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23
Semiparametric Regression During 2003–2007
, 2008
"... Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a ..."
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Cited by 17 (5 self)
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Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.
Multivariate Reduced Rank Regression in nonGaussian Contexts, Using Copulas
, 2004
"... ... canonical correlations, principal component analysis. We propose a new procedure to perform Reduced Rank Regression (RRR) in nonGaussian contexts, based on Multivariate Dispersion Models. ReducedRank Multivariate Dispersion Models (RRMDM) generalise RRR to a very large class of distributions, ..."
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Cited by 5 (0 self)
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... canonical correlations, principal component analysis. We propose a new procedure to perform Reduced Rank Regression (RRR) in nonGaussian contexts, based on Multivariate Dispersion Models. ReducedRank Multivariate Dispersion Models (RRMDM) generalise RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, Inverse Gaussian, and discrete distributions like the Poisson and the binomial. A multivariate distribution is created with the help of the Gaussian copula and estimation is performed using maximum likelihood. We show how this method can be amended to deal with the case of discrete data. We perform Monte Carlo simulations and show that our estimator is more efficient than the traditional Gaussian RRR. In the framework of MDM’s we introduce a procedure analogous to canonical correlations, which takes into account the distribution of the data.
Reduced rank vector generalized linear models for feature extraction
 Statistics and Its Interface
, 2013
"... iv ..."
Who's afraid of reducedrank parameterizations of multivariate models? Theory and example
, 2006
"... Abstract Reducedrank restrictions can add useful parsimony to coefficient matrices of multivariate models, but their use is limited by the daunting complexity of the methods and their theory. The present work takes the easy road, focusing on unifying themes and simplified methods. For Gaussian and ..."
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Abstract Reducedrank restrictions can add useful parsimony to coefficient matrices of multivariate models, but their use is limited by the daunting complexity of the methods and their theory. The present work takes the easy road, focusing on unifying themes and simplified methods. For Gaussian and nonGaussian (GLM, GAM, mixed normal, etc.) multivariate models, the present work gives a unified, explicit theory for the general asymptotic (normal) distribution of maximum likelihood estimators (MLE). MLE can be complex and computationally hard, but we show a strong asymptotic equivalence between MLE and a relatively simple minimum (Mahalanobis) distance estimator. The latter method yields particularly simple tests of rank, and we describe its asymptotic behavior in detail. We also examine the method's performance in simulation and via analytical and empirical examples.
Bayesian Modeling for Multivariate Mixed Outcomes with Applications to Cognitive Testing Data
, 2012
"... Statistics And Social Work This dissertation studies parametric and semiparametric approaches to latent variable models, multivariate regression and modelbased clustering for mixed outcomes. We use the term mixed outcomes to refer to binary, ordered categorical, count, continuous and other ordered ..."
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Statistics And Social Work This dissertation studies parametric and semiparametric approaches to latent variable models, multivariate regression and modelbased clustering for mixed outcomes. We use the term mixed outcomes to refer to binary, ordered categorical, count, continuous and other ordered outcomes in combination. Such data structures are common in social, behavioral, and medical sciences. We first review existing parametric approaches to mixed outcomes in latent variable models before developing extensions to accommodate outcome types specific to cognitive testing data. We subsequently develop two new regression approaches for mixed outcome data, the semiparametric Bayesian latent variable model and the semiparametric reduced rank multivariate regression model. In contrast to the existing parametric approaches, these models allow us to avoid specification of distributions for each outcome type. We apply the latent variable and multivariate regression models to investigate the association between cognitive outcomes and MRImeasured regional brain volumes using data from a study of dementia and compare results from the different models. Finally, we develop a new semiparametric correlated partial membership model for modelbased clustering of
Latent feature regression for multivariate count data
"... Abstract We consider the problem of regression on multivariate count data and present a Gibbs sampler for a latent feature regression model suitable for both underand overdispersed response variables. The model learns countvalued latent features conditional on arbitrary covariates, modeling them a ..."
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Abstract We consider the problem of regression on multivariate count data and present a Gibbs sampler for a latent feature regression model suitable for both underand overdispersed response variables. The model learns countvalued latent features conditional on arbitrary covariates, modeling them as negative binomial variables, and maps them into the dependent countvalued observations using a Dirichletmultinomial distribution. From another viewpoint, the model can be seen as a generalization of a specific topic model for scenarios where we are interested in generating the actual counts of observations and not just their relative frequencies and cooccurrences. The model is demonstrated on a smart traffic application where the task is to predict public transportation volume for unknown locations based on a characterization of the closeby services and venues.
VGAM Reference Card
"... VGAM package and some other documentation. This document is current for version VGAM0.91. The theory 1 underlying the software can be found in Yee ..."
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VGAM package and some other documentation. This document is current for version VGAM0.91. The theory 1 underlying the software can be found in Yee
1.0.1 Syntax
"... Use the bivariate logistic regression model if you have two binary dependent variables (Y1, Y2), and wish to model them jointly as a function of some explanatory variables. Each pair of dependent variables (Yi1, Yi2) has four potential outcomes, (Yi1 = 1, Yi2 = 1), (Yi1 = 1, Yi2 = 0), (Yi1 = 0, Yi2 ..."
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Use the bivariate logistic regression model if you have two binary dependent variables (Y1, Y2), and wish to model them jointly as a function of some explanatory variables. Each pair of dependent variables (Yi1, Yi2) has four potential outcomes, (Yi1 = 1, Yi2 = 1), (Yi1 = 1, Yi2 = 0), (Yi1 = 0, Yi2 = 1), and (Yi1 = 0, Yi2 = 0). The joint probability for each of these four outcomes is modeled with three systematic components: the marginal Pr(Yi1 = 1) and Pr(Yi2 = 1), and the odds ratio ψ, which describes the dependence of one marginal on the other. Each of these systematic components may be modeled as functions of (possibly different) sets of explanatory variables.
Reduced rank regression in Bayesian FDA
, 2010
"... In functional data analysis (FDA) it is of interest to generalize techniques of multivariate analysis like canonical correlation analysis or regression to functions which are often observed with noise. In the proposed Bayesian approach to FDA two tools are combined: (i) a special DemmlerReinsch lik ..."
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In functional data analysis (FDA) it is of interest to generalize techniques of multivariate analysis like canonical correlation analysis or regression to functions which are often observed with noise. In the proposed Bayesian approach to FDA two tools are combined: (i) a special DemmlerReinsch like basis of interpolation splines to represent functions parsimoniously and ‡exibly; (ii) latent variable models for probabilistic principal components analysis or canonical correlation analysis of the corresponding coe ¢ cients. In this way partial curves and nonGaussian measurement error schemes can be handled. Bayesian inference is based on a variational algorithm such that computations are straight forward and fast corresponding to an idea of FDA as a toolbox for explorative data analysis. The performance of the approach is illustrated with synthetic and real data sets. As detailed in the table of contents the paper has a “vertical ” structure corresponding to topics in data analysis and de…ning the sequence of chapters and a “horizontal ” structure referring to the most important special cases of the proposed model: FCCA, functional regression, scalar prediction, classi…cation. Within chapters the special cases are addressed in turn such that a reader interested only in a special application of the model may skip the other sections.
VGAM Reference Card
"... VGAM package and some other documentation. This document is current for version VGAM0.91. The theory 1 underlying the software can be found in Yee ..."
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VGAM package and some other documentation. This document is current for version VGAM0.91. The theory 1 underlying the software can be found in Yee