Joint Maximum Likelihood Estimation for Diagnostic Classification Models

Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees’ proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. As a practical application, JMLE is also used with “real world” educational data collected with a language proficiency test.     

Consistency Theory for the General Nonparametric Classification Method

Psychometrika - Parametric likelihood estimation is the prevailing method for fitting cognitive diagnosis models—also called diagnostic classification models (DCMs). Nonparametric concepts...     

On the Consistency of Q-Matrix Estimation: A Rejoinder

This rejoinder responds to the commentary by Liu (Psychometrika, 2015) entitled “On the consistency of Q-matrix estimation: A commentary” on the paper “A general method of empirical Q-matrix validation” by de la Torre and Chiu (Psychometrika, 2015). It discusses and addresses three concerns raised in the commentary, namely the estimation accuracy when a provisional Q-matrix is used, the consistency of the Q-matrix estimator, and the computational efficiency of the proposed method.     

Cluster Analysis for Cognitive Diagnosis: Theory and Applications

Latent class models for cognitive diagnosis often begin with specification of a matrix that indicates which attributes or skills are needed for each item. Then by imposing restrictions that take this into account, along with a theory governing how subjects interact with items, parametric formulations of item response functions are derived and fitted. Cluster analysis provides an alternative approach that does not require specifying an item response model, but does require an item-by-attribute matrix. After summarizing the data with a particular vector of sum-scores, K-means cluster analysis or hierarchical agglomerative cluster analysis can be applied with the purpose of clustering subjects who possess the same skills. Asymptotic classification accuracy results are given, along with simulations comparing effects of test length and method of clustering. An application to a language examination is provided to illustrate how the methods can be implemented in practice.     

Religious Characteristics,Spirituality, and Depressive Symptoms Among 10th- to 12th-Graders Living in a Buddhist or Daoist Culture: A Short-Term Longitudinal Study

This study examines changes in and the relationship among religiosity, spiritual well-being, and depressive symptoms in primarily Buddhist or Daoist Taiwanese adolescents. A total of 2,239 16- to 18-year-old adolescents from 4 high schools were randomly selected and completed a questionnaire at baseline and at 6-month follow-up. Half of the Taiwanese adolescents reported being religious (50%), with Buddhism or Daoism predominating in terms of religious affiliation. Around 80% of adolescents believed in a God, but less than 40% believed that religion is important. Mixed models found no significant relationships between religiosity and spirituality or between religiosity and depressive symptoms. Self-efficacy and life scheme are valid domains for the spirituality construct, and a reciprocal relationship was found between spiritual well-being and depressive symptoms. This reciprocal relationship in adolescents is discussed in terms of a Buddhist or Daoist cultural context.     

Predicting Creative Problem-Solving in Math From a Dynamic System Model of Creative Problem Solving Ability

Six attributes of creative problem-solving ability were investigated as predictors of creative problem solving ability in math. A total of 409 Taiwanese fifth and sixth graders were administered the recently developed Creative Problem Solving Attributes Inventory and other corresponding established instruments that measure similar attributes. The Creative Problem Solving Attributes Inventory yielded valid and reliable data on creative problem solving attributes. Results also demonstrated that divergent thinking and domain specific knowledge and skills directly predicted math problem-solving ability, whereas divergent thinking, convergent thinking, motivation, general knowledge and skills, and environment indirectly predicted math problem solving ability. Implications for nurturing creative problem solving ability and limitations of the study are discussed.     

Consistency of Cluster Analysis for Cognitive Diagnosis: The Reduced Reparameterized Unified Model and the General Diagnostic Model

The asymptotic classification theory of cognitive diagnosis (ACTCD) provided the theoretical foundation for using clustering methods that do not rely on a parametric statistical model for assigning examinees to proficiency classes. Like general diagnostic classification models, clustering methods can be useful in situations where the true diagnostic classification model (DCM) underlying the data is unknown and possibly misspecified, or the items of a test conform to a mix of multiple DCMs. Clustering methods can also be an option when fitting advanced and complex DCMs encounters computational difficulties. These can range from the use of excessive CPU times to plain computational infeasibility. However, the propositions of the ACTCD have only been proven for the Deterministic Input Noisy Output “AND” gate (DINA) model and the Deterministic Input Noisy Output “OR” gate (DINO) model. For other DCMs, there does not exist a theoretical justification to use clustering for assigning examinees to proficiency classes. But if clustering is to be used legitimately, then the ACTCD must cover a larger number of DCMs than just the DINA model and the DINO model. Thus, the purpose of this article is to prove the theoretical propositions of the ACTCD for two other important DCMs, the Reduced Reparameterized Unified Model and the General Diagnostic Model.     

A General Method of Empirical Q-matrix Validation

In contrast to unidimensional item response models that postulate a single underlying proficiency, cognitive diagnosis models (CDMs) posit multiple, discrete skills or attributes, thus allowing CDMs to provide a finer-grained assessment of examinees’ test performance. A common component of CDMs for specifying the attributes required for each item is the Q-matrix. Although construction of Q-matrix is typically performed by domain experts, it nonetheless, to a large extent, remains a subjective process, and misspecifications in the Q-matrix, if left unchecked, can have important practical implications. To address this concern, this paper proposes a discrimination index that can be used with a wide class of CDM subsumed by the generalized deterministic input, noisy “and” gate model to empirically validate the Q-matrix specifications by identifying and replacing misspecified entries in the Q-matrix. The rationale for using the index as the basis for a proposed validation method is provided in the form of mathematical proofs to several relevant lemmas and a theorem. The feasibility of the proposed method was examined using simulated data generated under various conditions. The proposed method is illustrated using fraction subtraction data.     

Fitting the Reduced RUM with Mplus: A Tutorial

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own code, are still rather limited. One option is to use a commercial software package that offers an implementation of the expectation maximization (EM) algorithm for fitting (constrained) latent class models like Latent GOLD or Mplus. But using a latent class analysis routine as a vehicle for fitting the Reduced RUM requires that it be re-expressed as a logit model, with constraints imposed on the parameters of the logistic function. This tutorial demonstrates how to implement marginal maximum likelihood estimation using the EM algorithm in Mplus for fitting the Reduced RUM.     

A study of Internet addiction through the lens of the interpersonal theory.

Previous studies have presented conflicting claims regarding reasons that people become addicted to the Internet. In this study, we attempted to identify predictors of Internet addiction based on Sullivan's interpersonal theory and Internet addiction literature. In our research model, it is hypothesized that good parent-child relationship positively correlates with good interpersonal relationships, which in turn are hypothesized to correlate with undesirable social anxiety. In addition, both parent-child and interpersonal relationships are hypothesized to negatively correlate with Internet addiction, whereas the level of social anxiety is hypothesized to positively correlate with Internet addiction. The results of this study confirm the research model hypotheses, indicating that the quality of parent-child relationship is indeed positively correlated to the quality of our participants' interpersonal relationships and that frustrating interpersonal relationships may raise the level of social anxiety. In addition, interpersonal relationships, the parent-child relationship, and social anxiety all influence Internet addiction, as predicted by the model. Finally, the more social anxiety and discontent with their peer interactions the participants experienced, the more addicted they were to the Internet.