Estimated Regression Coefficients Research Articles

Estimation of the Error Structure in Multivariate Response Linear Regression Models

ABSTRACTMultivariate response linear regression model considers how a set of covariates affects multiple responses. In contrast to separately running univariate regression for each response, multivariate response regression can better estimate the coefficient matrix by exploiting shared information among the responses. A key to effectively borrowing strength across different responses is to estimate and utilize the structure among random errors in responses. Moreover, certain applications seek to understand the interrelationships of the responses, which are directly encoded in the error structure. These observations call for the development of methods for estimating the error structure in multivariate response linear regression models. This article aims at providing a review of recent progress in this challenging and important problem. We also provide simulation studies demonstrating the empirical performance of recently developed methods for error structure estimation, as well as the benefit by exploiting these estimates for regression coefficients estimation.

A Note on Ordinal Modeling of Smoking Rate Data.

This paper discusses statistical models for ordinal data that may be more appropriate for smoking rate outcomes than are models that assume continuous measurement and normality. Smoking rate outcomes often have distributions that make them inappropriate for many popular statistical models that assume normality, and are more appropriately considered ordinal outcomes. This article describes how the ordinal logistic regression model can be used to obtain estimates of means, and comparisons of means, for smoking rate outcomes. Analyses of the daily smoking rate of a sample of 383 subjects are presented using linear regression and ordinal logistic regression. From the latter, we derive regression estimates (intercepts and slopes) in terms of the mean response without having to assume any distributional form for the smoking rate outcome variable. Regressors considered are the subject's gender and their level of dependency as assessed by the nicotine dependence symptom scale (NDSS). Estimated regression coefficients were similar, but the linear regression model indicated a significant gender effect, such that females had a higher smoking rate than males. Though similar, this effect was not quite significant (at the 0.05 level) in the ordinal model. The effect of dependency was significant in both models, with more dependent smokers having a higher smoking rate. Results and conclusions can depend on the assumptions of a statistical model. Methods relaxing the assumption of normality are useful to examine how robust effects are to this common assumption. Modeling of smoking rate outcomes can be performed without having to rely on methods that assume a normal distribution. The ordinal model can provide estimates relating to mean differences in smoking rate for the effects of regressors.

Association of reallocating time between physical activity and sedentary behavior on the risk of depression: a systematic review and meta-analysis

Background and aimsSedentary behavior (SB) is a prevalent lifestyle factor and a risk factor for various health conditions, including depression (encompassing both clinically diagnosed depressive disorders and depressive symptoms). This study aimed to summarize the estimated impact of reallocating time spent in SB to light-intensity physical activity (LPA) or moderate-to-vigorous physical activity (MVPA) on the risk of depression from observational studies, as well as the impact of reallocating time spent in MVPA and LPA to SB.MethodsFour databases [PubMed, Scopus, SPORTdiscus, and PsycINFO (via EBSCOhost platform)] were searched and analyzed for relevant studies published up to August 2024. Meta-analyses were performed on the estimated regression coefficients (b) and 95% confidence intervals (CIs) for depression symptom scores. All statistical analyses were performed using STATA 16.0.ResultsTwenty-seven studies involving 702,755 participants met the inclusion criteria. Reallocating SB to LPA and MVPA was significantly associated with reductions in depression risk (b = −0.04, 95% CI = −0.06 to −0.03, p < 0.001; b = −0.11, 95% CI = −0.19 to −0.03, p = 0.004). Subgroup analyses indicated that reallocating 30 and 60 min of SB to LPA or MVPA was significantly associated with reduced depression risk, with significant differences in PA intensity and age, but not for 10 and 15 min groups. Conversely, reallocating LPA and MVPA to SB was significantly associated with increased depression risk (b = 0.11, 95% CI = 0.01 to 0.21, p = 0.039; b = 0.17, 95% CI = 0.08 to 0.25, p < 0.001). Subgroup analyses indicated that reallocating 30 min of LPA or MVPA to SB was significantly associated with increased depression risk, with no difference in PA intensity.ConclusionsReallocating SB to PA was beneficial, whereas reallocating PA to SB was detrimental to the risk of depression. The results highlight the importance of considering PA intensity and duration in the development of behavioral guidelines aimed at reducing the risk of depression.Systematic review registrationhttps://www.crd.york.ac.uk/PROSPERO/display_record.php?RecordID=546666, identifier: CRD42024546666.

