Inverse Regression Model Research Articles

Influence diagnostics in the inverse Gaussian ridge regression model: Applications in chemometrics

AbstractThe influential observation affects the regression model inferences. Literature has shown that the problems of multicollinearity and influential observations can jointly exist in a model. The ridge regression estimator has been developed to handle the challenge of multicollinearity. The detection of influential observations with multicollinearity and its impact on the ridge estimates is necessary for better decision making. In this article, we proposed some influence diagnostics for the inverse Gaussian ridge regression model (IGRRM). The proposed diagnostics are evaluated with the help of a simulation study and two chemometric‐related data sets. We found that the covariance ratio (CVR) method is better than other methods for the detection of influential observations under smaller dispersion. While for larger dispersion, all the IGRRM diagnostics perform equally well for the identification of influential observations.

Bayesian Inverse Regression for Vascular Magnetic Resonance Fingerprinting.

Standard parameter estimation from vascular magnetic resonance fingerprinting (MRF) data is based on matching the MRF signals to their best counterparts in a grid of coupled simulated signals and parameters, referred to as a dictionary. To reach a good accuracy, the matching requires an informative dictionary whose cost, in terms of design, storage and exploration, is rapidly prohibitive for even moderate numbers of parameters. In this work, we propose an alternative dictionary-based statistical learning (DB-SL) approach made of three steps: 1) a quasi-random sampling strategy to produce efficiently an informative dictionary, 2) an inverse statistical regression model to learn from the dictionary a correspondence between fingerprints and parameters, and 3) the use of this mapping to provide both parameter estimates and their confidence indices. The proposed DB-SL approach is compared to both the standard dictionary-based matching (DBM) method and to a dictionary-based deep learning (DB-DL) method. Performance is illustrated first on synthetic signals including scalable and standard MRF signals with spatial undersampling noise. Then, vascular MRF signals are considered both through simulations and real data acquired in tumor bearing rats. Overall, the two learning methods yield more accurate parameter estimates than matching and to a range not limited to the dictionary boundaries. DB-SL in particular resists to higher noise levels and provides in addition confidence indices on the estimates at no additional cost. DB-SL appears as a promising method to reduce simulation needs and computational requirements, while modeling sources of uncertainty and providing both accurate and interpretable results.

TheKLestimator for the inverse Gaussian regression model

AbstractMulticollinearity poses an undesirable effect on the efficiency of the maximum likelihood estimator (MLE) in both Gaussian and non‐Gaussian regression models. The ridge and the Liu estimators have been developed as an alternative to the MLE. Both estimators possess smaller mean squared error (MSE) over the MLE. Recently, Kibria and Lukman developed KL estimator, which was found to outperform the ridge and the Liu estimators in the linear regression model. With this expectation, we developed the KL estimator for the inverse Gaussian regression model. We compare the proposed estimator's performance with some existing estimators in terms of theoretical comparison, the simulation study, and real‐life application. Smaller MSE criterion shows that the proposed estimator with one of its shrinkage parameter performs the best.

An Expectation-Maximization Algorithm for the Exponential-Generalized Inverse Gaussian Regression Model with Varying Dispersion and Shape for Modelling the Aggregate Claim Amount

This article presents the Exponential–Generalized Inverse Gaussian regression model with varying dispersion and shape. The EGIG is a general distribution family which, under the adopted modelling framework, can provide the appropriate level of flexibility to fit moderate costs with high frequencies and heavy-tailed claim sizes, as they both represent significant proportions of the total loss in non-life insurance. The model’s implementation is illustrated by a real data application which involves fitting claim size data from a European motor insurer. The maximum likelihood estimation of the model parameters is achieved through a novel Expectation Maximization (EM)-type algorithm that is computationally tractable and is demonstrated to perform satisfactorily.

