Multivariate Normal Regression Research Articles

대구 경북지역 병원종사자의 직무스트레스가 직무만족도에 미치는 영향에서 자아탄력성의 매개효과

Objectives The purpose of this study is to verify the mediating effect of ego resilience in the relationship between job stress and job satisfaction of hospital workers in the Daegu and Gyeongbuk regions. Methods An online survey was conducted targeting hospital workers working in the Daegu and Gyeongbuk regions from October 8, 2023 to October 15, 2023, and 86 copies were used in the final statistical analysis. The collected data were subjected to reliability analysis, frequency analysis, descriptive statistical analysis, multivariate normal distribution verification, correlation analysis, and regression analysis using SPSS V27.0, and the Sobel Test was performed to verify statistical significance. Results First, job stress of hospital workers in the Daegu and Gyeongbuk regions was found to have a significant negative effect on job satisfaction and ego resilience, and ego resilience was found to have a positive effect on job satisfaction. Second, ego resilience was found to mediate the relationship between job stress and job satisfaction among hospital workers in the Daegu and Gyeongbuk regions. Conclusions Through the results of this study, the relationship between job stress, job satisfaction, and ego resilience of hospital workers in the Daegu and Gyeongbuk regions was verified, and the relationship between major variables was confirmed theoretically and empirically, and key variables that affect hospital workers' job satisfaction were confirmed. It is meaningful in that it can provide basic data for early screening of hospital workers with low levels of job satisfaction and effective intervention by uncovering these factors. It is also significant in that it provided implications for the development of counseling and education programs related to job stress and ego resilience that can increase the job satisfaction of hospital workers in the Daegu and Gyeongbuk regions.

Bayesian profile regression for clustering analysis involving a longitudinal response and explanatory variables.

The identification of sets of co-regulated genes that share a common function is a key question of modern genomics. Bayesian profile regression is a semi-supervised mixture modelling approach that makes use of a response to guide inference toward relevant clusterings. Previous applications of profile regression have considered univariate continuous, categorical, and count outcomes. In this work, we extend Bayesian profile regression to cases where the outcome is longitudinal (or multivariate continuous) and provide PReMiuMlongi, an updated version of PReMiuM, the R package for profile regression. We consider multivariate normal and Gaussian process regression response models and provide proof of principle applications to four simulation studies. The model is applied on budding yeast data to identify groups of genes co-regulated during the Saccharomyces cerevisiae cell cycle. We identify 4 distinct groups of genes associated with specific patterns of gene expression trajectories, along with the bound transcriptional factors, likely involved in their co-regulation process.

A Comparison of Bayesian Multivariate Versus Univariate Normal Regression Models for Prediction

In many moderate dimensional applications we have multiple response variables that are associated with a common set of predictors. When the main objective is prediction of the response variables, a natural question is: do multivariate regression models that accommodate dependency among the response variables improve prediction compared to their univariate counterparts? Note that in this article, by univariate versus multivariate regression models we refer to regression models with a single versus multiple response variables, respectively. We assume that under both scenarios, there are multiple covariates. Our question is motivated by an application in climate science, which involves the prediction of multiple metrics that measure the activity, intensity, severity etc. of a hurricane season. Average sea surface temperatures (SSTs) during the hurricane season have been used as predictors for each of these metrics, in separate univariate regression models, in the literature. Since the true SSTs are yet to be observed during prediction, typically their forecasts from multiple climate models are used as predictors. Some climate models have a few missing values so we develop Bayesian univariate/multivariate normal regression models, that can handle missing covariates and variable selection uncertainty. Whether Bayesian multivariate normal regression models improve prediction compared to their univariate counterparts is not clear from the existing literature, and in this work we try to fill this gap.

Rectangular Confidence Regions and Prediction Regions in Multivariate Calibration

The multivariate calibration problem deals with inference concerning an unknown value of a covariate vector based on an observation on a response vector. Two distinct scenarios are considered in the multivariate calibration problem: controlled calibration where the covariates are non-stochastic, and random calibration where the covariates are random. Under controlled calibration, a problem of interest is the computation of a confidence region for the unknown covariate vector. Under random calibration, the problem is that of computing a prediction region for the covariate vector. Assuming the standard multivariate normal linear regression model, rectangular confidence and prediction regions are derived using a parametric bootstrap approach. Numerical results show that the regions accurately maintain the coverage probabilities. The results are illustrated using examples. The regions currently available in the literature are all ellipsoidal, and this work is the first attempt to derive rectangular regions.

