Liu-type Negative Binomial Regression: A Comparison of Recent Estimators and Applications

This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is inflated when there is multicollinearity between the explanatory variables, a new biased estimator is proposed to solve the problem and decrease the variance of MLE in order to make stable inferences. Moreover, we obtain some theoretical comparisons between the new estimator and some others via matrix mean squared error (MMSE) criterion. Furthermore, a Monte Carlo simulation study is designed to evaluate performances of the estimators in the sense of mean squared error. Finally, a real data application is used to illustrate the benefits of new estimator

Bayesian analysis of Turkish Income and Living Conditions data, using clustered longitudinal ordinal modelling with Bridge distributed random-effects

This paper is motivated by the panel surveys, called Statistics on Income and Living Conditions (SILC), conducted annually on (randomly selected) country-representative households to monitor EU 2020 aims on poverty reduction. We particularly consider the surveys conducted in Turkey, within the scope of integration to the EU, between 2010 and 2013. Our main interests are on health aspects of economic and living conditions. The outcome is {\it self-reported health} that is clustered longitudinal ordinal, since repeated measures of it are nested within individuals and individuals are nested within families. Economic and living conditions were measured through a number of individual- and family-level explanatory variables. The questions of interest are on the marginal relationships between the outcome and covariates that are addressed using a polytomous logistic regression with Bridge distributed random-effects. This choice of distribution allows one to {\it directly} obtain marginal inferences in the presence of random-effects. Widely used Normal distribution is also considered as the random-effects distribution. Samples from the joint posterior density of parameters and random-effects are drawn using Markov Chain Monte Carlo. Interesting findings from public health point of view are that differences were found between sub-groups of employment status, income level and panel year in terms of odds of reporting better health

Marginally specified models for analyzing multivariate longitudinal binary data

Marginally specified models have recently become a popular tool for discrete longitudinal data analysis. Nonetheless, they introduce complex constraint equations and model fitting algorithms. Moreover, there is a lack of available software to fit these models. In this paper, we propose a three-level marginally specified model for analysis of multivariate longitudinal binary response data. The implicit function theorem is introduced to approximately solve the marginal constraint equations explicitly. Furthermore, the use of \textit{probit} link enables direct solutions to the convolution equations. We propose an R package \textbf{pnmtrem} to fit the model. A simulation study is conducted to examine the properties of the estimator. We illustrate the model on the Iowa Youth and Families Project data set

Flexible multivariate marginal models for analyzing multivariate longitudinal data, with applications in R

Most of the available multivariate statistical models dictate on fitting different parameters for the covariate effects on each multiple responses. This might be unnecessary and inefficient for some cases. In this article, we propose a modeling framework for multivariate marginal models to analyze multivariate longitudinal data which provides flexible model building strategies. We show that the model handles several response families such as binomial, count and continuous. We illustrate the model on the Mother's Stress and Children's Morbidity data set. A simulation study is conducted to examine the parameter estimates. An R package mmm2 is proposed to fit the model

Efficiency of the principal component Liu-type estimator in logistic regression model

In this paper we propose a principal component Liu-type logistic estimator by combining the principal component logistic regression estimator and Liu-type logistic estimator to overcome the multicollinearity problem. The superiority of the new estimator over some related estimators are studied under the asymptotic mean squared error matrix. A Monte Carlo simulation experiment is designed to compare the performances of the estimators using mean squared error criterion. Finally, a conclusion section is presented.Comment: 16 pages, 4 table

On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression

In order to overcome multicollinearity, we propose a stochastic restricted Liu-type max- imum likelihood estimator by incorporating Liu-type maximum likelihood estimator (Inan and Erdo- gan, 2013) to the logistic regression model when the linear restrictions are stochastic. We also discuss the properties of the new estimator. Moreover, we give a method to choose the biasing parameter in the new estimator. Finally, a simulation study is given to show the performance of the new estimator.Comment: 8 pages, 2 table

Liu-type Shrinkage Estimations in Linear Models

In this study, we present the preliminary test, Stein-type and positive part Liu estimators in the linear models when the parameter vector $\boldsymbol{\beta}$ is partitioned into two parts, namely, the main effects $\boldsymbol{\beta}_1$ and the nuisance effects $\boldsymbol{\beta}_2$ such that $\boldsymbol{\beta}=\left(\boldsymbol{\beta}_1, \boldsymbol{\beta}_2 \right)$. We consider the case that a priori known or suspected set of the explanatory variables do not contribute to predict the response so that a sub-model may be enough for this purpose. Thus, the main interest is to estimate $\boldsymbol{\beta}_1$ when $\boldsymbol{\beta}_2$ is close to zero. Therefore, we conduct a Monte Carlo simulation study to evaluate the relative efficiency of the suggested estimators, where we demonstrate the superiority of the proposed estimators

On the restricted almost unbiased Liu estimator in the Logistic regression model

It is known that when the multicollinearity exists in the logistic regression model, variance of maximum likelihood estimator is unstable. As a remedy, in the context of biased shrinkage ridge estimation, Chang (2015) introduced an almost unbiased Liu estimator in the logistic regression model. Making use of his approach, when some prior knowledge in the form of linear restrictions are also available, we introduce a restricted almost unbiased Liu estimator in the logistic regression model. Statistical properties of this newly defined estimator are derived and some comparison result are also provided in the form of theorems. A Monte Carlo simulation study along with a real data example are given to investigate the performance of this estimator.Comment: 15 pages, 1 Figure, 9 Table

Stancu type generalization of the q-Favard-Szasz operators

In this paper, we introduce a Stancu type generalization of the q-Favard-Szasz operators, estimate the rates of statistical convergence and study the local approximation properties of these operators

Pretest and Stein-Type Estimations in Quantile Regression Model

In this study, we consider preliminary test and shrinkage estimation strategies for quantile regression models. In classical Least Squares Estimation (LSE) method, the relationship between the explanatory and explained variables in the coordinate plane is estimated with a mean regression line. In order to use LSE, there are three main assumptions on the error terms showing white noise process of the regression model, also known as Gauss-Markov Assumptions, must be met: (1) The error terms have zero mean, (2) The variance of the error terms is constant and (3) The covariance between the errors is zero i.e., there is no autocorrelation. However, data in many areas, including econometrics, survival analysis and ecology, etc. does not provide these assumptions. First introduced by Koenker, quantile regression has been used to complement this deficiency of classical regression analysis and to improve the least square estimation. The aim of this study is to improve the performance of quantile regression estimators by using pre-test and shrinkage strategies. A Monte Carlo simulation study including a comparison with quantile $L_1$--type estimators such as Lasso, Ridge and Elastic Net are designed to evaluate the performances of the estimators. Two real data examples are given for illustrative purposes. Finally, we obtain the asymptotic results of suggested estimatorsComment: arXiv admin note: text overlap with arXiv:1707.0105