Deep Neural Networks for Inverse Design of Nanophotonic Devices

Deep learning is now playing a major role in designing photonic devices, including nanostructured photonics. In this article, we investigate three models for designing nanophonic power splitters with multiple splitting ratios. The first model is a forward regression model, wherein the trained deep neural network (DNN) is used within the optimization loop. The second is an inverse regression model, in which the trained DNN constructs a structure with the desired target performance given as input. The third model is a generative network, which can randomly produce a series of optimized designs for a target performance. Focusing on the nanophotonic power splitters, we show how the devices can be designed by these three types of DNN models.

Quality of Diabetes Care in Blended Fee-for-Service and Blended Capitation Payment Systems

ObjectivesIn the middle to late 2000s, many family physicians switched from a Family Health Group (FHG; a blended fee-for-service model) to a Family Health Organization (FHO; a blended capitation model) in Ontario, Canada. The evidence on the link between physician remuneration schemes and quality of diabetes care is mixed in the literature. We examined whether physicians who switched from the FHG to FHO model provided better care for individuals living with diabetes relative to those who remained in the FHG model. MethodsUsing longitudinal health administrative data from 2006 to 2016, we investigated the impact of physicians switching from FHG to FHO on 8 quality indicators related to diabetes care. Because FHO physicians are likely to be systematically different from FHGs, we employed propensity-score-based inverse probability-weighted fixed-effects regression models. All analyses were conducted at the physician level. ResultsWe found that FHO physicians were more likely to provide glycated hemoglobin testing by 2.75% (95% confidence interval [CI], 1.89% to 3.60%), lipid assessment by 2.76% (CI, 1.95% to 3.57%), nephropathy screening by 1.08% (95% CI, 0.51% to 1.66%) and statin prescription by 1.08% (95% CI, 0.51% to 1.66%). Patients under FHOs had a lower estimated risk of mortality by 0.0124% (95% CI, 0.0123% to 0.0126%) per physician per year. However, FHG and FHO physicians were similar for annual eye examination, prescription of angiotensin-converting enzyme inhibitors (or angiotensin II receptor blockers) and patients’ risk of avoidable diabetes-related hospitalizations. ConclusionsCompared with blended fee-for-service, blended capitation payment is associated with a small, but statistically significant, improvement in some aspects of diabetes care.

Relationship of neighborhood social determinants of health on racial/ethnic mortality disparities in US veterans-Mediation and moderating effects.

ObjectiveTo examine mediation and moderation of racial/ethnic all‐cause mortality disparities among Veteran Health Administration (VHA)‐users by neighborhood deprivation and residential segregation.Data sourcesElectronic medical records for 10/2008‐9/2009 VHA‐users linked to National Death Index, 2000 Area Deprivation Index, and 2006‐2009 US Census.Study designRacial/ethnic groups included American Indian/Alaskan Native (AI/AN), Asian, non‐Hispanic black, Hispanic, Native Hawaiian/Other Pacific Islander, and non‐Hispanic white (reference). We measured neighborhood deprivation by Area Deprivation Index, calculated segregation for non‐Hispanic black, Hispanic, and AI/AN using the Isolation Index, evaluated mediation using inverse odds‐weighted Cox regression models and moderation using Cox regression models testing for neighborhood*race/ethnicity interactions.Principal findingsMortality disparities existed for AI/ANs (HR = 1.07, 95%CI:1.01‐1.10) but no other groups after covariate adjustment. Neighborhood deprivation and Hispanic segregation neither mediated nor moderated AI/AN disparities. Non‐Hispanic black segregation both mediated and moderated AI/AN disparities. The AI/AN vs. non‐Hispanic white disparity was attenuated for AI/ANs living in neighborhoods with greater non‐Hispanic black segregation (P = .047). Black segregation's mediating effect was limited to VHA‐users living in counties with low black segregation. AI/AN segregation also mediated AI/AN mortality disparities in counties that included or were near AI/AN reservations.ConclusionsNeighborhood characteristics, particularly black and AI/AN residential segregation, may contribute to AI/AN mortality disparities among VHA‐users, particularly in communities that were rural, had greater black segregation, or were located on or near AI/AN reservations. This suggests the importance of neighborhood social determinants of health on racial/ethnic mortality disparities. Living near reservations may allow AI/AN VHA‐users to maintain cultural and tribal ties, while also providing them with access to economic and other resources. Future research should explore the experiences of AI/ANs living in black communities and underlying mechanisms to identify targets for intervention.

