Coefficients In Linear Regression Model Research Articles

Group Inverse-Gamma Gamma Shrinkage for Sparse Linear Models with Block-Correlated Regressors

Heavy-tailed continuous shrinkage priors, such as the horseshoe prior, are widely used for sparse estimation problems. However, there is limited work extending these priors to predictors with grouping structures. Of particular interest in this article, is regression coefficient estimation where pockets of high collinearity in the covariate space are contained within known covariate groupings. To assuage variance inflation due to multicollinearity we propose the group inverse-gamma gamma (GIGG) prior, a heavy-tailed prior that can trade-off between local and group shrinkage in a data adaptive fashion. A special case of the GIGG prior is the group horseshoe prior, whose shrinkage profile is correlated within-group such that the regression coefficients marginally have exact horseshoe regularization. We show posterior consistency for regression coefficients in linear regression models and posterior concentration results for mean parameters in sparse normal means models. The full conditional distributions corresponding to GIGG regression can be derived in closed form, leading to straightforward posterior computation. We show that GIGG regression results in low mean-squared error across a wide range of correlation structures and within-group signal densities via simulation. We apply GIGG regression to data from the National Health and Nutrition Examination Survey for associating environmental exposures with liver functionality.

Enhanced body shape change coupled with PA is the key to hypertension management for urban residents.

The present study aimed to assess the relationship between bodyshape, physical activity (PA), and systolic blood pressure (SBP) and diastolic blood pressure (DBP). A novel visualization method was used to examine the effects of body shape combined with physical activity on hypertension. Data from 54,303 participants were obtained from the China Health and Nutrition Survey (CHNS) and analyzed using logistic regression models and standardized regression coefficients of linear models. These models were used to explore factors and effects of body shape indices and other parameters on SBP and DBP. The logistic regression model revealed that compared to transport-related PA, the aggregated variables (weight and waist) were associated with a 2.44-fold and 1.65-fold increase in the risk of hypertension, respectively (p<.05). The average aggregated standardized coefficient of the linear model, based on 1000 bootstrap resamples, indicated that the Base Shape group had the strongest explanatory power for hypertension, followed by the Habits group. However, the explanatory power of the PA group was around 10 and 22 times lower than that of the Base Shape group for DBP and SBP, respectively (p<.05). These results demonstrate that increasing physical activity, with emphasizing a healthy body shape, and adopting positive lifestyle habits can effectively contribute to the prevention and control of hypertension.

Validation of the Patient-Reported Outcomes Measurement Information System (PROMIS®) physical function questionnaire in late-onset Pompe disease using PROPEL phase 3 data

BackgroundThe construct validity and interpretation of the Patient-Reported Outcome Measurement Information System (PROMIS®) Physical Function short form 20a (PF20a) questionnaire were evaluated for patients with late-onset Pompe disease (LOPD), a rare, autosomal recessive, progressive neuromuscular disorder treatable by enzyme replacement therapy (ERT).MethodsIn the phase 3 PROPEL study, adults with LOPD underwent testing of physical functioning and had PRO measurements at baseline and at weeks 12, 26, 38, and 52 while receiving experimental or standard-of-care ERT. All patients were pooled for analyses, without comparisons between treatment groups. Associations and correlations between PROMIS PF20a scores and the 6-minute walk distance (6MWD), % predicted forced vital capacity (FVC), manual muscle test (MMT) of the lower extremities, Gait, Stairs, Gowers’ maneuver, Chair (GSGC) score, and Rasch-built Pompe-specific Activity (R-PAct) scale were evaluated by calculating regression coefficients in linear regression models and Pearson correlation coefficients (R); patients’ age, sex, race, ERT prior to study, body mass index, and study treatment were included as covariables. The minimal clinically important difference (MCID) of PROMIS PF20a was determined using distribution- and anchor-based methods.Results123 patients received at least 1 dose of ERT. In multivariable analyses, PROMIS PF20a scores had strong correlations with R-PAct scores (R = 0.83 at baseline and R = 0.67 when evaluating changes between baseline and 52 weeks) and moderate correlations with the 6MWD (R = 0.57 at baseline and R = 0.48 when evaluating changes between baseline and 52 weeks). Moderate correlations were also observed between PROMIS PF20a and MMT (R = 0.54), GSGC (R=-0.51), and FVC (R = 0.48) at baseline. In multivariable linear regression models, associations were significant between PROMIS PF20a and 6MWD (P = 0.0006), MMT (P = 0.0034), GSGC (P = 0.0278), and R-PAct (P < 0.0001) at baseline, between PROMIS PF20a and 6MWD (P < 0.0001), FVC (P = 0.0490), and R-PAct (P < 0.0001) when combining all measurements, and between PF20a and 6MWD (P = 0.0016) and R-PAct (P = 0.0001) when evaluating changes in scores between baseline and 52 weeks. The anchor-based and distribution-based MCID for a clinically important improvement for PROMIS PF20a were 2.4 and 4.2, respectively.ConclusionsPROMIS PF20a has validity as an instrument both to measure and to longitudinally follow physical function in patients with LOPD.Trial registrationClinicalTrials.gov, NCT03729362. Registered 2 November 2018, https://www.clinicaltrials.gov/search?term=NCT03729362.

