Help for package TDCM

Title:

The Transition Diagnostic Classification Model Framework

Version:

0.3.0

Description:

Estimate the transition diagnostic classification model (TDCM) described in Madison & Bradshaw (2018) <doi:10.1007/s11336-018-9638-5>, a longitudinal extension of the log-linear cognitive diagnosis model (LCDM) in Henson, Templin & Willse (2009) <doi:10.1007/s11336-008-9089-5>. As the LCDM subsumes many other diagnostic classification models (DCMs), many other DCMs can be estimated longitudinally via the TDCM. The 'TDCM' package includes functions to estimate the single-group and multigroup TDCM, summarize results of interest including item parameters, growth proportions, transition probabilities, transitional reliability, attribute correlations, model fit, and growth plots.

License:

MIT + file LICENSE

URL:

https://cotterell.github.io/tdcm/, https://github.com/cotterell/tdcm

BugReports:

https://github.com/cotterell/tdcm/issues

Encoding:

UTF-8

Language:

en-US

LazyData:

true

Depends:

R (≥ 4.2.0)

Suggests:

devtools, knitr, lintr, MASS, rmarkdown, ROI, roxygen2, rsconnect, styler (≥ 1.10.2), testthat (≥ 3.0.0), tinytex, V8

Config/testthat/edition:

Config/Needs/website:

pkgdown

SystemRequirements:

pandoc

VignetteBuilder:

knitr

RoxygenNote:

7.3.3

Imports:

CDM, gtools, polycor, stringr

NeedsCompilation:

Packaged:

2026-04-22 21:04:45 UTC; mepcott

Author:

Matthew J. Madison

[aut, cph], Sergio Haab [aut], Minjeong Jeon [aut, cph], Constanza Mardones-Segovia [aut, cph], Michael E. Cotterell

[aut, cre, cph], University of Georgia [cph] (The content and opinions expressed in this material do not necessarily reflect the views of nor are they endorsed by the University of Georgia or the University System of Georgia.), Institute of Education Sciences [fnd] (This work is supported by the U.S. Department of Education Institute of Education Sciences under IES Award Number R305D220020.), National Science Foundation [fnd] (This work is supported by the National Science Foundation under NSF Award Number 1921373.)

Maintainer:

Michael E. Cotterell <mepcott@uga.edu>

Repository:

CRAN

Date/Publication:

2026-04-22 21:20:02 UTC

The Transition Diagnostic Classification Model Framework

Description

The R package TDCM enables longitudinal diagnostic classification model (DCM) analyses within the transition diagnostic classification model (TDCM) framework.

Details

Diagnostic classification models (DCMs) are psychometric models designed to classify examinees according to their proficiency on a set of categorical latent traits, known as attributes. Longitudinal DCMs have been developed as psychometric options for modeling changes in attribute proficiency over time.

The TDCM implements estimation of the transition DCM (TDCM; Madison & Bradshaw, 2018a), a longitudinal extension of the log-linear cognitive diagnosis model (LCDM; Henson, Templin, & Willse, 2009). As the LCDM subsumes many other DCMs, many other DCMs can be estimated longitudinally via the TDCM. The package includes functions to estimate the single-group and multigroup TDCM, summarize results of interest including item parameters, growth proportions, transition probabilities, transitional reliability, attribute correlations, model fit, and growth plots.

For more details and examples, see vignette("TDCM", package = "TDCM").

Author(s)

The TDCM package was created by:

Matthew J. Madison, University of Georgia, mjmadison@uga.edu
Sergio Haab, University of Iowa, sergio-haab@uiowa.edu
Constanza Mardones-Segovia, University of Georgia, constanza.mardonessegovia@uga.edu
Minjeong Jeon, University of California - Los Angeles, mjjeon@ucla.edu
Michael E. Cotterell, University of Georgia, mepcott@uga.edu

More information about the TDCM package authors, copyright holders, funders, etc. is available in the package's DESCRIPTION file. You can see this information by executing utils::packageDescription("TDCM").

