arXiv subjects

Guanhua Fang

Publications and source records attributed to Guanhua Fang.

21 records · Page 2Linked to original sources

arXiv2020

Latent Theme Dictionary Model for Finding Co-occurrent Patterns in Process Data

Process data, temporally ordered categorical observations, are of recent interest due to its increasing abundance and the desire to extract useful information. A process is a collection of time-stamped events of different types, recording how an individual behaves in a given time period. The process data are too complex in terms of size and irregularity for the classical psychometric models to be applicable, at least directly, and, consequently, it is desirable to develop new ways for modeling and analysis. We introduce herein a latent theme dictionary model (LTDM) for processes that identifies co-occurrent event patterns and individuals with similar behavioral patterns. Theoretical properties are established under certain regularity conditions for the likelihood based estimation and inference. A non-parametric Bayes LTDM algorithm using the Markov Chain Monte Carlo method is proposed for computation. Simulation studies show that the proposed approach performs well in a range of situations. The proposed method is applied to an item in the 2012 Programme for International Student Assessment with interpretable findings.

stat.ME↗

arXiv2019

A Latent Topic Model with Markovian Transition for Process Data

We propose a latent topic model with a Markovian transition for process data, which consist of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinee's latent state. Using topic transition probabilities along with response times enables us to capture examinees' learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem solving item in 2012 Programme for International Student Assessment (PISA 2012).

stat.ME↗

arXiv2017

On the Identifiability of Diagnostic Classification Models

This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In particular, we establish identifiability results of various modeling parameters, notably item response probabilities, attribute distribution, and Q-matrix-induced partial information structure. Consistent estimators are constructed. Simulation results show that these estimators perform well under various modeling settings. We also use a real example to illustrate the new method. The results are stated under the setting of general latent class models. For DCM with a specific parameterization, the conditions may be adapted accordingly.

math.ST↗