My main research goals lie in the advancement of multivariate psychometric models. Specifically, I have focused my research on a class of contemporary item response models called diagnostic classification models [DCMs]. In addition to methodological research, I collaborate with applied researchers to use DCMs and other psychometric models to answer critical questions in educational contexts.

Recent Research

Recently, I have focused my research on the development and application of longitudinal DCMs. Differing from classical test theory, item response theory, and student growth percentiles, which support norm-referenced interpretations of growth, longitudinal DCMs support categorical and criterion-referenced interpretations of growth. I have three recent articles that detail these developments:

Madison, M. J., & Bradshaw, L. P. (2018). Assessing growth in a diagnostic classification model framework.                                            Psychometrika, 83(4), 963-990.

Madison, M. J., & Bradshaw, L. P. (2018). Evaluating intervention effects in a diagnostic classification model framework.                     Journal of Educational Measurement, 55(1), 32-51. 

Madison, M. J. (in press). Reliably assessing growth with longitudinal diagnostic classification models. Educational                             Measurement: Issues and Practice.  

The Psychometrika article details the foundations of the Transition Diagnostic Classification Model (TDCM). The TDCM is a general longitudinal DCM that combines latent transition analysis (LTA) with the Log-linear Cognitive Diagnosis Model (LCDM; Henson, Templin, Willse, 2009). Via simulation, we show that the TDCM provides accurate and reliable classifications in a pre-test post-test setting, and is robust in the presence of item parameter drift. The Journal of Educational Measurement article extends the TDCM to multiple groups, thereby enabling the examination of group‐differential growth in attribute mastery and the evaluation of intervention effects. The utility of the multigroup TDCM was demonstrated in the evaluation of an innovative instructional method in mathematics education. The EM:IP article introduces reliability measures for longitudinal DCMs. Below, I've included an R script to compute the reliability measures described in the article. 

All three articles use Mplus to estimate the TDCM. Below, I provide an example with TDCM Mplus input and output files. To estimate the TDCM, I combined Mplus's LCDM capabilities, described in Templin and Hoffman (2013) with Mplus's LTA capabilities. I'm currently developing a video walkthough of this example. Soon, I will add more examples and video tutorials that include a Wald test for testing growth in attribute mastery, and I will add a multigroup example. But in the meantime, let me know if you have any questions or comments. 

Example 1: Single-group TDCM, three attributes, 24 simple-structure items with measurement invariance, N = 2000.  

Data File

Input File

Output File

Computing Reliability for TDCM Estimates

R script to compute reliability of TDCM growth estimates

Transition probabilities text file 

CDM Package Demonstration Files and Video

Video demonstration 

CDM demo.docx

​​CDM demo.R




Matthew J. Madison

Psychometrician and Statistician