Robust distributed precision matrix estimation for high-dimensional data

Estimating high-dimensional precision matrix has caught much attention from researchers. In a distributed setting, it is always prohibitive to apply the traditional estimation methods directly due to concerns in privacy and cost in communication. This paper proposes a robust distributed high-dimensional precision matrix estimation for heavy-tailed or contaminated data. The purpose of estimating precision matrix is achieved by estimating regression coefficients and error variances based on modified Cholesky Decomposition (MCD). The robustness is realized by applying the shrinkage principle based loss function. The proposed algorithm is communication-efficient because node machines only transmit gradient information to the central machine in each iteration. Simulation studies and real data analysis demonstrate the superiority of the proposed method. The complete Python code supporting this study can be downloaded from https://github.com/littletesla/RDPM.

The impact of bias due to exponentiation in the estimation of hazard, risk, and odds ratios: an empirical investigation from 1,495,059 effect sizes from MEDLINE/PubMed abstracts

BackgroundParameter estimation using regression methods plays a vital role in medical research. Often a non-linear transformation of a regression parameter is preferred for its more intuitive interpretation. Important examples in medical research are odds ratios, risk ratios, and hazard ratios, which are obtained by exponentiating the estimated regression coefficients of the logit link binomial generalized linear model, log link Poisson generalized linear model or Cox proportional hazards model, respectively. A lot of attention has been devoted to studying and removing the bias of the estimators on the scale of the regression, but the bias of the transformed parameters is rarely addressed.MethodsTwo approaches for reducing the bias due to the exponentiation are reviewed and applied to odds ratios, risk ratios, and hazard ratios reported in the abstracts published in the MEDLINE subset of English-language PubMed records.ResultsWe show that correcting for the bias due to the exponentiation may yield substantially different estimates, potentially resulting in a large shrinkage of the reported effect size estimates.ConclusionGiven the wide availability of methods to reduce the bias on the scale of regression, we encourage their routine use to improve estimation. In situations where the consequences of biased estimation are larger at the exponentiated scale than at the scale of regression, as for example in some policy and planning settings, we additionally encourage the removal of the bias due to the exponentiation.

Theory and computational tool for interval estimation in linear regressions under heteroscedasticity of unknown form using double bootstrap methods

. Linear regression models are widely used due to their simplicity and interpretability. However, the assumption of homoscedasticity (constant error variance) is often violated in practice, complicating inference. This article introduces two double bootstrap strategies—the double percentile bootstrap and the double bootstrap-t—to construct interval estimates for regression coefficients under heteroscedasticity of unknown form. The double percentile bootstrap is straightforward to implement and avoids reliance on explicit covariance matrix estimates, while the double bootstrap-t incorporates heteroscedasticity-consistent covariance matrix estimators to enhance precision. Using extensive Monte Carlo simulations, we show that both methods outperform conventional single-bootstrap approaches in maintaining nominal coverage probabilities, with the double bootstrap-t offering superior accuracy in small samples. An empirical application further illustrates the practical benefits of these methods. Additionally, we provide an open-source R package, hcci, enabling researchers to implement these algorithms effectively.

Robust inverse probability weighted estimators for doubly truncated Cox regression with closed-form standard errors.

Survival data is doubly truncated when only participants who experience an event during a random interval are included in the sample. Existing methods typically correct for double truncation bias in Cox regression through inverse probability weighting via the nonparametric maximum likelihood estimate (NPMLE) of the selection probabilities. This approach relies on two key assumptions, quasi-independent truncation and positivity of the sampling probabilities, yet there are no methods available to thoroughly assess these assumptions in the regression context. Furthermore, these estimators can be particularly sensitive to extreme event times. Finally, current double truncation methods rely on bootstrapping for variance estimation. Aside from the unnecessary computational burden, there are often identifiability issues with the NPMLE during bootstrap resampling. To address these limitations of current methods, we propose a class of robust Cox regression coefficient estimators with time-varying inverse probability weights and extend these estimators to conduct sensitivity analysis regarding possible non-positivity of the sampling probabilities. Also, we develop a nonparametric test and graphical diagnostic for verifying the quasi-independent truncation assumption. Finally, we provide closed-form standard errors for the NPMLE as well as for the proposed estimators. The proposed estimators are evaluated through extensive simulations and illustrated using an AIDS study.

New Robust Beta Regression Estimation to Overcome the Effect of High Leverage Points

Beta regression models are widely used to model continuous data with a unit interval (0,1), such as ratios, fractions, and rates. The maximum likelihood method is typically used to estimate regression coefficients in beta regression models. However, the maximum likelihood estimator is highly sensitive to outliers. Several studies have proposed methods to address this problem, such as the M-Huber, S-estimator, LMS, and LTS estimators. However, these methods suffer from the problem of high leverage points (HLPoints) in the independent variables. The GM-estimator is one of the methods that address this problem. This study examines beta regression analysis, focusing on the effect of high leverage points (HLPoints) on parameter estimates. Monte Carlo simulations and real data are conducted to evaluate and compare the performance of the proposed robust method, Generalized M-Beta Regression (GMBr), with the existing beta regression method estimated using Maximum Likelihood (MLBr).

