A random effects model for analyzing mixed rank and binomial data with considering the missing values is presented. Occurring of missing data is an important problem in all research fields. The most ...common approach to dealing with missing data is to delete cases containing missing observations. However, this approach reduces statistical power and mislead us to biased statistical results. This paper aims to prepare guidance for researchers facing missing data problems and to provide techniques for jointly modeling of binomial and rank responses. We compare the cognitive abilities of different primates based on their performance on 17 cognitive assessments obtained on either a rank or binomial scale using Bayesian latent variable with random effects models. Random effects are used to take into account the correlation between responses of the same individual.
The purpose of this paper is to investigate the simultaneous effect of research outputs such as the number of articles indexed in Scopus on economic indicators such as inflation rate, unemployment ...rate and GDP of selected countries in the period of 2016 and 2020. Many articles have been studied in this regard, but none of them have focused on the simultaneous examination of research achievements on economic indicators. In some articles, research outputs on each of the economic growth indicators have been examined separately. Furthermore, separate analysis give biased estimates for the parameters and misleading inference. Consequently, we need to consider a method in which these variables can be modelled jointly. For this study, a random sample of 39 countries has been collected from the World Bank data to extract the economic index and Scopus data to extract the number of articles. In this paper, a joint model with random effects for longitudinal economic growth indicators is proposed. For these data, the simultaneous effects of some covariate for example the number of articles indexed in Scopus on the economic growth indicators as three mixed correlated responses are explored. There are main findings. Firstly, in the simultaneous examination of the effect of research outputs on economic indicators, some latent influencing factors related to each country under the title of random effects that have significant on economic indicators. Secondly, research achievements on economic indicators are significant at the same time. This significance is due to the simultaneous examination of economic indicators and appropriate statistical models are obtained with the least error compared to separate analysis.
A Gaussian Copula-based regression model is proposed that accounts for associations between count responses with extra zeros. Our approach entails underlying latent variables to indicate the latent ...mechanisms which generate the count responses where some of the count responses are inflated in a zero point. The model contains, as special sub-models, several important distributions such as the power series distributions with and without extra zeros, for example, Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions. The full likelihood-based inference method is applied for the estimation of parameters to obtain maximum likelihood estimates of the parameters. Modified Pearson residuals, where the correlation between responses is taken into account, are used for finding abnormal observations. To illustrate the utility of the models, some simulations are illustrated. Finally, the proposed models are applied to an insurance data set for insurers, obtained from an observational study, where the number of automobile claims and the number of third party claims are the correlated count responses. The effects of car age and the type of car, driving place on both responses are investigated simultaneously.
A joint mixture model for analyzing mixed longitudinal continuous and count data is presented. The continuous response is inflated in a set
, and a set-inflated normal (SIN) distribution is used as ...its distribution. The count response is inflated in a set
.
includes one or more points of sample space and a set-inflated power series (SIPS) distribution is used as its distribution. A full likelihood-based approach is used to obtain the maximum likelihood estimates of parameters via the EM algorithm. A random effects approach is applied to investigate the correlated longitudinal responses and correlated inflation mechanisms of each subject through time. Also, to consider the correlation between the mixed continuous and count responses of each individual at each time, the correlated random effects are used. In order to assess the performance of the model, some simulation studies are performed. An application of our models is illustrated for joint analysis of (1) number of days in the last month that the individual drank alcohol, and (2) weight of respondent for the first two waves of the American's Changing Lives survey.
Using a multivariate latent variable approach, this article proposes some new general models to analyze the correlated bounded continuous and categorical (nominal or/and ordinal) responses with and ...without non-ignorable missing values. First, we discuss regression methods for jointly analyzing continuous, nominal, and ordinal responses that we motivated by analyzing data from studies of toxicity development. Second, using the beta and Dirichlet distributions, we extend the models so that some bounded continuous responses are replaced for continuous responses. The joint distribution of the bounded continuous, nominal and ordinal variables is decomposed into a marginal multinomial distribution for the nominal variable and a conditional multivariate joint distribution for the bounded continuous and ordinal variables given the nominal variable. We estimate the regression parameters under the new general location models using the maximum-likelihood method. Sensitivity analysis is also performed to study the influence of small perturbations of the parameters of the missing mechanisms of the model on the maximal normal curvature. The proposed models are applied to two data sets: BMI, Steatosis and Osteoporosis data and Tehran household expenditure budgets.