ВИВЧЕННЯ ВПЛИВУ МЕТЕОРОЛОГІЧНИХ УМОВ НА ВЕЛИЧИНУ НОРМАЛІЗОВАНОГО ДИФЕРЕНЦІЙНОГО ІНДЕКСУ НА ПОСІВАХ СІЛЬСЬКОГОСПОДАРСЬКИХ КУЛЬТУР У ХЕРСОНСЬКІЙ ОБЛАСТІ

The article is devoted to the issue of establishing a correlation-regression relationship between meteorological parameters and the values of NDVI in crops such as sunflower, soybean, grain corn, and rapeseed. The purpose of the scientific work was to study the influence of meteorological conditions, namely air temperature, and precipitation, on the value of the satellite Normalized Differential Vegetation Index in the crops grown in the Kherson region, and to establish a correlation-regression relationship between meteorological parameters and spectral characteristics of the crops. Methods. The research was carried out on the territory of the Kherson region. Meteorological data were retrieved from the archives of the Kherson Regional Hydrometeorological Center and the data of the MeteoBlue open meteorological hub. Data on the values of NDVI were adapted and calculated using GIMMS Global Agricultural Monitoring. The data on the values of NDVI were calculated for each studied crop using their crop mask. The study was carried out for 2017 and 2020 for corn, 2017 for soybeans, 2021 and 2022 for sunflower and rapeseed, respectively. Correlation-regression analysis was performed according to standard methodology with a calculation of Pearson correlation coefficients, coefficients of determination, and coefficients of linear regression models. All calculations were performed at P&lt;0.05 in the statistical package BioStat v.7. Results. It was established that the maximum closeness of the relationship is for the values of NDVI on sunflower and soybean crops with the air temperature (r=0.84 and 0.80, respectively). The closeness of the relationship between the NDVI values and the amount of precipitation was much smaller for all studied crops and can be considered significant only for soybean (r=0.45) and rapeseed (r=0.58). The calculation of regression coefficients and corresponding statistics proved that reliable models can be obtained for all studied crops in the pair “NDVI – air temperature”, and in the pair “NDVI – precipitation” a reliable model was obtained only for soybean. The best accuracy parameters are observed for the models in the pair “NDVI – air temperature” for such crops as sunflower, soybean, and corn – the relative error was 10.98, 19.97 and 22.15%, respectively. As for the model in the pair “NDVI – precipitation” for soybeans, the relative error of 52.26% indicates the limited possibilities of its theoretical use and absolute unacceptability for practical purposes. Conclusions. The study’s results testify to a high closeness and reliability of the correlation relationship between the values of satellite NDVI and air temperature in all the studied crops. The closeness of the relationship between NDVI and precipitation is average or low, and the construction of a reliable and accurate regression mathematical model for the pair “NDVI – precipitation” is impossible. In the future, the study will continue with the expansion of the geographical component to the entire zone of the Southern Steppe of Ukraine to establish the characteristics of the relationships between the NDVI and the parameters of the weather conditions of the agroecological zone. Keywords: precipitation, correlation, regression, satellite monitoring, air temperature.

