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Application of the Rasch model in categorical pedigree analysis using MCEM: I binary data

100%
Qian G., Huggins R., Loesch D.
Discussiones Mathematicae Probability and Statistics
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2004
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tom 24
|
nr 2
255-280
EN
An extension of the Rasch model with correlated latent variables is proposed to model correlated binary data within families. The latent variables have the classical correlation structure of Fisher (1918) and the model parameters thus have genetic interpretations. The proposed model is fitted to data using a hybrid of the Metropolis-Hastings algorithm and the MCEM modification of the EM-algorithm and is illustrated using genotype-phenotype data on a psychological subtest in families where some members are affected by the genetic disorder fragile X. In addition, hypothesis testing and model selection methods based on the Wald statistic are discussed.
2
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Compact hypothesis and extremal set estimators

88%
Mexia J., Corte Real P.
Discussiones Mathematicae Probability and Statistics
|
2003
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tom 23
|
nr 2
103-121
EN
In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space. Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U. A strongly consistent test is presented for this assumption. Moreover, when the true parameter value $\vec{β₀}^{k}$ is the sole point in ∇, strongly consistent pointwise estimators, ${ \^{\vec{βₙ}}^{k}: n ∈ ℕ }$ for $\vec{β₀}^{k}$ are derived and confidence ellipsoids for $\vec{β₀}^{k}$ centered at $\^{\vec{βₙ}}^{k}$ are obtained, as well as, strongly consistent tests. Lastly an application to binary data is presented.
3
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A joint regression modeling framework for analyzing bivariate binary data in R

63%
Marra G., Radice R.
Dependence Modeling
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2017
|
tom 5
|
nr 1
268-294
EN
We discuss some of the features of the R add-on package GJRM which implements a flexible joint modeling framework for fitting a number of multivariate response regression models under various sampling schemes. In particular,we focus on the case inwhich the user wishes to fit bivariate binary regression models in the presence of several forms of selection bias. The framework allows for Gaussian and non-Gaussian dependencies through the use of copulae, and for the association and mean parameters to depend on flexible functions of covariates. We describe some of the methodological details underpinning the bivariate binary models implemented in the package and illustrate them by fitting interpretable models of different complexity on three data-sets.
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