Search results for "Regression"
showing 10 items of 2619 documents
Fitting generalized linear models with unspecified link function: A P-spline approach
2008
Generalized linear models (GLMs) outline a wide class of regression models where the effect of the explanatory variables on the mean of the response variable is modelled throughout the link function. The choice of the link function is typically overlooked in applications and the canonical link is commonly used. The estimation of GLMs with unspecified link function is discussed, where the linearity assumption between the link and the linear predictor is relaxed and the unspecified relationship is modelled flexibly by means of P-splines. An estimating algorithm is presented, alternating estimation of two working GLMs up to convergence. The method is applied to the analysis of quit behavior of…
dglars: An R Package to Estimate Sparse Generalized Linear Models
2014
dglars is a publicly available R package that implements the method proposed in Augugliaro, Mineo, and Wit (2013), developed to study the sparse structure of a generalized linear model. This method, called dgLARS, is based on a differential geometrical extension of the least angle regression method proposed in Efron, Hastie, Johnstone, and Tibshirani (2004). The core of the dglars package consists of two algorithms implemented in Fortran 90 to efficiently compute the solution curve: a predictor-corrector algorithm, proposed in Augugliaro et al. (2013), and a cyclic coordinate descent algorithm, proposed in Augugliaro, Mineo, and Wit (2012). The latter algorithm, as shown here, is significan…
Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter
2018
A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the $$\ell _1$$ or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this…
Differential geometric least angle regression: a differential geometric approach to sparse generalized linear models
2013
Summary Sparsity is an essential feature of many contemporary data problems. Remote sensing, various forms of automated screening and other high throughput measurement devices collect a large amount of information, typically about few independent statistical subjects or units. In certain cases it is reasonable to assume that the underlying process generating the data is itself sparse, in the sense that only a few of the measured variables are involved in the process. We propose an explicit method of monotonically decreasing sparsity for outcomes that can be modelled by an exponential family. In our approach we generalize the equiangular condition in a generalized linear model. Although the …
A differential-geometric approach to generalized linear models with grouped predictors
2016
We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important properties that distinguish it from the group lasso. First, its solution curve is based on the invariance properties of a generalized linear model. Second, it adds groups of variables based on a group equiangularity condition, which is shown to be related to score statistics. An adaptive version, which includes weights based on the Kullback-Leibler divergence, improves its variable selection fea…
Premature conclusions about the signal‐to‐noise ratio in structural equation modeling research : A commentary on Yuan and Fang (2023)
2023
In a recent article published in this journal, Yuan and Fang (British Journal of Mathematical and Statistical Psychology, 2023) suggest comparing structural equation modeling (SEM), also known as covariance-based SEM (CB-SEM), estimated by normal-distribution-based maximum likelihood (NML), to regression analysis with (weighted) composites estimated by least squares (LS) in terms of their signal-to-noise ratio (SNR). They summarize their findings in the statement that “[c]ontrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller stan…
Accounting for previous events to model and predict traffic accidents at the road segment level: A study in Valencia (Spain)
2022
Abstract Predicting the occurrence of traffic accidents is essential for establishing preventive measures and reducing the impact of traffic accidents. In particular, it is fundamental to make predictions using fine spatio-temporal units. In this paper, the daily risk of traffic accident occurrence across the road network of Valencia (Spain) is modeled through logistic regression models. The spatio-temporal dependence between the observations is accounted for through the inclusion of lagged binary covariates representing the previous occurrence of a traffic accident within a spatio-temporal window centered at each combination of day and segment of the network. A temporal distance of 28 days…
Multiple smoothing parameters selection in additive regression quantiles
2021
We propose an iterative algorithm to select the smoothing parameters in additive quantile regression, wherein the functional forms of the covariate effects are unspecified and expressed via B-spline bases with difference penalties on the spline coefficients. The proposed algorithm relies on viewing the penalized coefficients as random effects from the symmetric Laplace distribution, and it turns out to be very efficient and particularly attractive with multiple smooth terms. Through simulations we compare our proposal with some alternative approaches, including the traditional ones based on minimization of the Schwarz Information Criterion. A real-data analysis is presented to illustrate t…
Bayesian analysis of a disability model for lung cancer survival
2016
Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncolog…
Sparse kernel methods for high-dimensional survival data
2008
Abstract Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be ‘kernelized’. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, dependin…