Gaussian Regression Model Research Articles

Examining Factors That Affect Movie Gross Using Gaussian Copula Marginal Regression

In this research, we investigate the relationship between a movie’s gross and its budget, year of release, season of release, genre, and rating. The movie data used in this research are severely skewed to the right, resulting in the problems of nonlinearity, non-normal distribution, and non-constant variance of the error terms. To overcome these difficulties, we employ a Gaussian copula marginal regression (GCMR) model after adjusting the gross and budget variables for inflation using a consumer price index. An analysis of the data found that year of release, budget, season of release, genre, and rating were all statistically significant predictors of movie gross. Specifically, one unit increases in budget and year were associated with an increase in movie gross. G movies were found to gross more than all other kinds of movies (PG, PG-13, R, and Other). Movies released in the fall were found to gross the least compared to the other three seasons. Finally, action movies were found to gross more than biography, comedy, crime, and other movie genres, but gross less than adventure, animation, drama, fantasy, horror, and mystery movies.

Effect of Socio-Economic Status on Perioperative Outcomes After Robotic-Assisted Pulmonary Lobectomy

Background: Lower socioeconomic status (SES) has been correlated with poor survival rates and surgical outcomes following lung cancer resection. This study sought to determine whether this disparity exists perioperatively in lung cancer patients following robotic-assisted video-thoracoscopic pulmonary lobectomy. Methods: We retrospectively reviewed 447 consecutive patients who underwent robotic-assisted pulmonary lobectomy by one surgeon for known or suspected lung cancer. Ten patients were excluded due to incomplete data. We used median income by residential ZIP code as a surrogate for SES status and grouped patients based on whether ZIP-based median income was less than (Group 1) or greater than (Group 2) 300% of the federal poverty income level. The effects of SES status groups on incidence of postoperative complications, chest tube duration, hospital length of stay (LOS), and in-hospital mortality were evaluated by the logistic regression model and Inverse Gaussian regression model, respectively.Results: Without adjustment, Group 1 tended to have a higher rate of postoperative complications, with 54% of patients experiencing complications compared to 34% of patients in Group 2 (p=0.007). Median chest tube duration and hospital LOS were also significantly longer in Group 1 than in Group 2 (p=0.034). In multivariable logistical regression analysis, while controlling for covariates and considering effect modifications, lower SES was significantly and positively associated with postoperative complications (odds ratio (OR)=1.98, p=0.039). Preoperative chronic obstructive pulmonary disease (COPD) was also a positive and significant predictor of postoperative complications (OR=1.89, p=0.017), chest tube duration (p=0.020), and LOS (p=0.010).Conclusions: Lower median income is associated with a greater number of postoperative complications following pulmonary resection for lung cancer when controlling for covariates.

Five-Year Outcomes After Decompression and Fusion Versus Decompression Alone in the Treatment of Lumbar Synovial Cysts

Spinal synovial cysts are acquired, fluid-filled lesions of the facet joint that most commonly occur in the lumbar spine. They are thought to arise from degenerative changes and to result from segmental instability. Although the treatment of these lesions has been studied, the long-term implications and effects of the different strategies for surgical intervention (i.e., decompression and fusion vs. decompression alone) have not yet been elucidated or established. Using an all-payer database with 53 million patient records (MARINER-53), patients with a diagnosis of lumbar synovial cysts were identified. Patients who had undergone lumbar fusion versus laminectomy were matched 1:1 using binomial and gaussian logistic regression models to evaluate the need for future lumbar surgery within 5 years after their index procedure. No statistically significant differences were noted between the 5-year rates of subsequent intervention, additional laminectomy, or fusion among patients who had undergone index decompression and fusion (n= 51; 10.5%) versus decompression alone (n= 43; 8.8%; P= 0.39). Furthermore, no significant differences were found in the odds of intervention type after index decompression and fusion versus decompression alone (subsequent laminectomy: odds ratio, 0.59; 95% confidence interval, 0.32-1.09; subsequent fusion: odds ratio, 1.14; 95% confidence interval, 0.64-2.02). Patient-specific factors and surgeon-patient-shared decision-making should be used when planning interventions for these lesions. However, synovial cysts might not require a fusion procedure for presumed instability. Further investigation is required, using randomized and prospective studies, to further evaluate the effective treatment of this entity.