Mixed-type multivariate response regression with covariance estimation.

We propose a new method for multivariate response regression and covariance estimation when elements of the response vector are of mixed types, for example some continuous and some discrete. Our method is based on a model which assumes the observable mixed‐type response vector is connected to a latent multivariate normal response linear regression through a link function. We explore the properties of this model and show its parameters are identifiable under reasonable conditions. We impose no parametric restrictions on the covariance of the latent normal other than positive definiteness, thereby avoiding assumptions about unobservable variables which can be difficult to verify in practice. To accommodate this generality, we propose a novel algorithm for approximate maximum likelihood estimation that works “off‐the‐shelf” with many different combinations of response types, and which scales well in the dimension of the response vector. Our method typically gives better predictions and parameter estimates than fitting separate models for the different response types and allows for approximate likelihood ratio testing of relevant hypotheses such as independence of responses. The usefulness of the proposed method is illustrated in simulations; and one biomedical and one genomic data example.

Bayesian meta-elliptical multivariate regression models with fixed marginals on unit intervals

In this paper, we make use of meta-elliptical copula functions to build a new multivariate distribution with fixed marginal distributions and dependence structure to analyze bounded data. Specifically, we present a flexible p-elliptical multivariate probability distribution in the hypercube p with fixed marginal GF-quantile distributions. We then present some illustrative examples and a meta-elliptical multivariate regression model as a flexible alternative to the multivariate normal regression model on unit intervals. A simulation study and real-life data analysis using a Bayesian framework with the extreme-value quantile functions show the flexibility of the proposed meta-multivariate normal regression model for modeling the observed proportion response variables.

A multivariate normal regression model for survival data subject to different types of dependent censoring

In survival analysis observations are often right censored and this complicates considerably the analysis of these data. Right censoring can have several underlying causes: administrative censoring, loss to follow up, competing risks, etc. The (latent) censoring times corresponding to the latter two types of censoring are possibly related to the survival time of interest, and in that case this should be taken into account in the model. A unifying model is presented that allows these censoring mechanisms in one single model, and that is also able to incorporate the effect of covariates on these times. Each time variable is modeled by means of a transformed linear model, with the particularity that the error terms of the transformed times follow a multivariate normal distribution allowing for non-zero correlations. It is shown that the model is identified and the model parameters are estimated through a maximum likelihood approach. The performance of the proposed method is compared with methods that assume independent censoring using finite sample simulations. The results show that the proposed method exhibits major advantages in terms of reducing the bias of the parameter estimates. However, a strong deviation from normality and/or a strong violation of the homogeneous variance assumption may lead to biased estimates. Finally, the model and the estimation method are illustrated using the analysis of data coming from a prostate cancer clinical trial.

CA125 as a Marker of Heart Failure in the Older Women: Population-Based Analysis.

(1) Background: Cancer antigen 125 (CA125) is a glycoprotein that is expressed by tissue derived from coelomic epithelium in the pleura, peritoneum, pericardium. It has been shown that CA125 concentrations are correlated with NT-proBNP in older people with congestive heart failure (HF). We conducted a study on the association between concentrations of CA125 and NT-proBNP in a population-based cohort of older Polish women. (2) Methods: The current research is sub-study of a large, cross-sectional research project (PolSenior). The study group consisted of 1565 Caucasian women aged 65–102 years. To assess the relationship between CA125 and other variables a stepwise backward multivariate normal and skew-t regression analyses were performed. (3) Results: The median of CA125 concentration was 13.0 U/mL and values over the upper normal range limit (35 U/mL) were observed in 5.1% (n = 79) of the study cohort. The concentration of CA125 was positively related to age, hospitalization for HF and history of atrial fibrillation and chronic obstructive pulmonary disease, levels of NT-proBNP, IL-6, hs-CRP and triglycerides. We found in the multivariate analyses, that increased CA125 levels were independently associated with log10 (IL-6) (β = 11.022), history of hospitalization for HF (β = 4.619), log10 (NT-proBNP) (β = 4.416) and age (β = 3.93 for 10 years). (4) Conclusions: Despite the association between CA125 and NT-proBNP, the usefulness of CA125 for the detection of HF in older women is limited by factors such as inflammatory status and age.