A computationally efficient approach to false discovery rate control and power maximisation via randomisation and mirror statistic.

Simultaneously performing variable selection and inference in high-dimensional regression models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of specific statistical procedures to accurately select the most important predictors in a high-dimensional space, while controlling the false discovery rate (FDR) associated with the variable selection procedure. In this paper, we propose the joint adoption of the Mirror Statistic approach to FDR control, coupled with outcome randomisation to maximise the statistical power of the variable selection procedure, measured through the true positive rate. Through extensive simulations, we show how our proposed strategy allows us to combine the benefits of the two techniques. The Mirror Statistic is a flexible method to control FDR, which only requires mild model assumptions, but requires two sets of independent regression coefficient estimates, usually obtained after splitting the original dataset. Outcome randomisation is an alternative to data splitting that allows to generate two independent outcomes, which can then be used to estimate the coefficients that go into the construction of the Mirror Statistic. The combination of these two approaches provides increased testing power in a number of scenarios, such as highly correlated covariates and high percentages of active variables. Moreover, it is scalable to very high-dimensional problems, since the algorithm has a low memory footprint and only requires a single run on the full dataset, as opposed to iterative alternatives such as multiple data splitting.

Efficient case-cohort design using balanced sampling

The case-cohort design is a cost-efficient two-phase design for analyzing survival data when key risk factors are expensive to assess and the event rate is low. Traditionally, subcohorts are selected via simple random sampling, which might not fully utilize available information. This paper introduces an efficient sampling design using balanced sampling for subcohort selection within the case-cohort design. A notable benefit of employing balanced sampling is the automatic calibration of auxiliary variables available for the entire cohort. Under a Cox model, it has been demonstrated that the calibration of sampling weights, utilizing auxiliary variables highly correlated with the main risk factor, significantly enhances the efficiency of regression coefficient estimators. Extensive simulation experiments show the reduced variabilities under the proposed approach in comparison to those under both simple random sampling. The proposed design and estimation procedure are further illustrated using the well-established National Wilms Tumor Study dataset.

The impact of central sensitization on perioperative pain in TKA: a retrospective cohort study

BackgroundTotal knee arthroplasty (TKA) is an established surgical procedure for severe knee osteoarthritis (KOA) that has provided excellent outcomes. While several studies have reported that patients with preoperative central sensitization (CS) experienced worse pre- and post-operative pain and outcomes, the evidence is limited. We conducted this study to determine the impact of CS on perioperative knee pain in TKA for severe KOA.MethodsA retrospective cohort study of 66 patients who underwent bilateral TKA for bilateral severe KOA was conducted. Multiple linear regression models that included covariates and scaled estimated regression coefficients were used to examine the impact of CS on the patients’ pre- and post-operative pain subscale values on the Knee Injury and Osteoarthritis Outcome Score (KOOS) and the improvement of KOOS pain. Postoperative KOOS pain was assessed at 3 months postoperatively, while other evaluation items including preoperative KOOS pain, CS, and pain self-efficacy were assessed on admission.ResultsCS had a negative impact on pre- and post-operative KOOS pain (preoperative, β: −0.28, 95% confidence interval [CI] −18.53, −0.92; postoperative, β: −0.26, 95%CI −14.09, −0.44; p < 0.05). High pain self-efficacy had a positive impact on preoperative KOOS pain (β: 0.25, 95%CI 0.32, 18.08; p < 0.05). However, CS did not influence the improvement of KOOS pain.ConclusionsThese results demonstrate that CS had a negative impact on pre- and post-TKA knee pain in patients but did not affect the improvement of knee pain. TKA provides sufficient pain relief for severe KOA, with or without CS. Further research is required to improve pre- and post-operative knee pain in KOA patients with CS.

Examining maternal social perceptions and stress responses during pregnancy.

Examining maternal social perceptions and stress responses during pregnancy.

Preoperative Calcimimetic Treatment may Prevent Serum Creatinine Elevation after Parathyroidectomy in Kidney Transplant Recipients: A Retrospective Cohort Study.

Preoperative Calcimimetic Treatment may Prevent Serum Creatinine Elevation after Parathyroidectomy in Kidney Transplant Recipients: A Retrospective Cohort Study.

The relationship between milk urea nitrogen content and urinary nitrogen excretion as determined in 4 Swiss dairy breeds.