Improving the Effectiveness оf Radio Advertising Campaigns вy Integrating Digital Monitoring Tools

The article discusses the method of increasing the effectiveness of advertising campaigns on the radio through by integrating digital monitoring tools. A methodology for evaluating the effectiveness of an advertising campaign on the radio based on the analysis of the linear regression model coefficients is proposed. The advertiser’s web application traffic, which directly affects the sales volume, is used as a target variable. The investments in various advertising channels for a certain period of time is considered as factors influencing the target variable. A structural model of an advertising campaign is presented. As a result of the research, an advertising system was implemented in the form of a web application (radioskidki.ru), which allows the integration of Internet and radio advertising channels. Traffic measurements were carried out over a time interval of 1 month with sampling in one day. The analysis of the measurement results proved the effectiveness of the proposed methodology and the developed tool. Thus, the proposed technique allows to generate additional web application traffic, and thereby increase the effectiveness of advertising campaigns on the radio.

A study of the correlation between total lung volume and the percent of low attenuation volume and PFT indicators in patients with preoperative lung cancer.

The objective was to explore the relationships between computed tomography (CT) lung volume parameters and pulmonary function test (PFT) indexes and develop predictive scores to predict PFT indexes in Chinese preoperative patients suspected with lung cancer. Preoperative patients suspected with lung cancer aged 18 years or more and examined by chest CT scan and PET were consecutively recruited from April to August 2020, at Yunnan Cancer Hospital. CT and PET data were selected from medical record. Pearson correlation was used to explore the relationships between CT parameters and PFT indexes. Predictive scores of PFT indexes were developed from unstandardized coefficients of linear regression models of using CT parameters as predictors. The assessments of predictive ability of scores were conducted by receiver operating characteristics curves. A total of 124 preoperative patients suspected with lung cancer participated in this study. Total lung volume significantly correlated with total lung capacity (r = 0.708), residual volume (r = 0.411), forced expiratory volume in one second (FEV1, r = 0.535), forced vital capacity (FVC, r = 0.687), and FEV1/FVC (r = -0.319). Percent of low attenuation volume significantly correlated with total lung capacity (r = 0.200), residual volume (r = 0.215), FEV1 percentage of predictive value (FEV1%, r = -0.204) and FEV1/FVC (r = -0.345). Four predictive scores for FEV1, FEV1%, FEV1/FVC and FVC% were developed. The area under the curve of receiver operating characteristics for FEV1 <2L, FEV1% <80%, FEV1/FVC <80% and FVC% <80% were 0.856, 0.667, 0.749 and 0.715, respectively. A prediction of poor lung function in preoperative patients suspected with lung cancer, using total lung volume and percent of low attenuation volume was possible. The predictive scores should be further evaluated for external validity.

The A Priori Procedure (APP) for estimating regression coefficients in linear models

Regression coefficients are crucial in the sciences, as researchers use them to determine which independent variables best explain the dependent variable. However, researchers obtain regression coefficients from data samples and wish to generalize to populations; without reason to believe that sample regression coefficients are good estimates of corresponding population regression coefficients, their usefulness would be curtailed. In turn, larger sample sizes provide better estimates than do smaller ones. There is much recent literature on the a priori procedure (APP) that was designed for the general purpose of determining the sample sizes needed to obtain sample statistics that are good estimates of corresponding population parameters. We provide an extension of the APP to regression coefficients, which works for standardized or unstandardized regression coefficients. A simulation study and real data example support the mathematical derivations. Also, we include a free and user-friendly computer program to aid researchers in making the calculations.

