Parameter Estimation Of Regression Model Research Articles

Unbiased Proxy Calibration

The linear calibration model is a powerful statistical tool that can be utilized to predict an unknown response variable, Y, through observations of a proxy or predictor variable, X. Since calibration involves estimation of regression model parameters on the basis of a limited amount of noisy data, an unbiased calibration slope estimation is of utmost importance. This can be achieved by means of state-of-the-art, data-driven statistical techniques. The present paper shows that weighted least-squares for both variables estimation (WLSXY) is able to deliver unbiased slope estimations under heteroscedasticity. In the case of homoscedasticity, besides WLSXY, ordinary least-squares (OLS) estimation with bias correction (OLSBC) also performs well. For achieving unbiasedness, it is further necessary to take the correct regression direction (i.e., of Y on X) into account. The present paper introduces a pairwise moving block bootstrap resampling approach for obtaining accurate estimation confidence intervals (CIs) under real-world climate conditions (i.e., non-Gaussian distributional shapes and autocorrelations in the noise components). A Monte Carlo simulation experiment confirms the feasibility and validity of this approach. The parameter estimates and bootstrap replications serve to predict the response with CIs. The methodological approach to unbiased calibration is illustrated for a paired time series dataset of sea-surface temperature and coral oxygen isotopic composition. Fortran software with implementation of OLSBC and WLSXY accompanies this paper.

Robust penalized empirical likelihood estimation method for linear regression

Maximum likelihood estimation is a popular method for parameter estimation in regression models. However, since in some data sets it may not be possible to make any distributional assumptions on the error term, the likelihood method cannot be used to estimate the parameters of interest. For those data sets, one can use the empirical likelihood estimation method to estimate the parameters of a linear regression model. The aim of this study is to propose a robust penalized empirical likelihood estimation method to estimate the regression parameters and select significant variables, simultaneously, for data scenarios for which a well-defined likelihood function may not be available. This will be achieved by combining a robust empirical estimation method and the bridge penalty function. We investigate the asymptotic properties of the proposed estimator and explore the finite sample behaviour with a simulation study and a real data example.

Comparative analysis of commercial partnership in the context of changes in Polish tax law

The aim of the article was to examine the implications of changes in the rules of taxation of the income of limited joint-stock partnerships (LJSP) and limited partnerships (LP) for their dynamics and structure, especially against the background of other commercial partnerships. The hypothesis is that the changes in the rules of taxation of the income of limited joint-stock partnerships and limited partnerships negatively influenced their attractiveness as legal forms of running a business. The research methods used in the article were the analysis of the dynamics of time series, the Fisher-Snedecor test to verify the hypothesis of equality variance and the least squares method. It turns out that the amendment to the tax laws of legal persons/ entities (01.01.2014) by equalising the tax status of the LJSP with the status of legal persons/entities contributed to the increase in the tax burden of those companies, the decline in their numbers in both the commercial partnerships (CP), as well as companies in total in Poland, and in this way the decrease of the structure and dynamics indices. In turn, further changes from 1 January 2021 meant that not only the LJSP ceased to be attractive as a tool to minimise the tax burden for the owners, but also LP. In 2020, the highest decrease in the number of all companies in Poland, amounting to 6.8%, was recorded by LJSP, while in 2021 – LP (7.1%). The results of the Fisher-Snedecor test for the difference in the number of companies calculated year on year confirmed that after 2014 there was a large change in the level of differentiation in the number of limited joint-stock partnerships compared to the previous years. The number of companies decreased rapidly from year to year, which proves the decline in interest in this form of business, and the decline was manifested by a significant increase in data variability, as demonstrated by the Fisher-Snedecor test. The author observed a similar situation for limited partnerships as the change in their number year-on-year was also very differentiated before and after 2014. However, such a conclusion cannot be drawn in relation to general partnerships and partnerships, which indicates that the change in regulations introduced on 1 January 2014 did not affect the trend to create these activities. Additionally, the estimation of regression model parameters for CP group companies showed that the change in the number of LJSP year on year did not change the number of companies of other types.