Analysis of probability matrix model for seismic damage vulnerability of highway bridges

The present study was aimed at assessing more accurately the seismic vulnerability and performance of highway bridges in an earthquake-damaged area. Based on mathematical statistics (data collection) and a probability model, (i) survey data for 2134 bridges in 22 highway sections (47 sub-sections) affected by the Wenchuan earthquake on May 12, 2008 were obtained and analysed, (ii) Gaussian and exponential regression models were developed, (iii) the empirical seismic-damage vulnerability function, plane, surface and curve model of the 22 highway sections with sample number and failure ratio were established, and (iv) a regression parameter matrix was constructed considering the empirical seismic-damage data. Using the method of probability exceedance, the bridge vulnerability curve models considering the seismic-damage exceedance probability of each section were analysed, and a parameter matrix model (mean seismic-damage index) was proposed to evaluate and predict the seismic vulnerability of regional bridges. Based on creating the actual seismic-damage sample database, vulnerability point-cloud models of the 22 highway bridges were constructed, and the vulnerability probability matrix, function, curve and point-cloud model of each highway section can be used to evaluate and estimate the vulnerability of regional bridges in the future.

EM Estimation for the Bivariate Mixed Exponential Regression Model

In this paper, we present a new family of bivariate mixed exponential regression models for taking into account the positive correlation between the cost of claims from motor third party liability bodily injury and property damage in a versatile manner. Furthermore, we demonstrate how maximum likelihood estimation of the model parameters can be achieved via a novel Expectation-Maximization algorithm. The implementation of two members of this family, namely the bivariate Pareto or, Exponential-Inverse Gamma, and bivariate Exponential-Inverse Gaussian regression models is illustrated by a real data application which involves fitting motor insurance data from a European motor insurance company.

Into the Depths: A New Activity Metric for High-precision Radial Velocity Measurements Based on Line Depth Variations

The discovery and characterization of extrasolar planets using radial velocity (RV) measurements is limited by noise sources from the surfaces of host stars. Current techniques to suppress stellar magnetic activity rely on decorrelation using an activity indicator (e.g., strength of the Ca ii lines, width of the cross-correlation function, broadband photometry) or measurement of the RVs using only a subset of spectral lines that have been shown to be insensitive to activity. Here, we combine the above techniques by constructing a high-signal-to-noise activity indicator, the depth metric , from the most activity-sensitive spectral lines using the “line-by-line” method of Dumusque (2018). Analogous to photometric decorrelation of RVs or Gaussian progress regression modeling of activity indices, time series modeling of reduces the amplitude of magnetic activity in RV measurements; in an αCenB RV time series from HARPS, the RV rms was reduced from 2.67 to 1.02 m s−1. modeling enabled us to characterize injected planetary signals as small as 1 m s−1. In terms of noise reduction and injected signal recovery, modeling outperforms activity mitigation via the selection of activity-insensitive spectral lines. For Sun-like stars with activity signals on the m s−1 level, the depth metric independently tracks rotationally modulated and multiyear stellar activity with a level of quality similar to that of the FWHM of the CCF and log. The depth metric and its elaborations will be a powerful tool in the mitigation of stellar magnetic activity, particularly as a means of connecting stellar activity to physical processes within host stars.

The 2021 Western North American heat dome increased climate change anxiety among British Columbians: Results from a natural experiment

Extreme weather events caused by climate change pose a risk to mental health. Illustrating this reality, this study estimates the impact of the 2021 Western North American heat dome (June 25th, 2021 – July 1st, 2021) on climate change anxiety among British Columbians. We conducted an online survey of British Columbians, aged ≥ 16. Participants were recruited using paid advertisements on social media. Data were collected pre- and post- heat dome between May 12th, 2021 – June 21st, 2021 (n = 439), and July 15th, 2021 – July 18th, 2021 (n = 420), respectively. A multivariable inverse Gaussian regression model tested differences in Climate Change Anxiety Scale (CCAS) scores pre- and post- heat dome. Potential confounders measured included age, gender, ethnicity, education, income, and political orientation. CCAS reliability was assessed using Cronbach's alpha. Most participants indicated that they were much (40.1%) or somewhat (18.4%) more worried about climate change due to the heat dome. Mean CCAS scores increased from 1.66 (standard deviation [SD]= 0.80) to 1.87 (SD = 0.87) pre- and post- heat dome, respectively. In multivariable modeling, this effect was significant after controlling for potential confounders (Estimate = 0.057, standard error = 0.148, p < 0.001). The CCAS reliability was high (Cronbach's alpha = 0.94). Our results found that British Columbians had significantly higher climate change anxiety following the 2021 Western North American heat dome. Ongoing monitoring of climate change anxiety is needed to understand the impact of individual and compounding climate change-related weather events over time.