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods.

Two-parameter estimator for the inverse Gaussian regression model

The inverse Gaussian regression model (IGRM) is frequently applied in the situations, when the response variable is positively skewed and well fitted to the inverse Gaussian distribution. The maximum likelihood estimator (MLE) is generally used to estimate the unknown regression coefficients of the IGRM. The performance of the MLE method is better if the explanatory variables are uncorrelated with each other. But the presence of multicollinearity generally inflates the variance and standard error of the MLE resulting the loss of efficiency of estimates. So, for the estimation of unknown regression coefficients of the IGRM, the MLE is not a trustworthy method. To combat multicollinearity, we propose two parameter estimators (TPE) for the IGRM to improve the efficiency of estimates. Moreover, mean squared error criterion is taken into account to compare the performance of TPE with other biased estimators and MLE using Monte Carlo simulation study and a real example. Based on the results of Monte Carlo simulation study and a real example, we may suggest that the TPE based on Asar and Genç method for the IGRM is better than the other competitive estimators.

Diagnostic techniques for the inverse Gaussian regression model

In this article, we propose some diagnostic techniques for the inverse Gaussian regression model (IGRM), which are appropriate for modeling the response variable that undertakes positively skewed continuous dataset. Moreover, two new diagnostic methods are mainly proposed for the IGRM, which named as covariance ratio (CVR) and Welsch’s distance (WD). The comparison of our proposed methods of influence diagnostics with the existing approaches has been made through Monte Carlo simulation under different factors. In addition, the benefit of the proposed methods is assessed using a real application. Based on the simulation and empirical application results, we observed that the performance of the proposed method is better than the existing methods for detection of influential observations.

Alcohol Consumption, Brain Amyloid-β Deposition, and Brain Structural Integrity Among Older Adults Free of Dementia.

Light to moderate alcohol consumption has been variably associated with lower or higher risk of dementia, but effects on Alzheimer's disease pathology are less clear. We determined whether late-life alcohol consumption was associated with Alzheimer's disease pathology among older adults. We assessed the associations of alcohol consumption self-reported in 2000-2002 with brain amyloid-β deposition on PET scans, and white matter lesion and hippocampal volume on MRIs measured 7-9 years later in 189 participants of the Ginkgo Evaluation of Memory Study (age 75-87 years at baseline) who were free of clinical dementia, using multivariable-adjusted and inverse probability-weighted robust linear regression models. Alcohol consumption was not statistically significantly associated with amyloid-β deposition (standardized uptake value ratio difference per drink: -0.013 [95% CI: -0.027, 0.002]). Both non-drinkers and participants consuming ≥1 drink(s)/week had higher white matter lesion volume (% intracranial volume) than did the reference group of those consuming <1 drink/week (differences: 0.25 % [95% CI: 0.01, 0.50]; 0.26 % [95% CI: 0.02, 0.50]). The association of alcohol consumption and hippocampal volume was modified by age (p = 0.02). Among participants younger than 77 years, participants consuming 1-7 drinks/week had larger hippocampal volume compared with participants consuming <1 drink/week. Alcohol consumption was not statistically significantly associated with amyloid-β deposition 7-9 years later. Non-drinking and greater alcohol consumption were associated with higher white matter lesion volume compared with drinking <1 drink/week. Moderate drinking was associated with higher hippocampal volume in younger individuals. Given the selective nature of this population and adverse health effects of excessive alcohol consumption, these findings warrant further investigation, but cannot be translated into clinical recommendations.