Two-Year Longitudinal Changes in Lower Limb Strength and Its Relation to Loss in Function in a Large Cohort of Patients With Duchenne Muscular Dystrophy.

The main objective of this study was to examine the effect of disease on strength in two functionally important lower limb muscles for a period of 2 yrs in children with Duchene muscular dystrophy. Seventy-seven Duchene muscular dystrophy children participated in this study. Plantar flexors, knee extensors, strength, and performance on timed tests (6-min walk, 4-stairs, 10-m walk, supine-up) were assessed yearly for 2 yrs. Multivariate normal regression was used to assess changes in strength over time in the Duchene muscular dystrophy group. Spearman correlations were computed to examine relationship between strength and function. Normalized plantar flexor and knee extensor strength showed a significant decrease (P < 0.05) over 2 yrs, with larger declines in knee extensor. At baseline, knee extensor strongly correlated with performance on timed tests. However, plantar flexor strength was found to be a stronger predictor of loss in ambulatory function. Modest correlations (r = 0.19-0.34) were found between the decline in strength and functional performance over 2 yrs. This study describes the loss of lower limb strength in a large cohort of Duchene muscular dystrophy children for 2 yrs. The findings support that lower limb strength alone cannot account for the decline in performance on functional tests, and the role of other contributing factors, such as compensatory strategies, should be considered.

Modeling a Simultaneous Confidence Band of the Mean Value of Multiple Responses with a Rectangular Domain for Predictors

The problem is considered of modeling simultaneous confidence intervals for the mean values of multiple responses in a linear multivariate normal regression model with predictor variables defined in intervals. To solve it, a numerical way of calculating the critical value that determines the simultaneous confidence interval of a given level is used. Simultaneous confidence intervals are numerically modelled and analyzed by comparison for regression, the mean value of multiple responses, and individual observation.

Effects of minor household interventions to block draughts on social housing temperatures: a before and after study

ABSTRACTHalf of New Zealand’s renters report damp or mould problems with their homes, which can have negative health implications. Tenants in a newly upgraded social housing complex complained of being cold. Sealing strips around doors and baffles in rangehoods were installed. This exploratory study’s objectives were to determine: (1) whether the interventions influenced indoor temperature, (2) the extent to which indoor temperature changed and (3) benefits to the tenants. The before-and-after rapid response study was conducted in five social housing units. Indoor temperature was subjectively and objectively measured. Using multivariate normal linear regression, units were found to be on average 1.36°C warmer post-intervention after adjusting for outdoor temperature. Tenants’ daily diary entries also claimed units were warmer post-intervention. Simple minor interventions to block draughts made a relatively big difference to indoor temperature and comfort of those living there. Such interventions are worthwhile, especially when housing is tenanted by vulnerable populations.

Confidence prediction of the mean values of multiple observations

The confidence prediction of the mean value ofmultiple responses in a linear multivariate normal regression model is considered. In order to solve it, confidence intervals of the mean value of multiple responses and its predicted value are obtained. They are numerically modeled and analyzed in comparison with known analogues for regression and individual response.

Likelihood Based Finite Sample Inference for Singly Imputed Synthetic Data Under the Multivariate Normal and Multiple Linear Regression Models

In this paper we develop likelihood-based finite sample inference based on singly imputed partially synthetic data, when the original data follow either a multivariate normal or a multiple linear regression model. We assume that the synthetic data are generated by using the plug-in sampling method, where unknown parameters in the data model are set equal to observed values of their point estimators based on the original data, and synthetic data are drawn from this estimated version of the model. Empirical studies are presented to show that the proposed methods do indeed perform as the theory predicts, and to compare the proposed methods for singly imputed synthetic data with the combining rules that are used to analyze multiply imputed partially synthetic data. Some theoretical comparisons between singly and multiply imputed partially synthetic data inference are also provided. A data analysis example and disclosure risk evaluation of singly and multiply imputed partially synthetic data is presented based on public use data from the Current Population Survey. We discuss the specific conditions under which the proposed methodology will yield valid inference, and evaluate the performance of the methodology when certain conditions do not hold. We outline some ways to extend the proposed methodology for certain scenarios where the required set of conditions do not hold.

Studies on ageing and the severity of radiographic joint damage in rheumatoid arthritis.

