in returns differs from normal. Probably due to this reason the proposed SPL-GARCH model was able to demonstrate an advantage over alternative GARCH models according to the information criteria.

Application of Linear Discriminant Model to Evaluate the Association Between Milk Production, Reproductive Performance, and Calving Season in Dairy Cattle

This study was aimed to determine the performance of linear discriminant analysis (LDA) for differentiation between seasons of calving on the basis of305day- milk yield, fat %, protein %, days open (DO), days to first insemination (DFI), and number of services per conception. By considering the assumption of this method, a random sample was selected from the animals being represented by all explanatory variables. The discrimination between seasons of calving was depended on the significance of coefficients, classification rate, in addition to the group centroids. Results showed that LDA method selected 305day-milk yield (kg), days open (DO), days to first insemination and number of services per conception, as the significant (P < 0.05) contributors for data classification. The total variance explained by 2 functions was 79.2% and 15.9%, respectively. So, the 1st function can do well in discrimination process than the 2ndone. The percentage of correct classification was 64.6%. In conclusion, LDA can be used effectively for classification of calving seasons, even with violation of normality assumption.

A confirmatory factor analysis of the knowledge, attitude and practice questionnaire towards prevention of respiratory tract infections during Hajj and Umrah

BackgroundRespiratory tract infections are one of the common infection associated with Hajj pilgrimage that is of great public health and global concern. This study is aimed at determining the factor structure of the knowledge, attitude, and practice questionnaire for the prevention of respiratory tract infections during Hajj by confirmatory factor analysis (CFA).MethodsA multistage cluster sampling method was conducted on Malaysian Umrah pilgrims during the weekly Umrah orientation course. A total of 200 Umrah pilgrims participated in the study. The knowledge, attitude and practice (KAP) questionnaire was distributed to pilgrims at the beginning of the orientation and retrieved immediately at the end of the orientation. Data analysis was done using R version 3.5.0 after data entry into SPSS 24. The robust maximum likelihood was used for the estimation due to the multivariate normality assumption violation. A two-factor model was tested for measurement model validity and construct validity for each of the attitude and practice domains.ResultsCFA of a 25-item in total, the two-factor model yielded adequate goodness-of-fit values. The measurement model also showed good convergent and discriminant validity after model re-specification. A two-factor model was tested for measurement model validity and construct validity for each of the attitude and practice domains. The result also showed a statistically significant value (p < 0.001) with χ2 (df) values of 76.8 (43) and 121 (76) for attitude and practice domains, respectively.ConclusionThe KAP questionnaire was proven to have a valid measurement model and reliable constructs. It was deemed suitable for use to measure the KAP of Hajj and Umrah pilgrims towards the prevention for all respiratory tract infections.

Comparison of random‐effects meta‐analysis models for the relative risk in the case of rare events: A simulation study

Pooling the relative risk (RR) across studies investigating rare events, for example, adverse events, via meta-analytical methods still presents a challenge to researchers. The main reason for this is the high probability of observing no events in treatment or control group or both, resulting in an undefined log RR (the basis of standard meta-analysis). Other technical challenges ensue, for example, the violation of normality assumptions, or bias due to exclusion of studies and application of continuity corrections, leading to poor performance of standard approaches. In the present simulation study, we compared three recently proposed alternative models (random-effects [RE] Poisson regression, RE zero-inflated Poisson [ZIP] regression, binomial regression) to the standard methods in conjunction with different continuity corrections and to different versions of beta-binomial regression. Based on our investigation of the models' performance in 162 different simulation settings informed by meta-analyses from the Cochrane database and distinguished by different underlying true effects, degrees of between-study heterogeneity, numbers of primary studies, group size ratios, and baseline risks, we recommend the use of the RE Poisson regression model. The beta-binomial model recommended by Kuss (2015) also performed well. Decent performance was also exhibited by the ZIP models, but they also had considerable convergence issues. We stress that these recommendations are only valid for meta-analyses with larger numbers of primary studies. All models are applied to data from two Cochrane reviews to illustrate differences between and issues of the models. Limitations as well as practical implications and recommendations are discussed; a flowchart summarizing recommendations isprovided.

Effects of Cross-loadings on Determining the Number of Factors to Retain

ABSTRACT In exploratory factor analysis (EFA), cross-loadings frequently occur in empirical research, but its effects on determining the number of factors to retain are seldom known. In this paper, we analyzed whether and how cross-loadings affected the performance of the parallel analysis (PA), the empirical Kaiser criterion (EKC), the likelihood ratio test (LRT), the comparative fit index (CFI), the Tucker-Lewis index (TLI), and the root mean square error of approximation (RMSEA) in determining the number of factors to retain. A large-scale simulation study was also conducted. A few conclusions can be drawn: (1) overall, PA provides the most accurate performance, especially when data are non-normally distributed; (2) cross-loadings noticeably affect the performance of PA, CFI, and TLI with different patterns, and they virtually have no effect on EKC, LRT, and RMSEA; (3) no method is immune to the sizable detrimental effect of normality assumption violation. Several recommendations were provided.

