Search results for " Generalized Linear Model"
showing 10 items of 12 documents
Scale dependence of species–area relationships is widespread but generally weak in Palaearctic grasslands
2021
Questions: Species–area relationships (SARs) are fundamental for understanding biodiversity patterns and are generally well described by a power law with a constant exponent z. However, z-values sometimes vary across spatial scales. We asked whether there is a general scale dependence of z-values at fine spatial grains and which potential drivers influence it. Location: Palaearctic biogeographic realm. Methods: We used 6,696 nested-plot series of vascular plants, bryophytes and lichens from the GrassPlot database with two or more grain sizes, ranging from 0.0001 m² to 1,024 m² and covering diverse open habitats. The plots were recorded with two widespread sampling approaches (rooted presenc…
Differential geometric LARS via cyclic coordinate descent method
2012
We address the problem of how to compute the coefficient path implicitly defined by the differential geometric LARS (dgLARS) method in a high-dimensional setting. Although the geometrical theory developed to define the dgLARS method does not need of the definition of a penalty function, we show that it is possible to develop a cyclic coordinate descent algorithm to compute the solution curve in a high-dimensional setting. Simulation studies show that the proposed algorithm is significantly faster than the prediction-corrector algorithm originally developed to compute the dgLARS solution curve.
A Widrow–Hoff Learning Rule for a Generalization of the Linear Auto-associator
1996
Abstract A generalization of the linear auto-associator that allows for differential importance and nonindependence of both the stimuli and the units has been described previously by Abdi (1988). This model was shown to implement the general linear model of multivariate statistics. In this note, a proof is given that the Widrow–Hoff learning rule can be similarly generalized and that the weight matrix will converge to a generalized pseudo-inverse when the learning parameter is properly chosen. The value of the learning parameter is shown to be dependent only upon the (generalized) eigenvalues of the weight matrix and not upon the eigenvectors themselves. This proof provides a unified framew…
Model averaging estimation of generalized linear models with imputed covariates
2015
a b s t r a c t We address the problem of estimating generalized linear models when some covariate values are missing but imputations are available to fill-in the missing values. This situation generates a bias-precision trade- off in the estimation of the model parameters. Extending the generalized missing-indicator method proposed by Dardanoni et al. (2011) for linear regression, we handle this trade-off as a problem of model uncertainty using Bayesian averaging of classical maximum likelihood estimators (BAML). We also propose a block model averaging strategy that incorporates information on the missing-data patterns and is computationally simple. An empirical application illustrates our…
Weighted-average least squares estimation of generalized linear models
2018
The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework that allows the development of asymptotic model averaging theory. We also investigate t…
Using the dglars Package to Estimate a Sparse Generalized Linear Model
2015
dglars is a publicly available R package that implements the method proposed in Augugliaro et al. (J. R. Statist. Soc. B 75(3), 471-498, 2013) developed to study the sparse structure of a generalized linear model (GLM). This method, called dgLARS, is based on a differential geometrical extension of the least angle regression method. The core of the dglars package consists of two algorithms implemented in Fortran 90 to efficiently compute the solution curve. dglars is a publicly available R package that implements the method proposed in Augugliaro et al. (J. R. Statist. Soc. B 75(3), 471-498, 2013) developed to study the sparse structure of a generalized linear model (GLM). This method, call…
On Rao Score and Pearson X2 Statistics in Generalized Linear Models
2005
The identity of the Rao score and PearsonX 2 statistics is well known in the areas where the latter was first introduced: goodness-of-fit in contingency tables and binary responses. We show in this paper that the same identity holds when the two statistics are used for testing goodness-of-fit of Generalized Linear Models. We also highlight the connections that exist between the two statistics when they are used for the comparison of nested models. Finally, we discuss some merits of these unifying results.
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…
Modeling Posidonia oceanica growth data: from linear to generalized linear mixed models
2010
The statistical analysis of annual growth of Posidonia oceanica is traditionally carried out through Gaussian linear models applied to untransformed, or log-transformed, data. In this paper, we claim that there are good reasons for re-considering this established practice, since real data on annual growth often violate the assumptions of Gaussian linear models, and show that the class of Generalized Linear Models (GLMs) represents a useful alternative for handling such violations. By analyzing Sicily PosiData-1, a real dataset on P. oceanica growth data gathered in the period 2000–2002 along the coasts of Sicily, we find that in the majority of cases Normality is rejected and the effect of …
Spatial analysis of lanner falcon habitat preferences: Implications for agro-ecosystems management at landscape scale and raptor conservation
2014
Abstract Sicily hosts the largest European population of the endangered lanner falcon, a poorly known species which needs conservation planning based on habitat preferences. A distribution model on 10 × 10 km cells of Sicily was described using Generalized Linear Models and variation partitioning methods. This modelling approach extracted explanatory factors, pure and joint effects of greatest influence from subsets of variables controlled for multi-collinearity and spatial autocorrelation. Analytical cartography used the environmental favourability function to assess habitat preferences, and the insecurity index estimated the degree to which lanner falcon occupancy is represented in the Na…