No Arabic abstract
In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and complementary log-log) can be obtained as limiting cases. We further compare the proposed model with some other asymmetrical models. The Bayesian as well as frequentist estimation procedures for binomial and multinomial data responses are presented in details. The analysis of two data sets to show the efficiency of the proposed model is performed.
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that the covariance matrix is positive definite. To address the issue, we propose to use convolved Gaussian process (CGP) in this paper. The approach provides a semi-parametric model and offers a natural framework for modeling common mean structure and covariance structure simultaneously. The CGP enables the model to define different covariance structure for each component of the response variables. This flexibility ensures the model to cope with data coming from different resources or having different data structures, and thus to provide accurate estimation and prediction. In addition, the model is able to accommodate large-dimensional covariates. The definition of the model, the inference and the implementation, as well as its asymptotic properties, are discussed. Comprehensive numerical examples with both simulation studies and real data are presented.
This paper investigates the problem of making inference about a parametric model for the regression of an outcome variable $Y$ on covariates $(V,L)$ when data are fused from two separate sources, one which contains information only on $(V, Y)$ while the other contains information only on covariates. This data fusion setting may be viewed as an extreme form of missing data in which the probability of observing complete data $(V,L,Y)$ on any given subject is zero. We have developed a large class of semiparametric estimators, which includes doubly robust estimators, of the regression coefficients in fused data. The proposed method is DR in that it is consistent and asymptotically normal if, in addition to the model of interest, we correctly specify a model for either the data source process under an ignorability assumption, or the distribution of unobserved covariates. We evaluate the performance of our various estimators via an extensive simulation study, and apply the proposed methods to investigate the relationship between net asset value and total expenditure among U.S. households in 1998, while controlling for potential confounders including income and other demographic variables.
Correlated data are ubiquitous in todays data-driven society. A fundamental task in analyzing these data is to understand, characterize and utilize the correlations in them in order to conduct valid inference. Yet explicit regression analysis of correlations has been so far limited to longitudinal data, a special form of correlated data, while implicit analysis via mixed-effects models lacks generality as a full inferential tool. This paper proposes a novel regression approach for modelling the correlation structure, leveraging a new generalized z-transformation. This transformation maps correlation matrices that are constrained to be positive definite to vectors with un-restricted support, and is order-invariant. Building on these two properties, we develop a regression model to relate the transformed parameters to any covariates. We show that coupled with a mean and a variance regression model, the use of maximum likelihood leads to asymptotically normal parameter estimates, and crucially enables statistical inference for all the parameters. The performance of our framework is demonstrated in extensive simulation. More importantly, we illustrate the use of our model with the analysis of the classroom data, a highly unbalanced multilevel clustered data with within-class and within-school correlations, and the analysis of the malaria immune response data in Benin, a longitudinal data with time-dependent covariates in addition to time. Our analyses reveal new insights not previously known.
We propose a parsimonious extension of the classical latent class model to cluster categorical data by relaxing the class conditional independence assumption. Under this new mixture model, named Conditional Modes Model, variables are grouped into conditionally independent blocks. The corresponding block distribution is a parsimonious multinomial distribution where the few free parameters correspond to the most likely modality crossings, while the remaining probability mass is uniformly spread over the other modality crossings. Thus, the proposed model allows to bring out the intra-class dependency between variables and to summarize each class by a few characteristic modality crossings. The model selection is performed via a Metropolis-within-Gibbs sampler to overcome the computational intractability of the block structure search. As this approach involves the computation of the integrated complete-data likelihood, we propose a new method (exact for the continuous parameters and approximated for the discrete ones) which avoids the biases of the textsc{bic} criterion pointed out by our experiments. Finally, the parameters are only estimated for the best model via an textsc{em} algorithm. The characteristics of the new model are illustrated on simulated data and on two biological data sets. These results strengthen the idea that this simple model allows to reduce biases involved by the conditional independence assumption and gives meaningful parameters. Both applications were performed with the R package texttt{CoModes}
Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data and there is no strong and similar competitor having its main features. A class of normalized inverse-Gaussian (N-IG) process was introduced in the literature, being explored in the Bayesian context as a powerful alternative to the Dirichlet process. Until this moment, no attention has been paid for the univariate N-IG distribution in the classical inference. In this paper, we propose the bessel regression based on the univariate N-IG distribution, which is a robust alternative to the beta model. This robustness is illustrated through simulated and real data applications. The estimation of the parameters is done through an Expectation-Maximization algorithm and the paper discusses how to perform inference. A useful and practical discrimination procedure is proposed for model selection between bessel and beta regressions. Monte Carlo simulation results are presented to verify the finite-sample behavior of the EM-based estimators and the discrimination procedure. Further, the performances of the regressions are evaluated under misspecification, which is a critical point showing the robustness of the proposed model. Finally, three empirical illustrations are explored to confront results from bessel and beta regressions.