The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological assessments,
this type of multidimensional latent variable models may suffer from non-identifiability, which can further lead to inconsistent parameter estimation and invalid inference. The current work provides a relatively complete characterization of identifiability for the linear and dichotomous bifactor models and the linear extended bifactor model with correlated subdimensions. In addition, similar results for the two-tier models are also developed. Illustrative examples are provided on checking model identifiability through inspecting the factor loading structure. Simulation studies are reported that examine estimation consistency when the identifiability conditions are/are not satisfied.
A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, observed connections consist of events arriving as streams, which are then aggregated to form edges, ignoring the tempor
al dynamic component. A natural way to take account of this temporal dynamic component of interactions is to use point processes as the foundation of the network models for community detection. Computational complexity hampers the scalability of such approaches to large sparse networks. To circumvent this challenge, we propose a fast online variational inference algorithm for learning the community structure underlying dynamic event arrivals on a network using continuous-time point process latent network models. We provide regret bounds on the loss function of this procedure, giving theoretical guarantees on performance. The proposed algorithm is illustrated, using both simulation studies and real data, to have comparable performance in terms of community structure in terms of community recovery to non-online variants. Our proposed framework can also be readily modified to incorporate other popular network structures.
In this work, we study the event occurrences of user activities on online social network platforms. To characterize the social activity interactions among network users, we propose a network group Hawkes (NGH) process model. Particularly, the observe
d network structure information is employed to model the users dynamic posting behaviors. Furthermore, the users are clustered into latent groups according to their dynamic behavior patterns. To estimate the model, a constraint maximum likelihood approach is proposed. Theoretically, we establish the consistency and asymptotic normality of the estimators. In addition, we show that the group memberships can be identified consistently. To conduct estimation, a branching representation structure is firstly introduced, and a stochastic EM (StEM) algorithm is developed to tackle the computational problem. Lastly, we apply the proposed method to a social network data collected from Sina Weibo, and identify the infuential network users as an interesting application.
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 solv
ing 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 examinees 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).
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 indi
vidual 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.
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.
