variationalDCM vignette

Keiichiro Hijikata

2023-11-08

Introduction

variationalDCM is an R package that performs recently-developed variational Bayesian inference for diagnostic classification models (DCMs), which are a family of statistical models for collecting, analyzing, and reporting diagnostic information in Education and Psychology.

DCMs

Diagnostic assessment is a type of evaluation process that is used to diagnose the respondent’s current status of knowledge, skills, abilities, or other characteristics in a particular domain. These underlying traits are collectively called attributes in the literature of DCMs. By identifying the mastery status of each respondent, the diagnostic results can help tailor instruction, intervention, and support to address the specific needs of the respondent.

DCMs have a lot of sub-models and we introduce some models related to this package.

DINA model

The deterministic input noisy AND gate (DINA) model is representative of a non-compensatory model, which assumes that respondents must have mastered all the required attributes associated with a particular item to respond correctly.

DINO model

The deterministic input noisy OR gate (DINO) model is another well-known model. In contrast to the DINA model, the DINO model is one of the compensatory models, which assumes that obtaining a correct response to an item necessitates mastery of at least one of the relevant attributes.

saturated DCM

The saturated DCM is a saturated formulation of DCMs, which contain as many parameters as possible under the given item-attribute relationship. This generalized models include the DINA and DINO models as the most parsimonious special cases, as well as many other sub-models that differ in their degree of generalization and parsimony.

multiple choices DINA model

The multiple-choice format, in which respondents are required to select the most appropriate option from the given multiple options, is one of the most widely used formats of items in assessments. To provide a comprehensive and informative diagnostic assessment based on the responses for multiple-choice items, the multiple-choice DINA (MC-DINA) model was developed as an extension of the DINA model, which was originally for binary response data.

hidden Markov DCM

The hidden Markov DCM (HM-DCM) is an extended model to the longitudinal item response data to model the time course of learning multiple attributes. The HM-DCM allows researchers to model the transition in mastery statuses over time.

Functions

The below table summarizes the five functions that the variationalDCM package provides, corresponding models, and reference information for the papers that proposed their variational Bayesian estimation.

Function Name Functionality Reference
dina() the DINA model Yamaguchi & Okada (2020b)
dino() the DINO model slight modification of dina()
satu_dcm() the saturated DCM Yamaguchi & Okada (2020a)
mc_dina() the multiple-choice DINA model Yamaguchi (2020)
hm_dcm() the hidden Markov DCM Yamaguchi & Martinez (2023)

details of the above functions such as arguments and returns are given in .R script of each function.

References