Multivariate Statistical Modelling Based on Generalized Linear Models

By R. Chappell. 2003

261 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a50f52a94f82123d1fea3ef6f872c40d4b4b6c92

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In Statistics and Probability

Citations in the corpus

Random effect models for repeated measures of zero-inflated count data (2005, methodology): “Both the negative binomial random effect model and the zero-altered random effect model showed that the ordinary Poisson GLMM is inadequate.”
Generalized structured additive regression based on Bayesian P-splines (2006, methodology): “We first develop in Section 3.1 several sampling schemes based on iteratively weighted least squares (IWLS) used for estimating generalized linear models (Fahrmeir and Tutz, 2001).”
DEM: A variational treatment of dynamic systems (2008, methodology): “…shown how iterative optimisation reduces to expectation maximisation (EM; Dempster et al., 1977) and restricted maximum likelihood (ReML; Harville, 1977) for linear models (Friston et al., 2007; see also Fahrmeir and Tutz 1994 for a related discussion in the context of generalised linear models).”
Penalized Regression with Ordinal Predictors (2009, background): “Score function and Fisher matrix are explicitly given (for example in Fahrmeir & Tutz, 2001): s(β) = X T D(β) −1(β)[y − μ(β)], F(β) = X T W (β)X , with y = (y1, . . . , yN )T , μ(β) = (μ1(β), . . . , μN (β))T , (β) = diag(σ 21, . . . , σ 2N ), D(β) = diag(D1(β), . . . , DN (β)), W(β) = diag(w1(β),…”
PENALIZED STRUCTURED ADDITIVE REGRESSION FOR SPACE-TIME DATA: A BAYESIAN PERSPECTIVE (2004, methodology): “This broad class of structured additive regression (STAR) models contain several important subclasses as special cases e.g., state-space models for longitudinal data (Fahrmeir and Tutz (2001), Ch.8) or geoadditive models, introduced by Kammann and Wand (2003) within a mixed model setting.”
A Simple Model of Credit Contagion (2004, background): “2See, e.g., McCulloch and Nelder (1989) and Fahrmeir and Tutz (2001).”
Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction (2012, background): “…that peak wind speed observations follow a nonstationary GEV (7) where the parameters depend on covariates x through functions of the form .x/D 0C 1x1C 2x2C ; h. .x//D 0C 1x1C 2x2C ; D 0 (13) where h. / is a link function in analogy to generalized linear models (GLMs) (Fahrmeir and Tutz, 2001).”
Statistical process control for multistage processes with binary outputs (2013, methodology): “Their model and associated estimation approach can be regarded as an extension of the non-linear state-space model investigated by Carlin et al. (1992) and Fahrmeir and Tutz (1994).”
Hierarchical Insurance Claims Modeling (2008, methodology): “One approach to modeling this data set would be to use techniques from multivariate longitudinal data (see, e.g., Fahrmeir and Tutz 2001); however, as we have pointed out, in most years policyholders do not incur a claim, resulting in many repeated 0’s (see, e.g., Olsen and Shafer 2001), and when a…”
Bayesian varying-coefficient models using adaptive regression splines (2001, background): “For details on discrete survival models see Fahrmeir and Tutz (1997).”
A Family of Generalized Linear Models for Repeated Measures With Normal and Conjugate Random Effects (pp.188) (2010, background): “We will not consider explicit expressions for such models here, because they are relatively well studied (Fahrmeir and Tutz, 2001; Molenberghs and Verbeke, 2005) and, at any rate, conveniently follow as special cases from the combined models of Section 4.”
The VGAM Package for Categorical Data Analysis (2010, background): “Some general references for categorical data providing background to this article include Agresti (2002), Fahrmeir and Tutz (2001), Leonard (2000), Lloyd (1999), Long (1997), Mc-Cullagh and Nelder (1989) and Simonoﬀ (2003).”
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, unknown): “Latent Gaussian models have a numerous and wide ranging list of applications; most structured Bayesian models are in fact of this form; see for example Fahrmeir and Tutz (2001), Gelman et al. (2004) and Robert and Casella (1999).”
Estimation and prediction of the spatial occurrence of fish species using Bayesian latent Gaussian models (2013, background): “…with INLA The key idea underlying what follows is to realize that these hierarchical models can be seen as Structured Additive Regression (STAR) models (see, for instance Fahrmeir and Tutz 2001 for a detailed description of them and Chien and Bangdiwala 2012 for an applied example of their use).”
Asymptotic results with generalized estimating equations for longitudinal data (2005, unknown): “More precisely, we write λ H−1/2 n [Ẽ [1] n (β)− E [1] n (β)]H−1/2 n λ = T [1] n + T [3] n (β) + T [5] n (β) λ H−1/2 n [Ẽ [2] n (β)− E [2] n (β)]H−1/2 n λ = T [2] n + T [4] n (β) + T [6] n (β) where T [l] n (β) = ∑m j,k=1(q̃ (n) jk − q jk ) · S n,jk(β) for l = 1, .”
Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data (2015, background): “While it is common practice to introduce a single, scalar overdispersion parameter to inflate the expectation (Fahrmeir and Tutz, 2001), more complex forms of overdispersion where the amount of overdispersion depends on covariates and varies over the observations are often more adequate.”
Classical and Bayesian Inference in Neuroimaging: Theory (2002, methodology): “The operational equivalence between ReML and EM has been established for many years (see Fahrmeir and Tutz, 1994, p. 226).”