Search results for "Hierarchical generalized linear model"
showing 4 items of 4 documents
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.
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…
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 …
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…