Ammonia (NH3) originating from agriculture substantially contributes to the environmental nitrogen load and threatens sensitive ecosystems by inducing eutrophication and acidification of the soil. To strategically minimize NH3 emissions, this study aimed to develop a model to predict urinary nitrogen (UN) excretion (g/d), the major NH3 source of cows of different dairy breeds, based on an easy-to-determine proxy as an on-farm tool. For that purpose, dietary characteristics were not considered. One such proxy would be the MUN content, which could be determined in tank milk samples from dairy farms. We therefore investigated the UN and MUN values from 21 different feeding experiments performed in Switzerland with 4 contrasting dairy breeds. These were 162 Brown Swiss (BS), 348 Holstein (HO), 44 Jersey (JE), and 50 Swiss Fleckvieh (SF) cows. We investigated the relationship between the coefficients of the UN and MUN using various linear mixed models. The forward model selection demonstrated that it is essential to consider the interaction between MUN and breed, as well as BW and breed, when modeling UN. Furthermore, there was a pronounced heteroscedasticity between UN and MUN for higher MUN values (>14 mg/dL). This heteroscedasticity must be accounted for, either through explicit modeling or log transformation. The final model included fixed effects, MUN, BW, and breed, the interactions, MUN × breed and BW × breed, as well as the experiment as random effect. This model also considered the heteroscedasticity. In the final model, R2 was high, at 81.2%. The regression coefficients and highest posterior density intervals were 7.28 (5.42; 9.02), 10.41 (9.16; 11.65), 9.00 (6.20; 11.94) and 11.79 (9.15; 14.25) g/d of increase in UN per mg/dL of MUN for BS, HO, JE, and SF, respectively. The estimated regression coefficients for BW and highest posterior density intervals were 0.09 (-0.01; 0.19), 0.17 (0.11; 0.27), 0.51 (0.21; 0.80) and 0.28 (0.03; 0.53) for BS, HO, JE, and SF, respectively. The estimated marginal means ± SE for UN (g/d) were 117 ± 12, 147 ± 12, 119 ± 14, and 135 ± 14 for BS, HO, JE, and SF, respectively. These results confirm MUN content to be a useful tool to predict UN excretion in lactating dairy cows, as suggested by previous studies. However, in contrast to previous findings, our results underscore the necessity of accounting for breed and BW in the predictive model. The established model improves the accuracy of mass flow models that estimate NH3 emissions based on the UN excretion of livestock at the beginning of the manure management chain.

영과잉 일반화 포아송 회귀모형에서 산포모수의 효과에 관한 연구

In this study, we examine the influence of overdispersion on statistical inference in a zero-inflated generalized Poisson regression model by simulation experiments and real data analysis. In the simulation study, simulated data are generated from the zero-inflated generalized Poisson regression model, and the regression coefficients in the zero-inflated Poisson regression and the zero-inflated generalized Poisson regression models are estimated. The simulation experiment results show that the regression coefficient estimates for the mean and zero-inflation probability of the zero-inflated Poisson regression to ignore overdispersion underestimate the true value when overdispersion exists, and this underestimation problem becomes more severe as the overdispersion increases. In addition, the standard errors of the regression coefficient estimates of the zero-inflated Poisson regression model are more underestimated as the overdispersion increased. Ultimately, the zero-inflated Poisson regression model, which ignores the overdispersion despite its existence, shows a larger nominal significance level in the hypothesis test for the true value of the regression coefficient, and this problem of the nominal significance level becomes more severe as the overdispersion increased. The results of this simulation experiment could be confirmed through the analysis of real data on the number of boat trips to Lake Somerville in eastern Texas in the United States in 1980.

The Impact of Overweight on Wages of Russians

This paper examines the impact of Body Mass Index (BMI) on individual earnings. The study aims to determine whether there is weight–wage discrimination against individuals with higher BMI levels in the Russian labor market, resulting in lower wages, all other things being equal. The distinctive feature of this study is that the author analyzed the results of representative annual population surveys using regression analysis methods, allowing control for potential reverse causality between BMI and wages. The research used a panel dataset of officially employed respondents from the Russian Longitudinal Monitoring Survey collected by HSE University (RLMS–HSE) from 2013 to 2022.To address the endogeneity problem in studying the relationship between BMI and wages and to obtain consistent estimates of regression coefficients, the paper employs the instrumental variable (IV) method, which relies on the heteroscedasticity of residuals.The findings indicate that the wages of overweight or obese workers are significantly lower than those of normal-weight employees. Thus, an individual's BMI, in addition to other socio-economic and demographic characteristics, can be considered a factor affecting the wages of Russians.