Сравнение точности оценок параметрических и полупараметрических методов коррекции многомерного смещения отбора

This article is devoted to the comparative analysis of parametric and semiparametric sample selection models with two selection equations. Comparison has been conducted on simulated data under different random errors distributional assumptions: student, beta and mixture of normal. The results suggest that for student and beta distributions parametric models’ estimates are more or equally accurate as semiparametric. However, former methods provide more accurate estimates under mixture distribution case. Therefore, parametric sample selection model estimators seem to be robust to violations of normality assumption in terms of tails thickness and asymmetry but fail to account for bimodality as good as their semiparametric counterparts

Testing conditional independence and homogeneity in large sparse three‐way tables using conditional distance covariance

AbstractConditional independence test for three‐way contingency tables is a classic problem in multivariate statistics. Traditional methods including Cochran–Mantel–Haenszel test and conditional mutual information test are powerful under sufficient sample size; however, in sparse settings, these methods may fail to detect the association due to the violation of normality assumption. In this paper, we propose to use a recently developed measure, namely, conditional distance covariance, to test conditional independence in large sparse R×C×K tables. We derive the explicit formula of conditional distance covariance between three categorical variables, and we suggest a maximum‐type statistic for hypothesis testing. In addition, we introduce a new statistic based on distance covariance to test homogeneity in three‐way tables. We conduct an extensive simulation study to illustrate the superiority of our method to the existing ones.

Sequential Testing in Reliability and Validity Studies With Repeated Measurements per Subject

In medical, health, and sports sciences, researchers desire a device with high reliability and validity. This article focuses on reliability and validity studies with n subjects and m &amp;ge;2 repeated measurements per subject. High statistical power can be achieved by increasing n or m, and increasing m is often easier than increasing n in practice unless m is too high to result in systematic bias. The sequential probability ratio test (SPRT) is a useful statistical method which can conclude a null hypothesis H0 or an alternative hypothesis H1 with 50% of the required sample size of a non-sequential test on average. The traditional SPRT requires the likelihood function for each observed random variable, and it can be a practical burden for evaluating the likelihood ratio after each observation of a subject. Instead, m observed random variables per subject can be transformed into a test statistic which has a known sampling distribution under H0 and under H1. This allows us to formulate a SPRT based on a sequence of test statistics. In this article, three types of study are considered: reliabilityof a device, reliability of a device relative to a criterion device, and validity of a device relative to a&amp;nbsp; criterion device. Using SPRT for testing the reliability of a device, for small m, results in an average sample size of about 50% of the fixed sample size for a non-sequential test. For comparing a device to criterion, the average sample size approaches to 60% approximately as m increases. The SPRT tolerates violation of normality assumption for validity study, but it does not for reliability study.

Small, Prospective, Observational, Pilot Study in Patients with Severe Asthma after Discontinuation of Omalizumab Treatment

PurposeOmalizumab has demonstrated clinical efficacy in severe allergic asthma by reducing exacerbation rates and increasing quality of life. However, data concerning its sustained effect after treatment discontinuation are still needed. Methods: This analysis was an observational pilot study (simple within-subjects design) of 12 patients experiencing severe asthma, treated with omalizumab, for 1 year after treatment discontinuation. We prospectively analyzed clinical measurements (pulmonary functions, inhaled corticosteroid [ICS] doses, Asthma Control Test [ACT] scores, skin prick test [SPT] positivity, fraction of exhaled nitric oxide, and exacerbation rates) and laboratory test results (eosinophils and total immunoglobulin E levels) at the time of discontinuation and 6 and 12 months thereafter. Baseline data (before the treatment period; range, 11–61 months) were collected retrospectively. The treatment effect until discontinuation was calculated. To determine its persistence, repeated measures were compared with baseline levels and analyzed by using a general linear model for repeated measures or the Friedman ANOVA, and χ2 tests in case of normality assumption violation or frequencies. Post hoc analysis was applied by using a simple or repeated contrasts analysis or Wilcoxon signed rank test with Bonferroni correction. Findings: We proved a significant reduction in ICS doses and SPT reactivity and an increase in ACT score during the retrospective treatment phase. Moreover, persistence of these statistically significant effects was recorded 6 months after treatment discontinuation. ACT score and ICS doses (but not SPT reactivity) remained improved for 12 months after discontinuation of omalizumab treatment. ImplicationsOmalizumab treatment exhibited sustained treatment benefit after its discontinuation for patients experiencing severe allergic asthma.