Authors propose a joint random effect model for analyzing longitudinal mixed count, ordinal and continuous responses, where the count response is inflated in two points (k and l) and there is the ...possibility of non-ignorable missing values for all responses. The random effect approach is used to investigate both of the correlation between mixed responses and the correlation of longitudinal nature. The likelihood-based methods are used to inference about the parameters of the model. However, the interpretation of the fitted model highly depends on the assumptions imposed on the missing mechanism, so the authors extend a general index of sensitivity to non-ignorability (ISNI) methodology to assess the impact of the parameters of non-ignorability in the missing mechanisms on key inferences. A simulation study is performed in which for count response (k,l)-inflated Poisson and (k,l)-inflated negative binomial distributions are considered. Also, an application using a clinical data set is discussed.
In this paper, a joint model is presented to analyse longitudinal continuous and ordinal mixed responses. The ordinal longitudinal response inflates in the kth category, e.g., in the first, middle, ...or last. A k-category-inflated proportional odds (
) model with the random effects vectors is applied for modelling the ordinal response. The correlation of longitudinal responses through time as well as two response variables are modelled by utilizing the random effects vectors in the joint model. Further, a full likelihood-based approach is used to obtain the maximum likelihood estimates of parameters via the EM algorithm. Then, some simulation studies are performed to assess the performance of the model. Simulations show that the model performs well in coverage rates, estimation bias, and consistency. However, there are minor restrictions on the nature of the covariates for the identifiability of the model. Additionally, an application of our model is illustrated for joint analysis of the child's reading recognition skill (read) and the child's antisocial behaviour (anti) of the Peabody Individual Achievement Test (PIAT) dataset. The four-time points of the PIAT survey are evaluated.
The microdata of surveys are valuable resources for analyzing and modeling relationships between variables of interest. These microdata are often incomplete because of nonresponses in surveys and, if ...not considered, may lead to model misspecification and biased results. Nonresponse variable is usually assumed as a binary variable, and it is used to construct a sample selection model in many researches. However, this variable is a multilevel variable related to its reasons of occurring. Missing mechanism may differ among the levels of nonresponse, and merging the levels of nonresponse may cause bias in the results of the analysis. In this paper, a method is proposed for analyzing survey data with respect to reasons for the nonresponse based on sample selection model. Each nonresponse level is considered as a selection rule, and classical Heckman model is extended. Simulation studies and an analysis of a real data set from an establishment survey are presented to demonstrate the performance and practical usefulness of the proposed method.
Sample selection model is a solution to eliminate the nonresponse bias. In some applications nonresponse is a multilevel variable with respect to its reasons of occurring. In these cases, the sample ...selection model can be extended such that a model to be considered for each of the nonresponse reasons. Also, in many cases, the reasons for nonresponse have priority over each other. In other words, it is not possible to observe all of the nonresponse reasons simultaneously. For example, in a survey with two noncontact and refusal reasons, noncontact has priority over refusal and refusal can be observed if the contact to the respondent can be established. For analyzing such extended model, a Bayesian inference approach with multiple selection rules using multivariate normal, inverse gamma and LKJ distributions as prior distributions for parameters and possibility of priority for nonresponse reasons is presented. Simulation studies are performed and an establishment survey data set is analyzed to demonstrate the performance of the proposed method. For sensitivity analysis of nonresponse on the parameters of interest, posterior displacement is applied.
The identifiability of a statistical model is an essential and necessary property. When a model is not identifiable, even an infinite number of observations cannot determine the true parameter. ...Non-identifiablity problem in generalized linear models with and without random effects is very common. Also it can occur in such models when the response variable has non-ignorably missing. Since the structure of the beta regression model is similar to that of the generalized linear models and identifiability of many commonly used models such as the beta regression model has not been investigated in the literature, we establish a study about identifiability of some types of the beta regression models such as beta regression model with non-ignorable missing mechanism, zero and one inflated beta regression model, zero and one inflated beta regression model with non-ignorable missing mechanism, longitudinal beta regression model, longitudinal zero and one inflated beta regression model, longitudinal zero and one inflated beta regression model with non-ignorable missing mechanism, and longitudinal correlated bivariate Poisson and zero and one inflated beta regression model with non-ignorable missing mechanism. We construct estimators for the parameters in all mentioned models based on the EM algorithm and the likelihood-based approach. Simulation results and two applications of the Facebook network and FBI datasets are also presented.
