Bayesian estimation of a flexible bifactor generalized partial credit model to survey data

Item response theory (IRT) models provide an important contribution in the analysis of polytomous items, such as Likert scale items in survey data. We propose a bifactor generalized partial credit model (bifac-GPC model) with flexible link functions - probit, logit and complementary log-log - for use in analysis of ordered polytomous item scale data. In order to estimate the parameters of the proposed model, we use a Bayesian approach through the NUTS algorithm and show the advantages of implementing IRT models through the Stan language. We present an application to marketing scale data. Specifically, we apply the model to a dataset of non-users of a mobile banking service in order to highlight the advantages of this model. The results show important managerial implications resulting from consumer perceptions. We provide a discussion of the methodology for this type of data and extensions. Codes are available for practitioners and researchers to replicate the application.     

Sensitivity analysis and choosing between alternative polytomous IRT models using Bayesian model comparison criteria

Polytomous Item Response Theory (IRT) models are used by specialists to score assessments and questionnaires that have items with multiple response categories. In this article, we study the performance of five model comparison criteria for comparing fit of the graded response and generalized partial credit models using the same dataset when the choice between the two is unclear. Simulation study is conducted to analyze the sensitivity of priors and compare the performance of the criteria using the No-U-Turn Sampler algorithm, under a Bayesian approach. The results were used to select a model for an application in mental health data.     

Building up adjusted indicators of students’ evaluation of university courses using generalized item response models

This article advances a proposal for building up adjusted composite indicators of the quality of university courses from students’ assessments. The flexible framework of Generalized Item Response Models is adopted here for controlling the sources of heterogeneity in the data structure that make evaluations across courses not directly comparable. Specifically, it allows us to: jointly model students’ ratings to the set of items which define the quality of university courses; explicitly consider the dimensionality of the items composing the evaluation form; evaluate and remove the effect of potential confounding factors which may affect students’ evaluation; model the intra-cluster variability at course level. The approach simultaneously deals with: (i) multilevel data structure; (ii) multidimensional latent trait; (iii) personal explanatory latent regression models. The paper pays attention to the potential of such a flexible approach in the analysis of students evaluation of university courses in order to explore both how the quality of the different aspects (teaching, management, etc.) is perceived by students and how to make meaningful comparisons across them on the basis of adjusted indicators.     

An Investigation of Parameter Recovery in MCMC Estimation for the Additive IRT Model

The article aims at evaluating the parameter recovery for the multidimensional additive IRT model (Sheng, 2005 Sheng , Y. ( 2005 ). Bayesian Analysis of Hierarchical IRT Models: Comparing and Combining the Unidimensional & Multi-Unidimensional IRT Models. PhD thesis , Faculty of the Graduate SchoolUniversity of Missouri-Columbia . [Google Scholar]; Sheng and Wikle, 2009 Sheng , Y. , Wikle , C. K. ( 2009 ). Bayesian IRT models incorporating general and specific abilities . Behaviormetrika 36 : 27 – 48 .[Crossref] , [Google Scholar]). By estimating the model parameters via Gibbs sampler, a simulation study is conducted under different testing conditions, e.g., dimensionality, test and subtest lengths, correlation matrices, and different values of discrimination parameters. The results show that, especially when the test length is short and the abilities are highly correlated, the accuracy of the parameter estimates is reduced and more iterations are required to convergence. An application in educational testing is also described to show the effectiveness of the model in use.     

A Bayesian Analysis of Synchronous Distance Learning versus Matched Traditional Control in Graduate Biostatistics Courses

Distance learning can be useful for bridging geographical barriers to education in rural settings. However, empirical evidence on the equivalence of distance education and traditional face-to-face (F2F) instruction in statistics and biostatistics is mixed. Despite the difficulty in randomization, we minimized intra-instructor variation between F2F and online sections in seven graduate-level biostatistics service courses in a synchronous (live, real time) fashion; that is, for each course taught in a traditional F2F setting, a separate set of students were taught simultaneously via online learning technology, allowing for two-way interaction between instructor and students. Our primary objective was to compare student performance in the two courses that use these two teaching modes. We used a Bayesian hierarchical model to test equivalence of modes. The frequentist mixed model approach was also conducted for reference. The results of Bayesian and frequentist methods agree and suggest a difference of less than 1% in average final grades. Finally, we discuss barriers to instruction and learning using the applied online teaching technology.     