Joint assessment of temporal segmentation, time unit and detection algorithms in syndromic surveillance

The choice of the aggregation that defines the temporal unit of epidemiological surveillance is part of the more theoretical framework of the modifiable temporal unit problem (MTUP). It has been demonstrated that this choice influences temporal cluster detection and may lead to false-positive results and poor estimation of regression model parameters. In syndromic surveillance (SyS), despite the choice of which temporal aggregation to use being crucial, it has not yet been addressed in the literature. In most SyS systems, this choice is driven by the frequency of the data collection and/or human resources available, although neither the temporal unit’s influence on the performance of anomaly detection algorithms nor on the efficiency of the SyS are known.The main objective of our study was to analyze the influence of the temporal aggregation unit on the performances of SyS detection algorithms used routinely, according to the characteristics of specific syndromes and outbreaks. Simulating daily time series of various syndromes, we tested three different time series aggregation methods. For each of four anomaly detection algorithms and their variants, we calculated seven performance indicators and multi-criteria scores to guide epidemiologists in their choice of which temporal aggregation of surveillance to use. From 19,200 analyzed time series, we observed an effect of temporal aggregation on the performance of the detection algorithms tested. Results also showed that the time aggregation unit was linked to the detection algorithm used, and that strong aggregation-algorithm interactions need to be taken into account when deciding on which aggregation-algorithm pair to use. Using theoretical data, our study also showed that no one ideal aggregation-algorithm pair exists for all contexts when deciding on which temporal unit of surveillance to use, and that the choice depends on several parameters.Our results can help public health practitioners choose the most appropriate time series aggregation and algorithm according to their specific needs. Finally, the present work enabled us to develop recommendations for a One Health project where the same time aggregation type and detection method could be used for both human and animal syndromic surveillance data.

Simultaneous Semiparametric Estimation of Clustering and Regression

ABSTRACT We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group-related variables are available. This problem involves clustering to infer the missing group variable based on the group-related variables, and regression to build a model on the target variable given the group and eventually some additional variables. Thus, this problem can be formulated as the joint distribution modeling of the target and of the group-related variables. The usual parameter estimation strategy for this joint model is a two-step approach starting by learning the group variable (clustering step) and then plugging in its estimator for fitting the regression model (regression step). However, this approach is suboptimal (providing in particular biased regression estimates) since it does not make use of the target variable for clustering. Thus, we advise the use of a simultaneous estimation approach of both clustering and regression, in a semiparametric framework. Numerical experiments illustrate the benefits of our proposition by considering wide ranges of distributions and regression models. The relevance of our new method is illustrated on real data dealing with problems associated with high blood pressure prevention. The proposed approach is implemented in the R package ClusPred available on CRAN. Supplementary materials containing the technical details and the R codes are available online.

Iterative gradient descent for outlier detection

In linear regression, outliers have a serious effect on the estimation of regression model parameters and the prediction of final results, so outlier detection is one of the key steps in data analysis. In this paper, we use a mean shift model and then we apply the penalty function to penalize the mean shift parameters, which is conducive to get a sparse parameter vector. We choose Sorted L1 regularization (SLOPE), which provides a convex loss function, and shows good statistical properties in parameter selection. We apply an iterative process which using gradient descent method and parameter selection at each step. Our algorithm has higher computational efficiency since the calculation of inverse matrix is avoided. Finally, we use Cross-Validation rules (CV) and Bayesian Information Criterion (BIC) criteria to fine tune the parameters, which helps our program identify outliers and obtain more robust regression coefficients. Compared with other methods, the experimental results show that our program has a fantastic performance in all aspects of outlier detection.

The Effect of Compensation, Motivation and the Work Environment on Employee Performance (Pt Torabika Eka Semesta Tangerang)

Research objectives: This study aims to determine whether there is an influence between compensation, work motives and work environment on employee performance at PT. Torabika Eka Semesta Tangerang. The research method used is quantitative, when viewed from the level of explanation, this is an associative study with a casual relationship model. The population in this study were employees of PT. Torabika Eka Semesta, amounting to 100 respondents. The sampling technique used is the Probability Sampling method with simple random sampling technique, namely taking members and the population is done randomly without paying attention to the strata in the population. The data analysis technique used SPSS 22.0 (2013) software using multiple regression model parameter estimates and hypothesis testing was carried out by using the t test. The results show that the variable that has a major influence on employee performance is the work environment. Meanwhile, the variable that has a low influence on employee performance is compensation.

