Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent.

Investigating Factors Affecting Students\u27 Satisfaction with Computer-based Assessment

Despite the increasing use of computer-based assessment (CBA), there remains a dearth of evidence of what factors contribute to students’ satisfaction with CBA. We investigated four factors that are extracted from the TIMSS 2019 (Trends in International Mathematics and Science Study) Student Questionnaire eTIMSS Supplement – which was designed to examine student’s experience with the computer version of TIMSS (Mullis, Martin, Foy, Kelly, & Fishbein (2020)). The four factors were perceived technical difficulties, frequency of computer or tablet usage at school, self-confidence in computer or tablet usage, and familiarity with information and communication technology (ICT) terminology

Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent

Loglinear Models as Item Response Models

For analyzing item response data, item response theory (IRT) models treat the discrete responses to the items as driven by underlying continuous latent traits, and consider the form of conditional probability of the response to each item given the latent traits. In a similar fashion, log-linear models directly consider the form of the manifest probability of response patterns. Researchers have been connecting the two paradigms by establishing equivalence relationships between IRT models and log-linear models. This has lead to the notion of obtaining IRT solutions by fitting their equivalent log-linear models. In this research, I have established a family of log-linear models, log linear-by-linear association (LLLA) models, that incorporate a variety of IRT models, particularly, a family of generalized Rasch models. I have derived an extension of the Dutch Identity theorem to polytomous items and utilized it to develop the models that incorporate item covariates and person covariates. Noteworthy features of the models include both polytomous responses and multiple latent traits. Along with developing this new family of models, I have conducted extensive research on the development of an accompanying estimation method. Historically, a significant barrier to the application of log-linear models in analyzing item responses has been the high computational cost of maximum likelihood estimation (MLE), due to the fact that the number of response patterns grows exponentially as the number of items increases. To solve this computational problem, a pseudo-likelihood estimation (PLE) method is proposed and it dramatically decreases the computational cost. To demonstrate the effectiveness of the developed models and the pseudolikelihood estimation method, I will present results of a series of simulation studies. To demonstrate the practical advantages of the methods, I will give a detailed description of an application to a real data set from a study on verbally aggressive behavior

Performance Evaluation of Tunnel-Slag-Improved High Liquid Limit Soil in Subgrade: A Case Study

The application of tunnel-slag-improved high liquid limit soil as filling materials in subgrade is a green environmental technology. This study explored the influence of tunnel slag mixing on the physical and mechanical properties of improved soils, based on the engineering background of Liyu highway, Guangxi Province, China. Firstly, the optimal moisture content, maximum dry density, shear strength parameters, California bearing ratio (CBR) and resilience modulus of plain and tunnel-slag-improved high liquid limit soils were experimentally determined. Results showed that the direct utilization of untreated soil was unacceptable in subgrade practice. A significant enhancement of integrity of high liquid limit soils could be obtained by tunnel slag mixing, and the value of 15% was determined as the optimal tunnel slag content in soils, leading to improved soil performance meeting the specification requirements. Then, numerical simulation on the stability of subgrade slope of tunnel-slag-improved soils at the content of 15% was conducted. It also reported the long-term subgrade settlements. The feasibility of utilization of tunnel slag in improving properties of high liquid limit soils was further validated. Finally, a good application of tunnel-slag-improved high liquid limit soil as subgrade filling materials in Liyu highway was achieved. The findings in this study could provide useful guidance for similar engineering