Dropping out of university: A statistical analysis of the probability of withdrawal for UK university students

From individual level data for an entire cohort of undergraduate students in the 'old' universities in the UK, we use a binomial probit model to estimate the probability that an individual will 'drop out' of university before the completion of their degree course. We examine the cohort of students enrolling full time for a 3- or 4-year degree in the academic year 1989–1990. We find evidence to support both the hypothesis that the completion of courses by students is influenced by the extent of prior academic preparedness and the hypothesis that social integration at university is important. We also find an influence of unemployment in the county of prior residence, especially for poorer male students. Finally, we draw conclusions regarding the public policy of constructing university performance indicators in this area.     

Comparing methods for estimating the abilities for the multidimensional models of mixed item types

The maximum likelihood (MLE), the weighted maximum likelihood (WMLE), and the maximum a posteriori (MAP or BMLE) have been widely used to estimate ability parameters in item response theory (IRT), and their precisions and biases have been studied and compared. Multidimensional IRT (MIRT) has been shown to provide better subscore estimates in both paper-and-pencil and computer adaptive tests; thus, it is very important to have an accurate score estimate for the MIRT model. The purpose of this article is to compare the performances of the three estimation methods in the MIRT framework for tests of mixed item types that have both dichotomous and polytomously scored items, and for tests of mixed structured items (simple structured and complex structured). It is found that all three methods perform well for all conditions. For all models studied (one-, two-, three-, and four- dimensional model), WMLE has smaller BIAS and higher reliabilities, but larger RMSE and SE. WMLE and MLE are closer to each other than to BMLE. However, for higher dimensions, BMLE is recommended, especially when there are correlations between the dimensions.     

A multiple group item response theory model with centered skew-normal latent trait distributions under a Bayesian framework

Very often, in psychometric research, as in educational assessment, it is necessary to analyze item response from clustered respondents. The multiple group item response theory (IRT) model proposed by Bock and Zimowski [12] provides a useful framework for analyzing such type of data. In this model, the selected groups of respondents are of specific interest such that group-specific population distributions need to be defined. The usual assumption for parameter estimation in this model, which is that the latent traits are random variables following different symmetric normal distributions, has been questioned in many works found in the IRT literature. Furthermore, when this assumption does not hold, misleading inference can result. In this paper, we consider that the latent traits for each group follow different skew-normal distributions, under the centered parameterization. We named it skew multiple group IRT model. This modeling extends the works of Azevedo et al. [4], Bazán et al. [11] and Bock and Zimowski [12] (concerning the latent trait distribution). Our approach ensures that the model is identifiable. We propose and compare, concerning convergence issues, two Monte Carlo Markov Chain (MCMC) algorithms for parameter estimation. A simulation study was performed in order to evaluate parameter recovery for the proposed model and the selected algorithm concerning convergence issues. Results reveal that the proposed algorithm recovers properly all model parameters. Furthermore, we analyzed a real data set which presents asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of negative asymmetry for some latent trait distributions.     

A comparison of Monte Carlo methods for computing marginal likelihoods of item response theory models

Nowadays, Bayesian methods are routinely used for estimating parameters of item response theory (IRT) models. However, the marginal likelihoods are still rarely used for comparing IRT models due to their complexity and a relatively high dimension of the model parameters. In this paper, we review Monte Carlo (MC) methods developed in the literature in recent years and provide a detailed development of how these methods are applied to the IRT models. In particular, we focus on the “best possible” implementation of these MC methods for the IRT models. These MC methods are used to compute the marginal likelihoods under the one-parameter IRT model with the logistic link (1PL model) and the two-parameter logistic IRT model (2PL model) for a real English Examination dataset. We further use the widely applicable information criterion (WAIC) and deviance information criterion (DIC) to compare the 1PL model and the 2PL model. The 2PL model is favored by all of these three Bayesian model comparison criteria for the English Examination data.     