Conditional maximum Lq-likelihood estimation for regression model with autoregressive error terms

In this article, we consider the parameter estimation of regression model with pth-order autoregressive (AR(p)) error term. We use the maximum Lq-likelihood (MLq) estimation method proposed by Ferrari and Yang (Ann Stat 38(2):753–783, 2010), as a robust alternative to the classical maximum likelihood (ML) estimation method to handle the outliers in the data. After exploring the MLq estimators for the parameters of interest, we provide some asymptotic properties of the resulting MLq estimators. We give a simulation study and three real data examples to illustrate the performance of the proposed estimators over the ML estimators and observe that the MLq estimators have superiority over the ML estimators when some outliers are present in the data.

Parameter estimation of regression model with AR(p) error terms based on skew distributions with EM algorithm

In the linear regression model, the errors are usually assumed to be uncorrelated. However, in real-life data, this assumption is not often plausible. In this study, first, we will assume that the errors of the regression model have autoregressive structure. This type of regression models has been considered before. However, in those papers under this assumption usually, the symmetric distributions are used as error distribution. The main contribution of this work is to use skew distributions instead of symmetric distributions as error distribution in regression models with autoregressive errors. We provide expectation maximization algorithm to compute the maximum likelihood estimates for the parameters. The performances of the proposed estimators are demonstrated with a simulation study and a real data example. We also provide the confidence intervals using the observed Fisher information matrix for the corresponding estimators.

Least absolute deviation estimator‐bridge variable selection and estimation for quantitative structure–activity relationship model

AbstractRegression models are frequently encountered in many scientific fields, especially in quantitative structure–activity relationship (QSAR) modeling. The traditional estimation of regression model parameters is based on the normal assumption of the response variable, and, therefore, it is sensitive to outliers or heavy‐tailed distributions. Robust penalized regression methods have been given considerable attention because they combine the robust estimation method with penalty terms to perform parameter estimation and variable selection simultaneously. In this paper, based on the bridge penalty, a robust variable selection and parameter estimation is proposed as a method that is resistant to the existence of outliers or heavy‐tailed errors. The basic idea is to combine the least absolute deviation estimator (LAD) and the bridge penalty together to produce the LAD‐bridge method. The effectiveness of the proposed method is examined through simulation studies and application to real chemometrics data. The obtained results confirm that the LAD‐bridge can significantly reduce the prediction error compared with other existing methods.

A robust quantitative structure–activity relationship modelling of influenza neuraminidase a/PR/8/34 (H1N1) inhibitors based on the rank-bridge estimator

ABSTRACT Linear regression model is frequently encountered in quantitative structure–activity relationship (QSAR) modelling. The traditional estimation of regression model parameters is based on the normal assumption of the response variable (biological activity) and therefore, it is sensitive to outliers or heavy-tailed distributions. Robust penalized regression methods have been given considerable attention because they combine the robust estimation method with penalty terms to perform QSAR parameter estimation and variable selection (descriptor selection) simultaneously. In this paper, based on bridge penalty, a robust QSAR model of the influenza neuraminidase a/PR/8/34 (H1N1) inhibitors is proposed as a resistant method to the existence of outliers or heavy-tailed errors. The basic idea is to combine the rank regression and the bridge penalty together to produce the rank-bridge method. The rank-bridge model is internally and externally validated based on , , , , Y-randomization test, , and the applicability domain (AD). The validation results indicate that the rank-bridge model is robust and not due to chance correlation. In addition, the results indicate that the descriptor selection and prediction performance of the rank-bridge model for training dataset outperforms the other two used modelling methods. Rank-bridge model shows the highest , and , and the lowest . For the test dataset, rank-bridge model shows higher external validation value ( = 0.824), and lower value of compared with the other methods, indicating its higher predictive ability.