The Geographically Weighted Multivariate Poisson Inverse Gaussian Regression Model and Its Applications

This study aims to develop a method for multivariate spatial overdispersion count data with mixed Poisson distribution, namely the Geographically Weighted Multivariate Poisson Inverse Gaussian Regression (GWMPIGR) model. The parameters of the GWMPIGR model are estimated locally using the maximum likelihood estimation (MLE) method by considering spatial effects. Therefore, the significance of the regression parameter differs for each location. In this study, four GWMPIGR models are evaluated based on the exposure variable and the spatial weighting function. We compare the performance of those four models in real-world application using data on the number of infant, under-5 and maternal deaths in East Java in 2019 using five predictor variables. In this study, the GWMPIGR model uses one exposure variable and three exposure variables. Compared to the fixed kernel Gaussian weighting function, the GWMPIGR model with the fixed kernel bisquare weighting function and one exposure variable has a better fit based on the AICc value. Furthermore, according to the best GWMPIGR model, there are several regional groups formed based on predictors that significantly affected each event in East Java in 2019.

A new improved Liu estimator for the QSAR model with inverse Gaussian response

The regression model is one of the important quantitative structure-activity relationship (QSAR) model tools that is used chiefly in chemometrics studies. In chemometrics, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, then the inverse Gaussian regression model (IGRM) is a better choice QSAR model. Multicollinearity in the IGRM affects the IGRM estimation and inferences. To overcome the effect of multicollinearity, biased estimators such as ridge and Liu are discussed in the literature. However, the disadvantage of using the traditional Liu estimator is that the shrinkage parameter, d, returns a negative value that severely affects the estimator's performance. To mitigate this problem, we propose a new improved Liu estimator for the IGRM. The new estimator's performance is compared with the maximum likelihood estimator (MLE) and the other biased estimators. A Monte Carlo simulation study is conducted to assess the newly proposed estimator's performance under different parametric conditions. A QSAR chemometric application is also considered to see the clear picture of the proposed estimator. The simulation and QSAR application findings demonstrate that the newly proposed estimator consistently dominates the other competitive estimators in all the evaluated conditions.

High-Dimensional Gaussian Graphical Regression Models with Covariates

Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses both the mean and the precision matrix of a Gaussian graphical model on covariates. In the context of co-expression quantitative trait locus (QTL) studies, our method can determine how genetic variants and clinical conditions modulate the subject-level network structures, and recover both the population-level and subject-level gene networks. Our framework encourages sparsity of covariate effects on both the mean and the precision matrix. In particular for the precision matrix, we stipulate simultaneous sparsity, that is, group sparsity and element-wise sparsity, on effective covariates and their effects on network edges, respectively. We establish variable selection consistency first under the case with known mean parameters and then a more challenging case with unknown means depending on external covariates, and establish in both cases the convergence rates and the selection consistency of the estimated precision parameters. The utility and efficacy of our proposed method is demonstrated through simulation studies and an application to a co-expression QTL study with brain cancer patients. Supplementary materials for this article are available online.

Application of Combined Prediction Model Based on Core and Coritivity Theory in Continuous Blood Pressure Prediction.

Blood pressure is vital evidence for clinicians to predict diseases and check the curative effect of diagnosis and treatment. To further improve the prediction accuracy of blood pressure, this paper proposes a combined prediction model of blood pressure based on coritivity theory and photoplethysmography. First of all, we extract eight features of photoplethysmogram, followed by using eight machine learning prediction algorithms, such as K-nearest neighbor, classification and regression trees, and random forest, to predict systolic blood pressure. Secondly, aiming at the problem of sub-model selection of combination forecasting model, from the point of graph theory, we construct an undirected network graph G, the results of each single prediction model constitute a vertex set. If the maximum mutual information coefficient between vertices is greater than or equal to 0.69, the vertices are connected by edges. The maximum core of graph G is a submodel of the combinatorial model. According to the definition of core and coritivity, the maximum core of G is random forest regression and Gaussian kernel support vector regression model. The results show that the SDP estimation error of the combined prediction model based on random forest regression and Gaussian kernel support vector regression is 3.56 ±5.28mmhg, which is better than other single models and meets the AAMI standards. The combined model determined by core and coritivity has higher prediction performance for blood pressure.