An integrated analysis of lymphocytic reaction, tumour molecular characteristics and patient survival in colorectal cancer

BackgroundHistological lymphocytic reaction is regarded as an independent prognostic marker in colorectal cancer. Considering the lack of adequate statistical power, adjustment for selection bias and comprehensive tumour molecular data in most previous studies, we investigated the strengths of the prognostic associations of lymphocytic reaction in colorectal carcinoma by utilising an integrative database of two prospective cohort studies.MethodsWe examined Crohn’s-like reaction, intratumoural periglandular reaction, peritumoural reaction and tumour-infiltrating lymphocytes in 1465 colorectal carcinoma cases. Using covariate data of 4420 colorectal cancer cases in total, inverse probability-weighted Cox proportional hazard regression model was used to control for selection bias (due to tissue availability) and potential confounders, including stage, MSI status, LINE-1 methylation, PTGS2 and CTNNB1 expression, KRAS, BRAF and PIK3CA mutations, and tumour neoantigen load.ResultsHigher levels of each lymphocytic reaction component were associated with better colorectal cancer-specific survival (Ptrend < 0.002). Compared with cases with negative/low intratumoural periglandular reaction, multivariable-adjusted HRs were 0.55 (95% CI, 0.42–0.71) in cases with intermediate reaction and 0.20 (95% CI, 0.12–0.35) in cases with high reaction. These relationships were consistent in strata of MSI status or neoantigen loads (Pinteraction > 0.2).ConclusionsThe four lymphocytic reaction components are prognostic biomarkers in colorectal carcinoma.

A new Liu-type estimator for the Inverse Gaussian Regression Model

ABSTRACTThe Inverse Gaussian Regression Model (IGRM) is used when the response variable is positively skewed and follows the inverse Gaussian distribution. In this article, we propose a Liu-type estimator to combat multicollinearity in the IGRM. The variance of the Maximum Likelihood Estimator (MLE) is overstated due to the presence of severe multicollinearity. Moreover, some estimation methods are suggested to estimate the optimal value of the shrinkage parameter. The performance of the proposed estimator is compared with the MLE and some other existing estimators in the sense of mean squared error through Monte Carlo simulation and different real-life applications. Under certain conditions, it is concluded that the proposed estimator is superior to the MLE, ridge, and Liu estimator.

A note on confidence intervals for deblurred images

We consider pointwise asymptotic confidence intervals for images that are blurred and observed in additive white noise. This amounts to solving a stochastic inverse problem with a convolution operator. Under suitably modified assumptions, we fill some apparent gaps in the proofs published in [N. Bissantz, M. Birke, Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators, J. Multivariate Anal. 100 (2009), 2364-2375]. In particular, this leads to modified bootstrap confidence intervals with much better finite-sample behaviour than the original ones, the validity of which is, in our opinion, questionable. Some simulation results that support our claims and illustrate the behaviour of the confidence intervals are also presented.

Empirical Study on the Accuracy and Precision of Automatic Passenger Counting in European Bus Services

Background:An Automatic Passenger Counting system represents a powerful resource for an efficient operational planning of public transport companies, but it gives rise to several challenges such as accuracy and precision, which must be addressed in order to operate successfully.Objective:Unlike previous studies in the North American bus market, this paper evaluates the accuracy and precision of an infrared APC system in a European bus market.Methods:The accuracy is evaluated by considering: (i) the presence/absence of the error and its direction; (ii) the magnitude of the error disregarding the direction and (iii) some tests on the nature of the error. The precision is evaluated by direct and inverse regression models and somet-teston biases.Results:As for accuracy, a small average magnitude of the errors is observed. In addition, the APC accurately measures alighting passengers, while it presents a slight tendency to systematically undercount boarding passengers. As for precision, the amount of measurement error due to the APC system exists and, even if it is relatively contained, it is statistically significant for boarding and alighting passengers.Conclusion:Although one type of APC system is evaluated only on one bus, it seems quite accurate for recording alighting passengers, whereas a correction factor should be applied for boarding passengers.