Markov chain Monte Carlo estimation of a mixture item response theory model

Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods.     

中国信贷市场的配适性分析

为了研究中国信贷市场供求配适性状况,以及造成中国信贷投放总量错配的主要因素,文章利用1997-2009年2季度中国信贷市场季度数据,采用最大似然方法估计信贷供求非均衡模型参数,实证结果表明：（1）信贷供给小于信贷需求为32个季度,信贷供给大于信贷需求为15个季度,其中1997-2001年以及2005-2007年存在严重的供小于求现象;而2002-2004年及2008年3季度以来存在信贷供大于求现象,其中2009年第1季度信贷超额供给占观察到的实际信贷量的比例为18.37%;（2）中国信贷市场上银行信贷能力是影响信贷供给的重要变量,信贷能力越高,社会上的贷款就越多,而2009年来的信贷大幅投放已经超过了银行的实际信贷能力。     

农产品电商不同融资方式选择的影响因素研究

基于2 131份有效调查问卷数据,运用有序Probit模型对农产品电商不同融资方式选择的影响因素进行研究。研究发现:农产品电商选择从P2P等非正规金融机构融资,还是从农村信用社等正规金融机构融资,这与农产品电商的户主禀赋变量、家庭特征变量及区域特征变量紧密相关;在户主禀赋变量、家庭特征变量和区域特征变量方面具有优势的农产品电商,更倾向于从P2P等非正规金融机构融资,反之,则倾向于从农村信用社等正规金融机构融资。     

Accent on Teaching Materials: Notices and Reviews of Important Teaching Materials

This article examines the probabilities of outcomes from rolling dice with the dimension 1 × 1 × r for various values of r. Experiments were conducted by school students and university students. The results of the experiments are given and the probabilities examined using a generalized linear model. Notes are also made about the value of the experiment in teaching the groups of students.     

A joint marginalized multilevel model for longitudinal outcomes

The shared-parameter model and its so-called hierarchical or random-effects extension are widely used joint modeling approaches for a combination of longitudinal continuous, binary, count, missing, and survival outcomes that naturally occurs in many clinical and other studies. A random effect is introduced and shared or allowed to differ between two or more repeated measures or longitudinal outcomes, thereby acting as a vehicle to capture association between the outcomes in these joint models. It is generally known that parameter estimates in a linear mixed model (LMM) for continuous repeated measures or longitudinal outcomes allow for a marginal interpretation, even though a hierarchical formulation is employed. This is not the case for the generalized linear mixed model (GLMM), that is, for non-Gaussian outcomes. The aforementioned joint models formulated for continuous and binary or two longitudinal binomial outcomes, using the LMM and GLMM, will naturally have marginal interpretation for parameters associated with the continuous outcome but a subject-specific interpretation for the fixed effects parameters relating covariates to binary outcomes. To derive marginally meaningful parameters for the binary models in a joint model, we adopt the marginal multilevel model (MMM) due to Heagerty [13] and Heagerty and Zeger [14] and formulate a joint MMM for two longitudinal responses. This enables to (1) capture association between the two responses and (2) obtain parameter estimates that have a population-averaged interpretation for both outcomes. The model is applied to two sets of data. The results are compared with those obtained from the existing approaches such as generalized estimating equations, GLMM, and the model of Heagerty [13]. Estimates were found to be very close to those from single analysis per outcome but the joint model yields higher precision and allows for quantifying the association between outcomes. Parameters were estimated using maximum likelihood. The model is easy to fit using available tools such as the SAS NLMIXED procedure.     

