Lasso Estimation of an Interval-Valued Multiple Regression Model

A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried out by transforming a quadratic optimization problem with inequality constraints into a linear complementary problem and using Lemke's algorithm to solve it. Due to the irrelevance of certain cross-relationships, an alternative estimation process, the LASSO (Least Absolut Shrinkage and Selection Operator), is developed. A comparative study showing the differences between the proposed estimators is provided

a multiple linear regression model

The link between the indices of twelve atmospheric teleconnection patterns (mostly Northern Hemispheric) and gridded European temperature data is investigated by means of multiple linear regression models for each grid cell and month. Furthermore index-specific signals are calculated to estimate the contribution to temperature anomalies caused by each individual teleconnection pattern. To this extent, an observational product of monthly mean temperature (E-OBS), as well as monthly time series of teleconnection indices (CPC, NOAA) for the period 1951–2010 are evaluated. The stepwise regression approach is used to build grid cell based models for each month on the basis of the five most important teleconnection indices (NAO, EA, EAWR, SCAND, POLEUR), which are motivated by an exploratory correlation analysis. The temperature links are dominated by NAO and EA in Northern, Western, Central and South Western Europe, by EAWR during summer/autumn in Russia/Fenno-Scandia and by SCAND in Russia/Northern Europe; POLEUR shows minor effects only. In comparison to the climatological forecast, the presented linear regression models improve the temperature modelling by 30–40 % with better results in winter and spring. They can be used to model the spatial distribution and structure of observed temperature anomalies, where two to three patterns are the main contributors. As an example the estimated temperature signals induced by the teleconnection indices is shown for February 2010

Analysis of neutrosophic multiple regression

The idea of Neutrosophic statistics is utilized for the analysis of the uncertainty observation data. Neutrosophic multiple regression is one of a vital roles in the analysis of the impact between the dependent and independent variables. The Neutrosophic regression equation is useful to predict the future value of the dependent variable. This paper to predict the students' performance in campus interviews is based on aptitude and personality tests, which measures conscientiousness, and predict the future trend. Neutrosophic multiple regression is to authenticate the claim and examine the null hypothesis using the F-test. This study exhibits that Neutrosophic multiple regression is the most efficient model for uncertainty rather than the classical regression model

A Mathematical Programming Approach for Integrated Multiple Linear Regression Subset Selection and Validation

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are met. Most traditional approaches require human decisions at this step. For example, the user adding or removing a variable until a satisfactory model is obtained. However, this trial-and-error strategy cannot guarantee that a subset that minimizes the errors while satisfying all regression assumptions will be found. In this paper, we propose a fully automated model building procedure for multiple linear regression subset selection that integrates model building and validation based on mathematical programming. The proposed model minimizes mean squared errors while ensuring that the majority of the important regression assumptions are met. We also propose an efficient constraint to approximate the constraint for the coefficient t-test. When no subset satisfies all of the considered regression assumptions, our model provides an alternative subset that satisfies most of these assumptions. Computational results show that our model yields better solutions (i.e., satisfying more regression assumptions) compared to the state-of-the-art benchmark models while maintaining similar explanatory power

Risk factors associated with lambing traits

peer-reviewedThis article was first published in Animal (2016), 10:1, pp 89–95, © The Animal Consortium 2015The objective of this study was to establish the risk factors associated with both lambing difficulty and lamb mortality in the Irish sheep multibreed population. A total of 135 470 lambing events from 42 675 ewes in 839 Irish crossbred and purebred flocks were available. Risk factors associated with producer-scored ewe lambing difficulty score (scale of one (no difficulty) to four (severe difficulty)) were determined using linear mixed models. Risk factors associated with the logit of the probability of lamb mortality at birth (i.e. binary trait) were determined using generalised estimating equations. For each dependent variable, a series of simple regression models were developed as well as a multiple regression model. In the simple regression models, greater lambing difficulty was associated with quadruplet bearing, younger ewes, of terminal breed origin, lambing in February; for example, first parity ewes experienced greater (P7.0 kg) birth weights, quadruplet born lambs and lambs that experienced a more difficult lambing (predicted probability of death for lambs that required severe and veterinary assistance of 0.15 and 0.32, respectively); lambs from dual-purpose breeds and born to younger ewes were also at greater risk of mortality. In the multiple regression model, the association between ewe parity, age at first lambing, year of lambing and lamb mortality no longer persisted. The trend in solutions of the levels of each fixed effect that remained associated with lamb mortality in the multiple regression model, did not differ from the trends observed in the simple regression models although the differential in relative risk between the different lambing difficulty scores was greater in the multiple regression model. Results from this study show that many common flock- and animal-level factors are associated with both lambing difficulty and lamb mortality and management of different risk category groups (e.g. scanned litter sizes, ewe age groups) can be used to appropriately manage the flock at lambing to reduce their incidence

Estimators of the multiple correlation coefficient: local robustness and confidence intervals.

Many robust regression estimators are defined by minimizing a measure of spread of the residuals. An accompanying R-2-measure, or multiple correlation coefficient, is then easily obtained. In this paper, local robustness properties of these robust R-2-coefficients axe investigated. It is also shown how confidence intervals for the population multiple correlation coefficient can be constructed in the case of multivariate normality.Cautionary note; High breakdown-point; Influence function; Intervals; Model; Multiple correlation coefficient; R-2-measure; Regression analysis; Residuals; Robustness; Squares regression;

Alternating model trees

Model tree induction is a popular method for tackling regression problems requiring interpretable models. Model trees are decision trees with multiple linear regression models at the leaf nodes. In this paper, we propose a method for growing alternating model trees, a form of option tree for regression problems. The motivation is that alternating decision trees achieve high accuracy in classification problems because they represent an ensemble classifier as a single tree structure. As in alternating decision trees for classifi-cation, our alternating model trees for regression contain splitter and prediction nodes, but we use simple linear regression functions as opposed to constant predictors at the prediction nodes. Moreover, additive regression using forward stagewise modeling is applied to grow the tree rather than a boosting algorithm. The size of the tree is determined using cross-validation. Our empirical results show that alternating model trees achieve significantly lower squared error than standard model trees on several regression datasets