Assessing the competitiveness of Matera and the Basilicata Region (Italy) ahead of the 2019 European Capital of Culture

Cities/regions are increasingly using events to aid social/economic development. The European Capital of Culture promotes urban management and economic production using culture to drive social legacies, job creation and civic repositioning. This paper aims to understand how Matera and Basilicata’s residents perceive destination competitiveness ahead of the 2019 European Capital of Culture. This paper adapts the Integrated Model of Destination Competitiveness and suggests a new determinant to understand resident perceptions. This paper contributes a new determinant to consider in competitiveness research: social conditions to improve local wellbeing. Two hundred respondents identify strengths/weaknesses of each competitiveness determinant. The results presented in this study display sample mean values and standard deviations for each indicator, as well as Wilcoxon test statistic (z). Competitive indicators are those showing means above 4.0. Descriptive and inferential analyses using SPSS 17 show strengths/weaknesses comparing Matera (city) and Basilicata (region) with similarities and differences outlined to consider both urban and regional perspectives and differences. For the data analysis, Wilcoxon paired signed rank test displays differences in the competitiveness factors between Matera and Basilicata. Wilcoxon (a nonparametric alternative to paired sample t-test) was performed since the data distribution was left skewed and Kolmogorov–Smirnov statistic indicates violation of normality assumption. Results show the majority of inherited, created and supporting resources are competitive, as well as image and social conditions; however, management and organisation needs improvement. It is essential that European Capital of Culture hosts have long-term competitive strategies in place to strengthen urban and regional capacity when delivering diverse cultural programmes, at present, and into the future. This study offers insight before the 2019 European Capital of Culture to inform planners and policymakers ahead of the event and offers consideration and discussion of social impacts and the need to gain such insight in competitiveness research going forward.

Robust joint score tests in the application of DNA methylation data analysis

BackgroundRecently differential variability has been showed to be valuable in evaluating the association of DNA methylation to the risks of complex human diseases. The statistical tests based on both differential methylation level and differential variability can be more powerful than those based only on differential methylation level. Anh and Wang (2013) proposed a joint score test (AW) to simultaneously detect for differential methylation and differential variability. However, AW’s method seems to be quite conservative and has not been fully compared with existing joint tests.ResultsWe proposed three improved joint score tests, namely iAW.Lev, iAW.BF, and iAW.TM, and have made extensive comparisons with the joint likelihood ratio test (jointLRT), the Kolmogorov-Smirnov (KS) test, and the AW test. Systematic simulation studies showed that: 1) the three improved tests performed better (i.e., having larger power, while keeping nominal Type I error rates) than the other three tests for data with outliers and having different variances between cases and controls; 2) for data from normal distributions, the three improved tests had slightly lower power than jointLRT and AW. The analyses of two Illumina HumanMethylation27 data sets GSE37020 and GSE20080 and one Illumina Infinium MethylationEPIC data set GSE107080 demonstrated that three improved tests had higher true validation rates than those from jointLRT, KS, and AW.ConclusionsThe three proposed joint score tests are robust against the violation of normality assumption and presence of outlying observations in comparison with other three existing tests. Among the three proposed tests, iAW.BF seems to be the most robust and effective one for all simulated scenarios and also in real data analyses.

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering–at the same time–dimension reduction and model-based clustering. The high prevalence of spurious solutions and the disturbing effects of outlying observations in maximum likelihood estimation may cause biased or misleading inferences. Restrictions for the component covariances are considered in order to avoid spurious solutions, and trimming is also adopted, to provide robustness against violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology.

Effect of Environmental Factors on Obesity: A Quantile Regression Approach

Objectives: This study explored associations of environmental factors with percent trunk fat (PTF) and body mass index (BMI), using quantile regression to explain variability in these traits at percentiles of the distributions. Methods: Using a sample of 1695 adults from Newfoundland and Labrador, multiple and quantile regression models were used to analyse the significance of environmental factors on the average population and upper percentiles of the BMI and PTF distributions. Results: Higher physical activity was associated with significantly lower PTF and BMI in the average population and upper percentiles, regardless of age. Both genders in percentiles closer to the median of PTF had more benefit with increased physical activity compared to higher percentiles. Interestingly, adults in higher percentiles of BMI distribution seem to benefit more with increased physical activity compared to percentiles closer to the median. Conclusion: Using quantile regression as a robust approach toward violation of normality assumptions and outliers, variations in PTF and BMI for individuals across upper percentiles of the distributions based on some lifestyle factors were described. This method may be used to estimate the impact of certain lifestyle on different percentiles of BMI and PTF, rather than average population.