Modelling the effect of subject-specific covariates in paired comparison studies with an application to university rankings

Preference decisions will usually depend on the characteristics of both the judges and the objects being judged. In the analysis of paired comparison data concerning European universities and students' characteristics, it is demonstrated how to incorporate subject-specific information into Bradley–Terry-type models. Using this information it is shown that preferences for universities and therefore university rankings are dramatically different for different groups of students. A log-linear representation of a generalized Bradley–Terry model is specified which allows simultaneous modelling of subject- and object-specific covariates and interactions between them. A further advantage of this approach is that standard software for fitting log-linear models, such as GLIM, can be used.     

Reassessing service courses in statistics

Service courses in statistics are frequently criticized by students as being unnecessary or Irrelevant to their educational goals. This article examine the teaching of undergraduates service courses. Indentifying several areas critical to the sucess of the courses.General Philosphing conceriningthe resoultions of the problems associated with the teaching of an undergraduates service courses are proposed as well as the specific suggestionsfor a course for a social science majors     

Ethical Numbers: Ethics Training in U.S. Graduate Statistics Programs, 2013–2014

As important members of research teams, statisticians bear an ethical responsibility to analyze, interpret, and report data honestly and objectively. One way of reinforcing ethical responsibilities is through required courses covering a variety of ethics-related topics at the graduate level. We assessed ethics requirements for graduate-level statistics training programs in the United States for the 2013–2014 academic year using the websites of 88 universities, examining 103 biostatistics programs, and 136 statistics degree programs. We categorized programs’ ethics training requirements as required or not required. Thirty-one (35.1%) universities required an ethics course for at least some degree students. Sixty-two (25.5%) degree programs required an ethics course for at least some students. The majority (77.4%) of required courses were worth 0 or 1 credit. Of the 177 programs without an ethics requirement, 19 (10.7%) listed an ethics elective. Although a single ethics course is insufficient for instilling an ethical approach to science, degree programs that model expectations through coursework point to the value of ethics in science. More training programs should prepare statisticians to consider the ethical dimensions of their work through required coursework. Supplementary materials for this article are available online.     

适应经济发展的高校学科结构优化模型

文章利用1994~2003年的分学科高校在校生资料,进行一阶差分,用净增人数建立灰色动态模型,对2008年和2010年的在校生进行中期预测。并把分学科在校生与人均GDP的关联度作为灰色线性规划的贡献率灰数,优化出各学科在校生的结构。结果显示,需要适度减缓哲学、历史学、法学、经济学的发展速度,增加教育学、工学、医学的培养人数。     

MINIMUM RATE OF PROGRESS FORMULAE AT UNIVERSITIES1

In an earlier paper by the present author (1970) a comparison was made of graduation rates and pass rates under a pass-on-the-year system with those under a credit points system. In the present paper attention is focused on the effect, under these two systems, of regulations which exclude students who have not achieved the required minimum rate of progress. The paper traces the progress made by homogeneous groups of students when there is no exclusion formula, points out why such formulae are needed under both systems, and measures the efficiency of a university system in terms of the proportion of a given quality intake which it graduates and of the cost measured by the number of students required to be maintained on campus to produce one graduate. Precise definitions of the terms used are not repeated here because they are in common usage; they are, however, given in the earlier     

Bayesian binary quantile regression for the analysis of Bachelor-to-Master transition

The multi-cycle organization of modern university systems stimulates the interest in studying the progression to higher level degree courses during the academic career. In particular, after the achievement of the first level qualification (Bachelor degree), students have to decide whether to continue their university studies, by enrolling in a second level (Master) programme, or to conclude their training experience. In this work we propose a binary quantile regression (BQR) approach to analyse the Bachelor-to-Master transition phenomenon with the adoption of the Bayesian inferential perspective. In addition to the traditional predictors of academic outcomes, such as the personal characteristics and the field of study, different aspects of student's performance are considered. Moreover, the role of a new contextual variable, representing the type of university regulations experienced during the academic path, is investigated. The utility of the Bayesian BQR to characterize the non-continuation decision after the first cycle studies is illustrated with an application to administrative data of Bachelor graduates at the School of Economics of Sapienza University of Rome. The method favourably compares with more conventional model specifications concerning the conditional mean of the binary response.