Geographic context is a key driver of spatial variation of bird species richness during migration

AbstractAimDetermine whether primary productivity or location (distance to the coast) is more important to migrating bird habitat selection.LocationYucatan Peninsula, Mexico.Time periodAugust–December and February–May 2009–2016.TaxaMigratory birds.MethodsUsing eBird data, we modelled spatial variation in species richness as a function of primary productivity and distance to the coast and how the relationships vary with time during spring and autumn migration. We compared the standardized regression coefficients of linear models with a Poisson error distribution.ResultsWe found that three primary productivity indices [normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), heterogeneity] performed similarly in predicting species richness. However, species richness was more strongly associated with distance to the coast. In autumn, richness was higher closer to the coast through most of the season and then shifted inland late in autumn. Richness was also higher in more productive habitats. In spring, richness was higher inland early in the season but then increased closer to the coast. Species richness was relatively similar across the primary productivity gradient, even declining slightly with increasing NDVI.Main conclusionsWe did not find convincing evidence for a strong relationship between species richness and primary productivity. Instead, migration constrains birds such that they concentrate in coastal environments. In autumn, migrants may favour habitats that are both coastal and productive, such as those that occur along the Caribbean coast. In spring, migrants may also use the less productive Gulf of Mexico coast, possibly due to high arthropod production occurring during an otherwise dry time of year.

Quick Detection of Aldehydes and Ketones in Automotive Textiles

Abstract This study was aimed to develop a quick detection method to test aldehydes and ketones in textiles in order to control the quality of automotive textiles in the development process from fabric production to end-use in vehicles. In this study, a pretreatment of samples was applied to simulate the actual environment of textiles used in vehicles. Collected volatiles were reacted with 2,4-dinitrophenylhydrazine and then eluted with acetonitrile tetrahydrofuran. The eluent was analyzed with high-performance liquid chromatography. Findings showed more than 90% volatiles could be detected in the established method; the lowest determination limit was 0.0297 mg/mL; and the lowest quantification limit was 0.0991 mg/mL, which meant sensitivity and capability of the method were high. Regression coefficients of linear models between volatile concentrations and chromatographic peak characteristics were &gt;0.995, indicating that the method could effectively and efficiently determine the contents of volatiles in automotive textiles.

Residential exposure to outdoor air pollution and adult lung function, with focus on small airway obstruction

Although a growing body of evidence suggests that chronic exposure to outdoor air pollution is linked to a decline in lung function, data on flow at low lung volumes that may be more specific of small airway obstruction are still scarce. We aimed to study the associations between residential exposure to air pollution and lung function, with specific focus on small airways obstruction.We assessed 2995 French participants (aged between 40 and 65) in the ELISABET cross-sectional survey. Residential exposures to nitrogen dioxide (NO2), particulate matter with a diameter <10 μm (PM10) and sulphur dioxide (SO2) were assessed. The spirometric parameters were forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), and forced expiratory flow between 25% and 75% of FVC (FEF25-75) and at 75% of FVC (FEF75). Coefficients in linear regression models were expressed as the z-score [95% confidence interval] for an increment of 5 μg/m3 in NO2 and 2 μg/m3 in PM10 and SO2.NO2 was associated with significantly lower values of FEV1 (−0.10 [-0.15;-0.05]), FVC (−0.06 [-0.11;-0.02]), FEV1/FVC (−0.07 [-0.11;-0.03]), FEF25-75 (−0.09 [-0.14;-0.05]) and FEF75 (−0.08 [-0.12;-0.04]). PM10 was associated with significantly lower values of FEV1 (−0.10 [-0.15;-0.04]), FVC (−0.06 [-0.11;-0.01]), FEV1/FVC (−0.06 [‒0.11;-0.01]), FEF25-75 (−0.08 [-0.13;-0.03]) and FEF75 (−0.08 [-0.12;-0.04]). SO2 was associated with significantly lower values of FEV1 (−0.09 [-0.16;-0.02]), FEV1/FVC (−0.07 [-0.13;-0.01]), FEF25-75 (−0.09 [-0.15;-0.02]) and FEF75 (−0.08 [-0.14;-0.03]) but not FVC (−0.05 [-0.11; 0.009]).Even though spatial variations in pollutant levels were low, residential exposure to outdoor air pollution was associated with lower lung function, including lower FEF25-75 and FEF75 suggesting small airway obstruction.