IntroductionThe western population is ageing. It is unknown whether age at diagnosis affects the severity of Rheumatoid Arthritis (RA), we therefore performed the present study.Method1,875 RA-patients (7,219 radiographs) included in five European and North-American cohorts (Leiden-EAC, Wichita, Umeå, Groningen and Lund) were studied on associations between age at diagnosis and joint damage severity. In 698 Leiden RA-patients with 7-years follow-up it was explored if symptom duration, anti-citrullinated-peptide-antibodies (ACPA), swollen joint count (SJC) and C-reactive-protein (CRP) mediated the association of age with joint damage. Fifty-six other RA-patients of the EAC-cohort underwent baseline MRIs of wrist, MCP and MTP-joints; MRI-inflammation (RAMRIS-synovitis plus bone marrow edema) was also evaluated in mediation analyses. Linear regression and multivariate normal regression models were used.ResultsAnalysis on the five cohorts and the Leiden-EAC separately revealed 1.026-fold and 1.034-fold increase of radiographic joint damage per year increase in age (β=1.026, 1.034, both p<0.001); this effect was present at baseline and persisted over time. Age correlated stronger with baseline erosion-scores compared to joint space narrowing (JSN)-scores (r=0.38 versus 0.29). Symptom duration, ACPA, SJC and CRP did not mediate the association of age with joint damage severity. Age was significantly associated with the MRI-inflammation-score after adjusting for CRP and SJC (β=1.018, p=0.027). The association of age with joint damage (β=1.032, p=0.004) decreased after also including the MRI-inflammation-score (β=1.025, p=0.021), suggesting partial mediation.ConclusionRA-patients presenting at higher age have more severe joint damage; this might be partially explained by more severe MRI-detected inflammation at higher age.Electronic supplementary materialThe online version of this article (doi:10.1186/s13075-015-0740-0) contains supplementary material, which is available to authorized users.

Inference for Singly Imputed Synthetic Data Based on Posterior Predictive Sampling under Multivariate Normal and Multiple Linear Regression Models

Likelihood-based finite sample inference for singly imputed synthetic data generated via posterior predictive sampling is developed in this paper for multivariate normal and multiple linear regression models. Currently available methodology for drawing valid inference on population parameters using synthetic data is based on concepts of multiple imputation for missing data, and therefore requires the release of multiple synthetic datasets. The methodology developed in this paper demonstrates that, contrary to the usual belief, valid inference about meaningful model parameters can indeed be drawn based on a singly imputed synthetic dataset under the multivariate normal and multiple linear regression models, by fully utilizing the model structure.

Multiple Imputation to Correct for Nonresponse Bias: Application in Non-communicable Disease Risk Factors Survey.

Background:This study was carried out to use multiple imputation (MI) in order to correct for the potential nonresponse bias in measurements related to variable fasting blood glucose (FBS) in non-communicable disease risk factors survey conducted in Iran in 2007.Methods:Five multiple imputation methods as bootstrap expectation maximization, multivariate normal regression, univariate linear regression, MI by chained equation, and predictive mean matching were applied to impute variable fasting blood sugar. To make FBS consistent with normality assumption natural logarithm (Ln) and Box-Cox (BC) transformations were used prior to imputation. Measurements from which we intended to remove nonresponse bias included mean of FBS and percentage of those with high FBS.Results:For mean of FBS results didn’t considerably change after applying MI methods. Regarding the prevalence of high blood sugar all methods on original scale tended to increase the estimates except for predictive mean matching that along with all methods on BC or Ln transformed data didn’t change the results.Conclusions:FBS-related measurements didn’t change after applying different MI methods. It seems that nonresponse bias was not an important challenge regarding these measurements. However use of MI methods resulted in more efficient estimations. Further studies are encouraged on accuracy of MI methods in these settings.

Oxidative stress and inflammation associated with decreased fibrinolysis as an early marker for peripheral vascular disease stratification: A clinical study

