RESUMO
In the current literature on latent variable models, much effort has been put on the development of dichotomous and polytomous cognitive diagnostic models (CDMs) for assessments. Recently, the possibility of using continuous responses in CDMs has been brought to discussion. But no Bayesian approach has been developed yet for the analysis of CDMs when responses are continuous. Our work is the first Bayesian framework for the continuous deterministic inputs, noisy, and gate (DINA) model. We also propose new interpretations for item parameters in this DINA model, which makes the analysis more interpretable than before. In addition, we have conducted several simulations to evaluate the performance of the continuous DINA model through our Bayesian approach. Then, we have applied the proposed DINA model to a real data example of risk perceptions for individuals over a range of health-related activities. The application results exemplify the high potential of the use of the proposed continuous DINA model to classify individuals in the study.
Assuntos
Modelos Estatísticos , Modelos Teóricos , Humanos , Psicometria , Teorema de Bayes , PercepçãoRESUMO
The aim of the present paper is to collect evidence about validity of the cognitive structure proposed to solve the items of an arithmetic test using an cognitive diagnosis model (based on the Item Response Theory) called Least Squares Distance Model (LSDM). The test was applied to a sample of 382 students of 7th grade from five public high schools in Bogotá-Colombia. With this data the objective was addressed in three ways: first, the analysis of two statistical validity indices; second by a cross -validation of the LSDM results on attribute difficulties using other cognitive model (LLTM), and third, by comparing the LSDM results with the observed scores on individual attributes. The logical behavior of the probability curves for the five attributes under study provides important evidence for their overall validity. Additional specific evidences of validity are also presented in the results.
El objetivo del presente trabajo ha sido reunir evidencias sobre la validez de la estructura cognitiva propuesta para resolver los ítems de un test de aritmética, mediante la aplicación de un modelo de diagnóstico cognitivo basado en la Teoría de Respuesta al Item llamado Modelo de las Distancias Mínimo Cuadráticas (LSDM, por sus siglas en inglés). El test se aplicó a una muestra de 382 estudiantes de séptimo grado en cinco colegios públicos en Bogotá-Colombia. Usando estos datos el objetivo se abordó de tres maneras: en primer lugar se analizaron dos índices estadísticos de validez, en segundo lugar, se realizó una validación cruzada de los resultados del LSDM sobre las dificultades de atributos utilizando otro modelo cognitivo (LLTM) y en tercer lugar, se compararon los resultados del modelo con las puntuaciones observadas en atributos individuales. El comportamiento lógico de las curvas de probabilidad para los cinco atributos estudiados proporciona importante evidencia para su validez general. En los resultados se presentan también otras evidencias concretas de validez de la estructura propuesta.