Search results for " Regression"
showing 10 items of 1835 documents
Classification trees for multivariate ordinal response: an application to Student Evaluation Teaching
2016
Data from multiple items on an ordinal scale are commonly collected when qualitative variables, such as feelings, attitudes and many other behavioral and health-related variables are observed. In this paper we introduce a method to derive a distance-based tree for multivariate ordinal response that allows, when subject-specific characteristics are available, to derive common profiles for respondents giving the same/similar multivariate ratings. Special attention will be paid to the performance comparison in terms of AUC, for three different distances used as splitting criteria. Simulated data an a dataset from a Student Evaluation of Teaching survey will be used as illustrative examples. Th…
Exploring regression structure with graphics
1993
We investigate the extent to which it may be possible to carry out a regression analysis using graphics alone, an idea that we refer to asgraphical regression. The limitations of this idea are explored. It is shown that graphical regression is theoretically possible with essentially no constraints on the conditional distribution of the response given the predictors, but with some conditions on marginal distribution of the predictors. Dimension reduction subspaces and added variable plots play a central role in the development. The possibility of useful methodology is explored through two examples.
Simulation in the Simple Linear Regression Model
2002
Summary This article presents an activity which simulates the linear regression model in order to verify the probabilistic behaviour of the resulting least-squares statistics in practice.
Linear and ellipsoidal restrictions in linear regression
1991
The problem of combining linear and ellipsoidal restrictions in linear regression is investigated. Necessary and sufficient conditions for compactness of the restriction set are proved assuring the existence of a minimax estimator. When the restriction set is not compact a minimax estimator may still exist for special loss functions arid regression designs
Varying-coefficient functional linear regression models
2008
This article considers a generalization of the functional linear regression in which an additional real variable influences smoothly the functional coefficient. We thus define a varying-coefficient regression model for functional data. We propose two estimators based, respectively, on conditional functional principal regression and on local penalized regression splines and prove their pointwise consistency. We check, with the prediction one day ahead of ozone concentration in the city of Toulouse, the ability of such nonlinear functional approaches to produce competitive estimations.
Estimating regression models with unknown break-points.
2003
This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model. For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem. As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed. Differences between the other procedures available are shown and relative merits discussed. Simulations and two examples are presented to illustrate the method.
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Inferential tools in penalized logistic regression for small and sparse data: A comparative study.
2016
This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the ‘traditional’ Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penal…
Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling
2016
ABSTRACTWe introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from…
Estimating growth charts via nonparametric quantile regression: a practical framework with application in ecology.
2013
We discuss a practical and effective framework to estimate reference growth charts via regression quantiles. Inequality constraints are used to ensure both monotonicity and non-crossing of the estimated quantile curves and penalized splines are employed to model the nonlinear growth patterns with respect to age. A companion R package is presented and relevant code discussed to favour spreading and application of the proposed methods.