Abstract Background Peripheral vascular disease may manifest as either arterial stenosis or calcification of the arterial wall. Arterial stenosis is characterized by a lowered ankle-brachial-pressure index (ABPI), whereas calcified arteries lead to an increased ABPI. The current study investigates whether inflammatory and oxidative stress markers differ in low versus high ABPI groups suggesting different biochemical processes. Methods Eighty-seven patients attending the diabetes complications clinic agreed to the study. Participants were divided into a low ( 1.23) ABPI tertile groups and compared for traditional and emerging biomarker differences. A clinical history and demographic data were obtained. Emerging biomarkers included C-reactive protein, interleukin-6, 8-hydroxy deoxy-guanosine, D-dimer, reduced glutathione and malondialdehyde. Data was analyzed using a Student T-test with significance set at 0.05. A multivariate normal linear regression model was applied to determine the contributions of traditional and emerging biomarkers to the classification of low and high ABPI. Results No differences were observed between the two groups for the traditional biomarkers but D-dimer (p Discussion A decreased inflammatory component with increased oxidative stress is more likely to lead to calcification of the arteries and a higher ABPI, despite normal BGL, HbA1c and cholesterol profile. Our study shows that emerging biomarkers provide a sound basis for differentiating pathophysiological processes associated with low and high ABPI. Traditional biomarkers showed a high accuracy for identification of low ABPI in our model but failed to do better than chance for identification of high ABPI, suggesting different pathophysiological pathways that include oxidative stress and inflammatory components. Clinically, validation of novel and more comprehensive risk factors for PVD sheds light on the etiology of the disease and mechanics of progression toward better preventative care, early detection and targeted drug delivery.

A Bayesian method for analyzing combinations of continuous, ordinal, and nominal categorical data with missing values

From a Bayesian perspective, we propose a general method for analyzing a combination of continuous, ordinal (including binary), and categorical/nominal multivariate measures with missing values. We assume multivariate normal linear regression models for multivariate continuous measures, multivariate probit models for correlated ordinal measures, and multivariate multinomial probit models for multivariate categorical/nominal measures. Then we assume a multivariate normal linear model on the continuous vector comprised of continuous variables and those underlying normal variables for ordinal variables from multivariate probit models and for categorical variables from multinomial probit models. We develop a Markov chain Monte Carlo (MCMC) algorithm to estimate unknown parameters including regression parameters, cut-points for ordinal data from the multivariate probit models, and the covariance matrix encompassing both continuous variables and the underlying normal latent variables. Combining the continuous variables and the normal latent variables allows us to model combinations of continuous, ordinal, and categorical multivariate data simultaneously. The framework incorporates flexible priors for the covariance matrix, provides a foundation for inference about the underlying covariance structure, and imputes missing data where needed. The method is illustrated through simulated examples and two real data applications.

Statistical Prediction of Integrated Kinetic Energy in North Atlantic Tropical Cyclones

Abstract Integrated kinetic energy (IKE) is a useful quantity that measures the size and strength of a tropical cyclone wind field. As a result, it is inherently related to the destructive potential of these powerful storms. In most current operational settings, there are limited resources designed to assess the IKE of a tropical cyclone because storm track and maximum intensity are typically prioritized. Therefore, to complement existing forecasting tools, a statistical scheme is created to project fluctuations of IKE in North Atlantic tropical cyclones for several forecast intervals out to 72 h. The resulting scheme, named Statistical Prediction of Integrated Kinetic Energy (SPIKE), utilizes multivariate normal regression models trained on environmental and storm-related predictors from all North Atlantic tropical cyclones occurring from 1990 to 2011. During this training interval, SPIKE outperforms persistence and is capable of explaining more than 80% of observed variance in total IKE values at a forecast interval of 12 h, trailing down to just below 60% explained variance at an interval of 72 h. The skill of the SPIKE model is evaluated further using bootstrapping exercises in order to gauge the predictive abilities of the statistical scheme. In addition, the performance of the SPIKE model is also evaluated for the 2012 Atlantic hurricane season, which notably falls outside of the training interval. Ultimately, the validation exercises return shared variance scores similar to those found in the training exercises, serving as a proof of concept that the SPIKE model can be used to project IKE values when given accurate predictor data.

Central tolerance regions and reference regions for multivariate normal populations

Reference intervals and regions are widely used to identify the measurement range expected from a reference population. Such regions capture the central part of the population, and have potential applications in the field of laboratory medicine. Furthermore, the uncertainty in an estimated reference region can be assessed using a central tolerance region, namely, a region that will contain the population reference region, with a specified confidence level. The construction of a central tolerance region is investigated in this article for a multivariate normal population, and also for a multivariate normal linear regression model. A theoretical framework is developed that will facilitate the numerical computation of the tolerance factor. The performance of a prediction region is also evaluated, in terms of capturing the central part of the population, and the prediction region is found to be unsatisfactory. Some examples from laboratory medicine are used to illustrate the results.