The dynamic association between CEO-duality and bank performance: the moderating role of board size

Purpose - The aim of this study is to examine the association between CEO-duality and bank financial performance in Turkey. Methodology - All parameter estimates of regression models are based on the system GMM panel regression analyses. Our data covers all commercial banks operating in Turkish banking sector during the period 2007-2013. Findings - Our empirical results imply that CEO-duality has a significantly positive effect on bank financial performance measured by the ratio of net income to the average total assets. In addition, we find a negative moderating impact of board on the positive linkage between CEO-duality and bank performance. Conclusion - It can be concluded that as the number of members of the board raises, the positive influence of CEO-duality decreases for Turkish banking sector in the analyzed period.

Сравнительное исследование точности локального и глобального оценивания параметров регрессионных моделей при использовании различных типов M-оценок

Сравнительное исследование точности локального и глобального оценивания параметров регрессионных моделей при использовании различных типов M-оценок

Оценивание параметров регрессионных моделей методом усеченного максимального правдоподобия

Оценивание параметров регрессионных моделей методом усеченного максимального правдоподобия

TÜRKİYE’YE YÖNELİK TURİZM TALEBİNİN GÖRÜNÜRDE İLİŞKİSİZ REGRESYON MODELLERİ İLE İNCELENMESİ

Since the tourism sector is highly sensible to the factors affecting touristic product and services, it gives a significant importance to demand forecasting and analyses of the factors that affect the demand. This study aims to model the tourism demand of European countries, which have an important share of the Turkish tourism market. For this study, Seemingly Unrelated Regression (SUR) Model was used and the forecasting parameters were compared with Ordinary Least Square (OLS) outcomes. Addition to that, factors affecting European Countries’ tourism demand was analyzed and these countries were compared according to these factors. As a result of this study, parameter estimates of SUR model are more efficient than classical regression model parameter estimates. This study recommends SUR model, which is not widely used around the world and doesn’t take part in studies in Turkey to determine the tourism politics and tourism projection works, can be used as a decision method

Curve Fit: a pixel‐level raster regression tool for mapping spatial patterns

Summary Despite the fact that pixels (i.e. picture elements) are the basic sampling units of maps, we are aware of no software package or tool that allows users to model changes that may occur at such fine spatial resolutions over broad geographic extents. Curve Fit is an extension to the application ArcMap that allows users to conduct linear or nonlinear regression analysis on the range of values found within input raster data sets (geo‐referenced images), independently for each pixel. Outputs consist of raster surfaces of regression model parameter estimates, standard errors, goodness‐of‐fit estimates and multimodel inference measures. Curve fit outputs characterize continuous spatial or temporal change across a series of raster data sets.

PARTICLE SWARM OPTIMIZATION AN ALTERNATIVE FOR PARAMETER ESTIMATION IN REGRESSION

The practice of applying curve fitting techniques to describe data is widespread in many fields: in biology, in medicine, in engineer, in economy, etc. This paper presents a heuristic technique named Particle Swarm Optimization to be used for parameter estimation in regression models. The algorithm was tested on 27 databases for nonlinear models and 11 for linear models by collection NIST (2001), which are considered with different degrees of difficulty. We present experimental results

Bayesian models for comparative analysis integrating phylogenetic uncertainty

BackgroundUncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable.MethodsWe developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses.ResultsWe demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS.ConclusionsIncorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language.

Does aspirin use adversely influence intermediate-term postdischarge outcomes for hospitalized patients who are treated with angiotensin-converting enzyme inhibitors or angiotensin receptor blockers? Findings from Organized Program to Facilitate Life-Saving Treatment in Hospitalized Patients with Heart Failure (OPTIMIZE-HF)

Conflicting data exist regarding a potential deleterious association between aspirin (ASA) and angiotensin-converting enzyme inhibitors (ACEIs) when used concurrently in patients with heart failure (HF). How such an interaction may be influenced by underlying etiology of HF and whether it extends to patients treated with angiotensin receptor blockers (ARBs), however, are not known. Eligible patients from the OPTIMIZE-HF registry were dichotomized into those with ischemic or nonischemic HF. Potential associations between ASA and ACEI or ARB use and 60- to 90-day postdischarge outcomes were assessed using Cox proportional and logistic regression modeling. Models were adjusted for factors known to influence the outcome of interest and by propensity score for ACEI or ARB prescription after an index HF admission. Mortality was not increased (hazard ratio [95% CI]) when ASA was used in conjunction with ACEI (0.51 [0.29-0.87]) or ARB (0.29 [0.09-0.96]) in patients with ischemic or nonischemic (ACEI 0.71 [0.42-1.21], ARB 1.42 [0.74-2.74]) HF. Regression model parameter estimates trended toward harm reduction, but interaction terms for mortality and a composite of mortality or rehospitalization were nonsignificant (P for all >.05). When combined with ACEI or ARB, ASA had no demonstrable adverse effect on intermediate-term postdischarge outcomes for patients with ischemic or nonischemic HF.