A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables

In this paper, we focus on the comparison of the bivariate zero-inflated Poisson inverse Gaussian regression (BZIPIGR) type II model in two cases: with and without exposure variables. The BZIPIGR type II model is applied to analyze the occurrence of maternal and early neonatal mortality in South Sulawesi Province, Indonesia using 2019 data, which contain many zero values and have the issue of overdispersion in the response variable. Furthermore, to analyze the number of deaths in various areas, the exposure variable is considered. The maximum likelihood estimation (MLE) is used in parameter estimation, which involves numerical iteration and application of the Berndt–Hall–Hall–Hausman (BHHH) algorithm. Sum square error (SSE) serves as the criterion of model selection when exposure variables are included. The existence of exposure variables strongly affects the model’s accuracy, especially using the BZIPIGR type II model. According to the SSE and RMSE values, the BZIPIGR type II model with exposure variables performs better than the model without exposure variables in estimating parameter values. All predictors with exposure variables in this study had a significant influence on the number of maternal and early neonatal mortalities.

Joint analysis of the intention to vaccinate and to use contact tracing app during the COVID-19 pandemic

Pharmacological and non-pharmacological measures will overlap for a period after the onset of the pandemic, playing a strong role in virus containment. We explored which factors influence the likelihood to adopt two different preventive measures against the COVID-19 pandemic. An online snowball sampling (May–June 2020) collected a total of 448 questionnaires in Italy. A Bayesian bivariate Gaussian regression model jointly investigated the willingness to get vaccinated against COVID-19 and to download the national contact tracing app. A mixed-effects cumulative logistic model explored which factors affected the motivation to adopt one of the two preventive measures. Despite both COVID-19 vaccines and tracing apps being indispensable tools to contain the spread of SARS-CoV-2, our results suggest that adherence to the vaccine or to the national contact tracing app is not predicted by the same factors. Therefore, public communication on these measures needs to take in consideration not only the perceived risk associated with COVID-19, but also the trust people place in politics and science, their concerns and doubts about vaccinations, and their employment status. Further, the results suggest that the motivation to comply with these measurements was predominantly to protect others rather than self-protection.

Principal component ridge type estimator for the inverse Gaussian regression model

The inverse Gaussian regression model (IGRM) is applied when the response variable is continuous, positively skewed and well fitted to the inverse Gaussian distribution. In the presence of multicollinearity, the maximum likelihood estimation (MLE) is not a right choice. Therefore, we proposed a new estimator called the principal component ridge estimator for the IGRM which combines the principal component estimator and the ridge estimator. We also consider a two-parameter estimator (TPE) and other biased estimators to see a clear image of our proposed estimator. A Monte Carlo simulation study is also presented to examine the performance of the proposed estimators. Furthermore, we analysed a dataset to assess the superiority of the proposed estimator. Based on the simulation and application results, it is evident that the proposed estimator dominates the classical MLE, and other considered biased estimation methods.

Gaussian Regression Models for Evaluation of Network Lifetime and Cluster-Head Selection in Wireless Sensor Devices

The paper presents a model predictive approach for evaluating network lifetime and cluster head selection for a wireless sensor network. The dynamic parameters of a wireless sensor network are collected using Smart Mesh IP Power and performance calculator. The study considers a machine learning approach to combine clustering with the optimal routing protocol. The hop depth, advertising, number of Motes, backbone, routing, reporting interval, payload size, downstream frame size, supply voltage, and path stability are the predictors, and the current consumption, data latency, and build time are the response variables to establish the models for estimating the power and performance of the network. The remaining energy in each node, distance from the base station, and data transmission rate are the predictors, and the priority of the cluster head is the response variable to establish models for achieving an optimal routing path in a wireless sensor network. The standard tree, Support Vector Machine, Ensemble, and Gaussian process regression models for lifetime estimation are analyzed in comparison with the Smart Mesh IP tool, and the models for cluster head selection are investigated in comparison with ANFIS based models. This novel approach concentrates on the effect of various dynamic parameters on network lifetime prediction.

Semiparametric count data regression for self-reported mental health.

