The Relationship Between Parent-Adolescent Conflict Dynamics and Adolescent Depression

Journal of Child and Family Studies - This study investigated the relation between parent–adolescent conflict and adolescents’ depressive symptoms from a dynamic systems framework. Two...     

Subtask analysis of process data through a predictive model

Response process data collected from human–computer interactive items contain detailed information about respondents' behavioural patterns and cognitive processes. Such data are valuable sources for analysing respondents' problem-solving strategies. However, the irregular data format and the complex structure make standard statistical tools difficult to apply. This article develops a computationally efficient method for exploratory analysis of such process data. The new approach segments a lengthy individual process into a sequence of short subprocesses to achieve complexity reduction, easy clustering and meaningful interpretation. Each subprocess is considered a subtask. The segmentation is based on sequential action predictability using a parsimonious predictive model combined with the Shannon entropy. Simulation studies are conducted to assess the performance of the new method. We use a case study of PIAAC 2012 to demonstrate how exploratory analysis for process data can be carried out with the new approach.     

An exploratory analysis of the latent structure of process data via action sequence autoencoders

Computer simulations have become a popular tool for assessing complex skills such as problem-solving. Log files of computer-based items record the human–computer interactive processes for each respondent in full. The response processes are very diverse, noisy, and of non-standard formats. Few generic methods have been developed to exploit the information contained in process data. In this paper we propose a method to extract latent variables from process data. The method utilizes a sequence-to-sequence autoencoder to compress response processes into standard numerical vectors. It does not require prior knowledge of the specific items and human–computer interaction patterns. The proposed method is applied to both simulated and real process data to demonstrate that the resulting latent variables extract useful information from the response processes.     

A reinforcement learning approach to personalized learning recommendation systems

Personalized learning refers to instruction in which the pace of learning and the instructional approach are optimized for the needs of each learner. With the latest advances in information technology and data science, personalized learning is becoming possible for anyone with a personal computer, supported by a data-driven recommendation system that automatically schedules the learning sequence. The engine of such a recommendation system is a recommendation strategy that, based on data from other learners and the performance of the current learner, recommends suitable learning materials to optimize certain learning outcomes. A powerful engine achieves a balance between making the best possible recommendations based on the current knowledge and exploring new learning trajectories that may potentially pay off. Building such an engine is a challenging task. We formulate this problem within the Markov decision framework and propose a reinforcement learning approach to solving the problem.     

Hypothesis Testing of the <Emphasis Type="Italic">Q</Emphasis>-matrix

The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method.     

Latent Variable Selection for Multidimensional Item Response Theory Models via $$L_{1}$$ Regularization

We develop a latent variable selection method for multidimensional item response theory models. The proposed method identifies latent traits probed by items of a multidimensional test. Its basic strategy is to impose an \(L_{1}\) penalty term to the log-likelihood. The computation is carried out by the expectation–maximization algorithm combined with the coordinate descent algorithm. Simulation studies show that the resulting estimator provides an effective way in correctly identifying the latent structures. The method is applied to a real dataset involving the Eysenck Personality Questionnaire.     

On the Identifiability of Diagnostic Classification Models

Psychometrika - This paper establishes fundamental results for statistical analysis based on diagnostic classification models (DCMs). The results are developed at a high level of generality and are...     

Robust Measurement via A Fused Latent and Graphical Item Response Theory Model

Item response theory (IRT) plays an important role in psychological and educational measurement. Unlike the classical testing theory, IRT models aggregate the item level information, yielding more accurate measurements. Most IRT models assume local independence, an assumption not likely to be satisfied in practice, especially when the number of items is large. Results in the literature and simulation studies in this paper reveal that misspecifying the local independence assumption may result in inaccurate measurements and differential item functioning. To provide more robust measurements, we propose an integrated approach by adding a graphical component to a multidimensional IRT model that can offset the effect of unknown local dependence. The new model contains a confirmatory latent variable component, which measures the targeted latent traits, and a graphical component, which captures the local dependence. An efficient proximal algorithm is proposed for the parameter estimation and structure learning of the local dependence. This approach can substantially improve the measurement, given no prior information on the local dependence structure. The model can be applied to measure both a unidimensional latent trait and multidimensional latent traits.     

A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models

Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary estimates. This approach is equivalent to estimating variance parameters by their posterior mode, given a weakly informative prior distribution. By choosing the penalty from the log-gamma family with shape parameter greater than 1, we ensure that the estimated variance will be positive. We suggest a default log-gamma(2,λ) penalty with λ→0, which ensures that the maximum penalized likelihood estimate is approximately one standard error from zero when the maximum likelihood estimate is zero, thus remaining consistent with the data while being nondegenerate. We also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a noninformative prior. Our default method provides better estimates of model parameters and standard errors than the maximum likelihood or the restricted maximum likelihood estimators. The log-gamma family can also be used to convey substantive prior information. In either case—pure penalization or prior information—our recommended procedure gives nondegenerate estimates and in the limit coincides with maximum likelihood as the number of groups increases.