Diagnostics via partial residual plots in inverseGaussianregression

AbstractRegression diagnostics is the basic requirement to apply regression analysis to reach reliable conclusions. Generalized linear models also required diagnostics for its implementation. The construction of partial residuals using response residuals for the inverse Gaussian regression model is carried out to explore the structure and usefulness for visualizing diagnostics and curvature as a function of selected predictors. The current study established the performance of partial residual plots over conventional diagnostic methods. The comparison has been made using aerial biomass data and with the help of simulation study. It has been observed that partial residual plots provide much better diagnosis than do conventional methods. Moreover, multiple diagnostics in a single display provide better perceptive towards lack of fit, specification, and data anomalies.

Diagnostic analysis of a circular-circular regression model using asymmetric or asymmetric bi-modal circular errors

Many circular data sets encountered in practice are asymmetric or asymmetric bi-modal. In this paper, we propose a diagnostic analysis of a parametric circular regression model with a single circular explanatory variable by assuming asymmetric or asymmetric bi-modal circular errors. We develop a new test statistic for detecting outliers both in circular response and explanatory variables. For the case with a circular explanatory variable, we employ a parametric inverse circular-circular regression model. In addition, we provide a goodness of fit test to find whether circular errors are symmetric or not. Our methods are illustrated using a real data set arising from a study of Genomics.

Cause-specific investigation of primary delays of Wuhan–Guangzhou HSR

ABSTRACT This paper presents the results of acase study on the causes and effects of typical service disruptions in aHigh-speed rail (HSR) system in China–Wuhan–Guangzhou High-speed railway (WH-GZ HSR). With acause-specific approach, seven delay causalities leading to primary delays (PDs) are identified, and the properties and consequences of each primary delay (PD) factor is derived. The comparison of candidate distributional forms shows that the Log-normal distribution model can approximate better the length of all identified PDs. For each PD cause, the distribution of delay duration is estimated and tuned. Next, cause-specific distributional models for PDs severity are discussed. The models for the number of affected trains are presented in the form of inverse regression models with specific domains. Then, comparing five different kinds of candidate models, the results show that the Cubic is the best to approximate the distributions of total-affected time.

Data-Driven Power Flow Linearization: A Regression Approach

The linearization of a power flow (PF) model is an important approach for simplifying and accelerating the calculation of a power system’s control, operation, and optimization. Traditional model-based methods derive linearized PF models by making approximations in the analytical PF model according to the physical characteristics of the power system. Today, more measurements of the power system are available and thus facilitate data-driven approaches beyond model-driven approaches. This paper studies a linearized PF model through a data-driven approach. Both a forward regression model [( $ {P}, {Q}$ ) as a function of ( $ {\theta }, {V}$ )] and an inverse regression model [( $ {\theta }, {V}$ ) as a function of ( $ {P}, {Q}$ )] are proposed. Partial least squares- and Bayesian linear regression-based algorithms are designed to address data collinearity and avoid overfitting. The proposed approach is tested on a series of IEEE standard cases, which include both meshed transmission grids and radial distribution grids, with both Monte Carlo simulated data and public testing data. The results show that the proposed approach can realize a higher calculation accuracy than model-based approaches can. The results also demonstrate that the obtained regression parameter matrices of data-driven models reflect power system physics by demonstrating similar patterns with some power system matrices (e.g., the admittance matrix).

Prediction analysis for microbiome sequencing data.

One goal of human microbiome studies is to relate host traits with human microbiome compositions. The analysis of microbial community sequencing data presents great statistical challenges, especially when the samples have different library sizes and the data are overdispersed with many zeros. To address these challenges, we introduce a new statistical framework, called predictive analysis in metagenomics via inverse regression (PAMIR), to analyze microbiome sequencing data. Within this framework, an inverse regression model is developed for overdispersed microbiota counts given the trait, and then a prediction rule is constructed by taking advantage of the dimension-reduction structure in the model. An efficient Monte Carlo expectation-maximization algorithm is proposed for maximum likelihood estimation. The method is further generalized to accommodate other types of covariates. We demonstrate the advantages of PAMIR through simulations and two real data examples.