''For how many days during the past 30 days was your mental health not good?" The responses to this question measure self-reported mental health and can be linked to important covariates in the National Health and Nutrition Examination Survey (NHANES). However, these count variables present major distributional challenges: The data are overdispersed, zero-inflated, bounded by 30, and heaped in 5- and 7-day increments. To address these challenges-which are especially common for health questionnaire data-we design a semiparametric estimation and inference framework for count data regression. The data-generating process is defined by simultaneously transforming and rounding (star) a latent Gaussian regression model. The transformation is estimated nonparametrically and the rounding operator ensures the correct support for the discrete and bounded data. Maximum likelihood estimators are computed using an expectation-maximization (EM) algorithm that is compatible with any continuous data model estimable by least squares. star regression includes asymptotic hypothesis testing and confidence intervals, variable selection via information criteria, and customized diagnostics. Simulation studies validate the utility of this framework. Using star regression, we identify key factors associated with self-reported mental health and demonstrate substantial improvements in goodness-of-fit compared to existing count data regression models.

Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Model and Its Application

Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Model and Its Application

The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking

This paper is concerned with introducing a family of multivariate mixed Negative Binomial regression models in the context of a posteriori ratemaking. The multivariate mixed Negative Binomial regression model can be considered as a candidate model for capturing overdispersion and positive dependencies in multi-dimensional claim count data settings, which all recent studies suggest are the norm when the ratemaking consists of pricing different types of claim counts arising from the same policy. For expository purposes, we consider the bivariate Negative Binomial-Gamma and Negative Binomial-Inverse Gaussian regression models. An Expectation-Maximization type algorithm is developed for maximum likelihood estimation of the parameters of the models for which the definition of a joint probability mass function in closed form is not feasible when the marginal means are modelled in terms of covariates. In order to illustrate the versatility of the proposed estimation procedure a numerical illustration is performed on motor insurance data on the number of claims from third party liability bodily injury and property damage. Finally, the a posteriori, or Bonus-Malus, premium rates resulting from the bivariate Negative Binomial-Gamma and Negative Binomial-Inverse Gaussian regression model are compared to those determined by the bivariate Negative Binomial and Poisson-Inverse Gaussian regression models.

Exploring Dielectric Constant and Dissipation Factor of LTCC Using Machine Learning.

Low-temperature co-fired ceramics (LTCCs) have been attracting attention due to rapid advances in wireless telecommunications. Low-dielectric-constant (Dk) and low-dissipation-factor (Df) LTCCs enable a low propagation delay and high signal quality. However, the wide ranges of glass, ceramic filler compositions, and processing features in fabricating LTCC make property modulating difficult via experimental trial-and-error approaches. In this study, we explored Dk and Df values of LTCCs using a machine learning method with a Gaussian kernel ridge regression model. A principal component analysis and k-means methods were initially performed to visually analyze data clustering and to reduce the dimension complexity. Model assessments, by using a five-fold cross-validation, residual analysis, and randomized test, suggest that the proposed Dk and Df models had some predictive ability, that the model selection was appropriate, and that the fittings were not just numerical due to a rather small data set. A cross-plot analysis and property contour plot were performed for the purpose of exploring potential LTCCs for real applications with Dk and Df values less than 10 and 2 × 10−3, respectively, at an operating frequency of 1 GHz. The proposed machine learning models can potentially be utilized to accelerate the design of technology-related LTCC systems.

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Poisson inverse Gaussian regression model

One of the appropriate methods used to model count data response and its corresponding predictors is Poisson regression. Poisson regression strictly assumes that the mean and variance of response variables should be equal (equidispersion). Nonetheless, some cases of the count data unsatisfied this assumption because variance can be larger than mean (over-dispersion). If overdispersion is violated, causing the underestimate standard error. Furthermore, this will lead to incorrect conclusions in the statistical test. Thus, a suitable method for modelling this kind of data needs to develop. One alternative model to outcome the overdispersion issue in bivariate response variable is the Bivariate Poisson Inverse Gaussian Regression (BPIGR) model. The BPIGR model can produce a global model for all locations. On the other hand, each location and time have different geographic conditions, social, cultural, and economical so that Geographically and Temporally Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR)) is needed. The weighting function spatial-temporal in GTWBPIGR generates a different local model for each period. GTWBPIGR model solves the overdispersion case and generates global models for each period and location. The parameter estimation of the GTWBPIGR model uses the Maximum Likelihood Estimation (MLE) method, followed by Newton Raphson iteration. Meanwhile, the test statistics on the hypothesis testing is simultaneously testing of the GTWBPIGR model is obtained with the Maximum Likelihood Ratio Test (MLRT) approach, using n large samples of the statistical test is chi-square distribution. Moreover, the test statistics for partially testing used the Z-test statistic.