Optimal dates for assessing long-term changes in tree-cover in the semi-arid biomes of South Africa using MODIS NDVI time series (2001–2018)

The varying proportions of tree and herbaceous cover in the grassland and savanna biomes of Southern Africa determine their capacity to provide ecosystem services. The asynchronous phenologies e.g. annual NDVI profiles of grasses and trees in these semi-arid landscapes provide an opportunity to estimate percentage tree-cover by determining the period of maximum contrast between grasses and trees. First, a 16-day NDVI time series was generated from MODIS NDVI data, i.e. MOD13A2 16-day NDVI composite data. Secondly, percentage tree-cover data for 100 sample polygons (4 × 4) pixels for areas that have not undergone change in tree cover between 2001 and 2018 were derived using high resolution Google Earth imagery. Next, a time series consisting of the coefficients of determination (R2) for the NDVI/tree-cover linear regression were computed for the 100 polygons. Lastly, a threshold R2 > 0.5 was used to determine the optimal period of the year for mapping tree-cover. It emerged that the narrow period from Julian day 161–177 (June 10–26) was the most consistent period with R2 > 0.5 in the region. 18 tree-cover maps (2001–2018) were generated using linear regression model coefficients derived from Julian day 161 for each year. Kendall correlation coefficient (tau) was used to determine areas of significant (p < 0.05 and p < 0.01) increasing or decreasing trend in tree-cover. Areas (polygons) that showed increasing tree-cover appeared to be more widespread in the trend map as compared to areas of decreasing tree-cover. An accuracy assessment of the map of increasing tree-cover was conducted using Google Earth high resolution images. Out of 330 and 200 mapped polygons verified using p < 0.05 and 0.01 thresholds, respectively, 180 (54% accuracy) and 132 (65% accuracy) showed evidence of tree recruitment. Farm abandonment appeared to have been the most important factor contributing to increasing tree-cover in the region.

Comparison study on the confidence intervals in linear regression models with restricted parameter space

This paper proposes an empirical likelihood confidence region for the regression coefficients in linear regression models when the regression coefficients are subjected to some equality constraints. The shape of the confidence set does not depend on the re-parametrization of the regression model induced by the equality constraint. It is shown that the asymptotic coverage rate attains the nominal confidence level and the Bartlett correction can successfully reduce the coverage error rate from $O(n^{-1})$ to $O(n^{-2})$, where n denotes the sample size. Simulation studies are conducted to evaluate the finite sample performance of the proposed empirical likelihood empirical confidence estimation procedure. Finally, a comparison study is conducted to compare the finite sample performance of the proposed and the classical ellipsoidal confidence sets based on normal theory.

The Impact of Fiscal Deficit on Inflation Rate - Empirical Evidence Case of Eurozone

The purpose of this working paper is to investigate if determinants have an impact on inflation rate in Eurozone Countries by using times series data for 17 countries from year 1997 to 2017, in yearly basis in total 375 observations. The study used quantitative research approach and secondary data and is analyzed by using linear regression model measures: Inflation rate as a dependent variable, and five independent variables such us: GDP to growth rate, Deficit to GDP rate, Public debt to GDP rate, Government bond interest rate and Unemployment rate. Linear regression model was applied to investigate the impact of GDP to growth rate, deficit to the GDP rate, Public debt to the GDP rate, Government bond interest rate, and Unemployment rate to the dependent variable Inflation rate. From the Linear Regression Model coefficients for inflation rate as a dependent variable shows that three of five variables have a significance one with negative significance and two positive significance. The empirical result shows that the three of five ratios that we mentioned above have a strong influence on the Inflation rate.