Improved best linear unbiased estimators for the simple linear regression model using double ranked set sampling schemes

ABSTRACTIn this paper, we consider the best linear unbiased estimators (BLUEs) based on double ranked set sampling (DRSS) and ordered DRSS (ODRSS) schemes for the simple linear regression model with replicated observations. We assume three symmetric distributions for the random error term, i.e., normal, Laplace and some scale contaminated normal distributions. The proposed BLUEs under DRSS (BLUEs-DRSS) and ODRSS (BLUEs-ODRSS) are compared with the BLUEs based on ordered simple random sampling (OSRS), ranked set sampling (RSS), and ordered RSS (ORSS) schemes. These estimators are compared in terms of relative efficiency (RE), RE of determinant (RED), and RE of trace (RET). It is found that the BLUEs-ODRSS are uniformly better than the BLUEs based on OSRS, RSS, ORSS, and DRSS schemes. We also compare the estimators based on imperfect RSS (IRSS) schemes. It is worth mentioning here that the BLUEs under ordered imperfect DRSS (OIDRSS) are better than their counterparts based on IRSS, ordered IRSS (OIRSS), and imperfect DRSS (IDRSS) methods. Moreover, for sensitivity analysis of the BLUEs, we calculate REs and REDs of the BLUEs under the assumption of normality when in fact the parent distribution follows a non normal symmetric distribution. It turns out that even under violation of normality assumptions, BLUEs of the intercept and the slope parameters are found to be unbiased with equal REs under each sampling scheme. It is also observed that the BLUEs under ODRSS are more efficient than the existing BLUEs.

Control charts for flexible and multi-variety production systems

This study presents two new proposals of self-start statistical process control procedures for implementing quality control charts in mass customized production environments. Mass customization is characterized by high variety and/or low production volumes, or by current production strategies that increase the necessity of flexibility. The proposed approaches consider that the quality characteristic under monitoring is the same among the items, allowing the possibility of different averages and standard deviations for different products into the series. Analysis of the proposed approaches include assumption violations and the comparison of the new approaches to a Phase I–Phase II residual control chart, as benchmark. Simulation results show that one of the proposed approaches ties in performance with the benchmark, and the other can produce faster detection of deviations from the process mean, both without the need of a Phase I – retrospective analysis, thus increasing suitability for application in real environments. Also, the proposed approaches are made to handle with unitary production lots as well. Analysis performed in an extensive simulation procedure presents that normality assumption violation (with higher asymmetry) has the most degenerative effect on all tested control charts. The study also shown decreasing in performance on scenarios that violated the independence of the observations assumption.

Robust Bayesian analysis for autoregressive models

Abstract Time series data sometimes show violation of normal assumptions. For cases wherethe assumption of normality is untenable, more exible models can be adopted toaccommodate heavy tails. The exponential power distribution (EPD) is considered aspossible candidate for errors of time series model that may show violation of normalassumption. Besides, the use of exible models for errors like EPD might be able toconduct the robust analysis. In this paper, we especially consider EPD as the exibledistribution for errors of autoregressive models. Also, we represent this distribution asscale mixture of uniform and this form enables ecient Bayesian estimation via Markovchain Monte Carlo (MCMC) methods.Keywords: Autoregressive model, exponential power distribution, Gibbs sampler, ro-bustness. 1. Introduction Real data often show violation of normal assumptions. Heavy-tailed distributions are fre-quently encountered in empirical studies. For cases where the assumption of normality isuntenable, more exible models can be adopted to accommodate heavy tails. The exponen-tial power distribution (EPD) is considered as possible candidate for errors of time seriesmodel that may show violation of normal assumption. Besides, the use of exible modelsfor errors like EPD might be able to conduct the robust analysis. An exponential powerdistribution had been studied by Box and Tiao (1992) in the context of robustness studies.The exponential power density is given by (1.1)f(xj;˙;p) =12p

A robust factor analysis model using the restricted skew- $$t$$ t distribution

Factor analysis is a classical data-reduction technique that seeks a potentially lower number of unobserved variables that can account for the correlations among the observed variables. This paper presents an extension of the factor analysis model, called the skew-\(t\) factor analysis model, constructed by assuming a restricted version of the multivariate skew-\(t\) distribution for the latent factors and a symmetric \(t\)-distribution for the unobservable errors jointly. The proposed model shows robustness to violations of normality assumptions of the underlying latent factors and provides flexibility in capturing extra skewness as well as heavier tails of the observed data. A computationally feasible expectation conditional maximization algorithm is developed for computing maximum likelihood estimates of model parameters. The usefulness of the proposed methodology is illustrated using both simulated and real data.