scholarly journals A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models

2020 ◽  
Author(s):  
Kazuhiro Yamaguchi ◽  
Jonathan Templin
Keyword(s):  
Gibbs Sampling ◽  
Estimation Method ◽  
Latent Class Models ◽  
Diagnostic Classification ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Classification Models ◽  
Diagnostic Classification Models ◽  
International Student Assessment ◽  
Monotonicity Constraints

Diagnostic classification models (DCM) are restricted latent class models with a set of cross-class equality constraints and additional monotonicity constraints on their item parameters, both of which are needed to ensure the meaning of classes and model parameters. In this paper, we develop an efficient, Gibbs sampling-based Bayesian Markov chain Monte Carlo estimation method for general DCMs with monotonicity constraints. A simulation study was conducted to evaluate parameter recovery of the algorithm which showed accurate estimation of model parameters. An analysis of the 2000 Programme for International Student Assessment reading assessment data using this algorithm was also conducted.

scholarly journals Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm

2020 ◽  
Author(s):  
Kazuhiro Yamaguchi ◽  
Jonathan Templin
Keyword(s):  
Gibbs Sampling ◽  
Estimation Method ◽  
Real Data ◽  
Classification Model ◽  
Diagnostic Classification ◽  
Model Parameters ◽  
Sampling Algorithm ◽  
Diagnostic Classification Models ◽  
Gibbs Sampling Algorithm ◽  
Collapsed Gibbs Sampling

This paper proposes a novel collapsed Gibbs sampling algorithm that marginalizes model parameters and directly samples latent attribute mastery patterns in diagnostic classification models. This estimation method makes it possible to avoid boundary problems in the estimation of model item parameters by eliminating the need to estimate such parameters. A simulation study showed the collapsed Gibbs sampling algorithm can accurately recover the true attribute mastery status in various conditions. In a real data analysis, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

Model of the influence of Internet finance on monetary policy based on gibbs sampling and vector autoregression

2020 ◽  
pp. 1-11
Author(s):  
Hui Wang ◽  
Huang Shiwang
Keyword(s):  
Monetary Policy ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Estimation Method ◽  
Financial Supervision ◽  
Var Model ◽  
Model Parameters ◽  
State Variables ◽  
Frequency Data ◽  
Internet Finance

The various parts of the traditional financial supervision and management system can no longer meet the current needs, and further improvement is urgently needed. In this paper, the low-frequency data is regarded as the missing of the high-frequency data, and the mixed frequency VAR model is adopted. In order to overcome the problems caused by too many parameters of the VAR model, this paper adopts the Bayesian estimation method based on the Minnesota prior to obtain the posterior distribution of each parameter of the VAR model. Moreover, this paper uses methods based on Kalman filtering and Kalman smoothing to obtain the posterior distribution of latent state variables. Then, according to the posterior distribution of the VAR model parameters and the posterior distribution of the latent state variables, this paper uses the Gibbs sampling method to obtain the mixed Bayes vector autoregressive model and the estimation of the state variables. Finally, this article studies the influence of Internet finance on monetary policy with examples. The research results show that the method proposed in this article has a certain effect.

scholarly journals The Reliability of the Posterior Probability of Skill Attainment in Diagnostic Classification Models

2019 ◽  
Vol 45 (1) ◽  
pp. 5-31
Author(s):  
Matthew S. Johnson ◽  
Sandip Sinharay
Keyword(s):  
Posterior Probability ◽  
Real Data ◽  
Exact Calculation ◽  
Diagnostic Classification ◽  
Classification Models ◽  
Diagnostic Classification Models ◽  
Reliability Measure ◽  
Skill Mastery

One common score reported from diagnostic classification assessments is the vector of posterior means of the skill mastery indicators. As with any assessment, it is important to derive and report estimates of the reliability of the reported scores. After reviewing a reliability measure suggested by Templin and Bradshaw, this article suggests three new measures of reliability of the posterior means of skill mastery indicators and methods for estimating the measures when the number of items on the assessment and the number of skills being assessed render exact calculation computationally burdensome. The utility of the new measures is demonstrated using simulated and real data examples. Two of the suggested measures are recommended for future use.

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