Patients Are Willing to Trade off Efficacy, Safety, and Administration Attributes of Chronic Idiopathic Purpura (ITP) Therapy: Results from a Large North American Discrete Choice Study

OBJECTIVE: To quantify the willingness of patients with chronic idiopathic thrombocytopenic purpura (ITP) to trade off different attributes of ITP treatments, including efficacy, safety, and mode of administration. To determine the level of benefits, which balanced risks when faced with discrete choices.BACKGROUND: ITP is primarily a disorder of adults characterized by reduced platelet production and autoantibody-induced platelet destruction, leading to a low peripheral blood platelet count (<150 Gi/L; Cines, 2002). Patients may have few symptoms or may suffer bruising, purpura, or more serious complications, such as intracerebral bleeding. Treatment is aimed at elevating platelets to a hemostatic, safe range (≥50 to 400 Gi/L) to minimize the risk of bleeding. To date, the long-term management of patients with chronic ITP has been unsatisfactory, largely due to the variable efficacy, poor tolerability, and severe side effects associated with current treatment options. Treatment involves corticosteroids, intravenous immunoglobulins, immunosuppressive drugs, chemotherapy, splenectomy, and, more recently, monoclonal antibodies targeted against B cell antigens (Stasi, 2004). The relative importance of different treatment attributes from a patient perspective has not been previously studied.METHODOLOGY: Participants were recruited through an ITP patient support group and were to have reported a diagnosis of chronic ITP. They completed an online survey that included a series of stated-choice trade-off tasks. Respondents chose between pairs of hypothetical treatment alternatives defined by a different likelihood of achieving hemostatic platelet levels, need for concomitant corticosteroids, mode of treatment administration, risk of rebound thrombocytopenia, risk of elevated liver enzymes resulting in treatment discontinuation, and risk of blood clot. Mixed-logit methods were used to estimate relative preference weights for treatment attribute levels; regression model parameter estimates were used to derive the maximum accepted risk (MAR) of adverse events for specific increases in the likelihood of treatment success and the minimum acceptable benefit (MAB) required to justify a given level of adverse-event risk.RESULTS: The survey was completed by 1,542 respondents. Seventy-two percent of respondents were female, the mean age was 50 years, 92% were white, and 86% had education beyond high school. Patients with chronic ITP were willing to accept significant risks of side effects or adverse events to increase the likelihood of treatment success, to avoid the need for corticosteroids, and to attain a convenient mode of administration. In return for a 25–percentage-point increase in the likelihood of achieving a safe platelet level, patients were willing to accept an average risk for rebound thrombocytopenia of 18.8% (95% CI, 16.3%–21.3%). For avoiding corticosteroids, patients tolerated risk for rebound thrombocytopenia and blood clot of 20.2% (95% CI, 18.4%–23.7%) and 3.4% (95% CI, 2.7%–4.2%), respectively. Patients were willing to accept an additional risk of thromboembolism as high as 2% and a risk of liver-function test abnormalities or rebound thrombocytopenia as high as 13% if they could take 1 or 2 pills every day instead of going to a doctor's office for an injection once a week. When given a choice and all other factors being equal, 71% of patients stated that they would surely or probably choose 1 to 2 pills a day, while 8% of patients stated they would choose weekly injections in a physician's office (with remaining patients not stating a preference).CONCLUSIONS: In this large, rigorously conducted study, patients with chronic ITP were willing to accept significant risks of thromboembolic events, liver abnormalities, and rebound thrombocytopenia for greater efficacy benefit, as well as to avoid the use of corticosteroids. The majority of patients also preferred an orally administered therapy to an injectable therapy administered in a physician's office or at home.