The Impact of Fiscal Deficit on Inflation Rate - Empirical Evidence Case of Eurozone

The purpose of this working paper is to investigate if determinants have an impact on inflation rate in Eurozone Countries by using times series data for 17 countries from year 1997 to 2017, in yearly basis in total 375 observations. The study used quantitative research approach and secondary data and is analyzed by using linear regression model measures: Inflation rate as a dependent variable, and five independent variables such us: GDP to growth rate, Deficit to GDP rate, Public debt to GDP rate, Government bond interest rate and Unemployment rate. Linear regression model was applied to investigate the impact of GDP to growth rate, deficit to the GDP rate, Public debt to the GDP rate, Government bond interest rate, and Unemployment rate to the dependent variable Inflation rate. From the Linear Regression Model coefficients for inflation rate as a dependent variable shows that three of five variables have a significance one with negative significance and two positive significance. The empirical result shows that the three of five ratios that we mentioned above have a strong influence on the Inflation rate.

A Note on the UEK Method

The paper concerns certain pitfalls of using the Moore-Penrose pseudoinverse for estimating regression coefficients in linear regression models when the matrix of explanatory variables has not full column rank. The aim of the paper is to show that in this case estimator of parameters based on the Moore-Penrose pseudoinverse is biased, and the bias leads to biased forecasts.

Partial penalized empirical likelihood ratio test under sparse case

A consistent test via the partial penalized empirical likelihood approach for the parametric hypothesis testing under the sparse case, called the partial penalized empirical likelihood ratio (PPELR) test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypothesis and the local alternatives of order n−1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical likelihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection.

Two-sample high-dimensional empirical likelihood

ABSTRACTIn this paper, we apply empirical likelihood for two-sample problems with growing high dimensionality. Our results are demonstrated for constructing confidence regions for the difference of the means of two p-dimensional samples and the difference in value between coefficients of two p-dimensional sample linear model. We show that empirical likelihood based estimator has the efficient property. That is, as p → ∞ for high-dimensional data, the limit distribution of the EL ratio statistic for the difference of the means of two samples and the difference in value between coefficients of two-sample linear model is asymptotic normal distribution. Furthermore, empirical likelihood (EL) gives efficient estimator for regression coefficients in linear models, and can be as efficient as a parametric approach. The performance of the proposed method is illustrated via numerical simulations.

Constrained test in linear models with multivariate power exponential distribution

We investigate the problem of testing equality and inequality constraints on regression coefficients in linear models with multivariate power exponential (MPE) distribution. This distribution has received considerable attention in recent years and provides a useful generalization of the multivariate normal distribution. We examine the performance of the power of the likelihood ratio, Wald and Score tests for grouped data and in the presence of regressors, in small and moderate sample sizes, using Monte Carlo simulations. Additionally, we present a real example to illustrate the performance of the proposed tests under the MPE model.

ON SIZE AND POWER OF HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.

Fuzzy linear regression-based detection of earnings management

A large number of accounting studies have examined the occurrence of earnings management in various contexts. In most of these studies, the earnings management detection model is based on the linear regression model suggested by Jones (1991). A considerable problem with the Jones model is the requirement of long time series of financial statement data. An alternative to estimating the linear regression model coefficients with ordinary least squares (OLS) is to use fuzzy linear regression (FLR) instead. One of the main advantages with FLR described in the literature is its ability to handle small data sets. The purpose of this study is to compare the performance of the OLS-based Jones model with the performance of the FLR-based Jones model. The results show that the performance of both types of models decreases when the length of the time series decreases and that there is no significant difference in the estimated discretionary accruals between the models. The results also show that the FLR-based Jones model outperforms the OLS-based Jones model in detecting simulated earnings management when the estimation time series is short. Overall, the results show that the FLR-based Jones model is a feasible alternative to the OLS-based Jones model, especially when the length of the estimation time series is restricted by data availability.