Likelihood analysis of latent functional response regression models for sequences of correlated binary data

AbstractIn this article, we study a functional regression setting where the random response curve is unobserved, and only its dichotomized version observed at a sequence of correlated binary data is available. We propose a practical computational framework for maximum likelihood analysis via the parameter expansion technique. Our proposal relies on the use of a complete data likelihood which can handle non‐equally spaced and missing observations effectively. The proposed method is used in the Function‐on‐Scalar regression setting, with the latent response variable being a Gaussian random element taking values in a separable Hilbert space. Smooth estimates of functional regression coefficients and principal components are provided by introducing a novel adaptive EM algorithm. Finally, the performance of our novel method is demonstrated by various simulation studies and on a real case study. The proposed method is implemented in the R package dfrr. Supporting Information for this article are available online.

Skills and Labor Market Performance in Korea: An International Comparison Perspective

This study presents an international comparison of relations between skills and labor market performance. Human capital theory emphasizes that skills have a positive effect on labor market performance, which is evident in most countries. However, skill levels do not have a positive impact on employability and wage in South Korea, unlike other OECD countries. Using data from the Programme for the International Assessment of Adult Competencies (PIAAC), we analyze how various skill dimensions influence employment outcomes and wage levels. The skills measured in PIAAC are plausible values. Therefore, our methodology entails estimating regression coefficients and presenting the final estimates as the averages of these coefficients. Standard errors are computed through repeated sampling using the jackknife technique. The findings of this study indicate that policies focusing solely on the supply side of skills, such as expanding education and training, may have a limited impact on improving employment and wages in Korean labor market. While human capital investment remains crucial for labor market outcomes, the results suggest that Korea could achieve greater effectiveness by complementing these efforts with workplace innovation policies aimed at increasing the demand for skills.

A Bayesian approach to correcting the attenuation bias of regression using polygenic risk score.

Polygenic risk score has become increasingly popular for predicting the value of complex traits. In many settings, polygenic risk score is used as a covariate in regression analysis to study the association between different phenotypes. However, measurement error in polygenic risk score causes attenuation bias in the estimation of regression coefficients. In this paper, we employ a Bayesian approach to accounting for the measurement error of polygenic risk score and correcting the attenuation bias in linear and logistic regression. Through simulation, we show that our approach is able to obtain approximately unbiased estimation of coefficients and credible intervals with correct coverage probability. We also empirically compare our Bayesian measurement error model with the conventional regression model by analyzing real traits in the UK Biobank. The results demonstrate the effectiveness of our approach as it significantly reduces the error in coefficient estimates.

The Effect of Interpersonal Skills, Intrapersonal Skills, Suprapersonal Skills, and Career Adaptability on Employability Skills in Indonesian Aviation Polytechnic Cadets

This study aims to determine the influence effect of Interpersonal skills, Intrapersonal skills, Suprapersonal skills, and Career adaptability on Employability skills in Aviation Polytechnic Cadets. This research was conducted in seven official schools under the Indonesian Civil Aviation Human Resources Development Centre. The sample of this study amounted to 300 cadets who were determined using purposive random sampling. Data collection techniques consisted of distributing questionnaires and documentation. The data analysis technique in this study uses the Structural Equation Model (SEM), which consists of a measurement model and a structural model. The measurement model produces research constructs that fit the data. The structural model describes the causal or predictive relationship between exogenous and endogenous variables. The exogenous variables consist of Intrapersonal skills, Interpersonal skills, Suprapersonal skills, and Career adaptability. The endogenous variable is Employability skills. Structural model testing uses the SEM-PLS Program. The structural model analysis shows that the model fits significantly with the data, with the standardized regression coefficient (SRW) estimates being significant (p&lt;0.001). The results showed: (1) There is a significant positive influence between Intrapersonal Skills on Career Adaptability; (2) There is a significant positive influence between Interpersonal Skills on Career Adaptability; (3) There is a significant positive influence between Suprapersonal Skills on Career Adaptability; (4) There is a significant positive influence between Career Adaptability on Employability Skills; (5) There is a significant positive influence between Intrapersonal Skills on Employability Skills through the mediator Career Adaptability; (6) There is a significant positive influence between Interpersonal Skills on Employability Skills through the mediator Career Adaptability; (7) There is a significant positive influence between Suprapersonal Skills on Employability Skills through the mediator Career Adaptability. The research implies that it is recommended that lecturers in teaching not only pay attention to academic aspects (cognitive) but also pay attention to other aspects such as Intrapersonal, Interpersonal, Suprapersonal, Employability, and Career adaptability.