References

de la Torre, J. (2011). The Generalized DINA model framework. Psychometrika, 76, 179–199. doi:10.1007/s11336-011-9207-7.

George, A. C., Robitzsch, A., Kiefer, T., Gross, J., & Ünlü , A. (2016). The R package CDM for cognitive diagnosis models. Journal of Statistical Software,74(2), 1-24. doi:10.18637/jss.v074.i02

Henson, R., Templin, J., & Willse, J. (2009). Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74, 191-21. doi:10.1007/s11336-008-9089-5.

Johnson, M. S., & Sinharay, S. (2020). The reliability of the posterior probability of skill attainment in diagnostic classification models. Journal of Educational Measurement, 47(1), 5–31. doi:10.3102/1076998619864550.

Kaya, Y., & Leite, W. (2017). Assessing change in latent skills across time With longitudinal cognitive diagnosis modeling: An evaluation of model performance. Educational and Psychological Measurement, 77(3), 369–388. doi:10.1177/0013164416659314.

Li, F., Cohen, A., Bottge, B., & Templin, J. (2015). A latent transition analysis model for assessing change in cognitive skills. Educational and Psychological Measurement, 76(2), 181–204. doi:10.1177/0013164415588946.

Madison, M. J. (2019). Reliably assessing growth with longitudinal diagnostic classification models. Educational Measurement: Issues and Practice, 38(2), 68-78. doi:10.1111/emip.12243.

Madison, M. J., & Bradshaw, L. (2018a). Assessing growth in a diagnostic classification model framework. Psychometrika, 83(4), 963-990. doi:10.1007/s11336-018-9638-5.

Madison, M. J., & Bradshaw, L. (2018b). Evaluating intervention effects in a diagnostic classification model framework. Journal of Educational Measurement, 55(1), 32-51. doi:10.1111/jedm.12162.

Madison, M.J., Chung, S., Kim, J., & Bradshaw, L.P. (2024) Approaches to estimating longitudinal diagnostic classification models. Behaviormetrika, 51(7), 7-19. doi:10.1007/s41237-023-00202-5.

Madison, M. J., Jeon, M., Cotterell, M., Haab, S., & Zor, S. (2025). TDCM: An R package for estimating longitudinal diagnostic classification models. Multivariate Behavioral Research, 1–10. doi:10.1080/00273171.2025.2453454.

Ravand, H., Effatpanah, F., Kunina-Habenicht, O., & Madison, M. J. (2025). A didactic illustration of writing skill growth through a longitudinal diagnostic classification model. Frontiers in Psychology. doi:10.3389/fpsyg.2024.1521808.

Rupp, A. A., Templin, J., & Henson, R. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: Guilford. ISBN: 9781606235430.

Schellman, M., & Madison, M. J. (2024). Estimating the reliability of skill transition in longitudinal DCMs. Journal of Educational and Behavioral Statistics.doi:10.3102/10769986241256032.

Templin, J., & Bradshaw, L. (2013). Measuring the reliability of diagnostic classification model examinee estimates. Journal of Classification, 30, 251-275. doi:10.1007/s00357-013-9129-4.

Wang. S., Yang. Y., Culpepper, S. A., & Douglas, J. (2018). Tracking skill acquisition with cognitive diagnosis models: A higher-order, hidden Markov model With covariates. Journal of Educational and Behavioral Statistics, 43(1), 57-87. doi:10.3102/1076998617719727.

Several data sets for the TDCM package.

Description

Several data sets for the TDCM package.

Usage

data.tdcm01

data.tdcm02

data.tdcm03

data.tdcm04

data.tdcm05

Format

data.tdcm01 is a simulated dataset with two time points, four attributes, twenty items, one group of size 1000, and a single Q-matrix. The format is a list of two:

data: a data frame of binary item responses
q.matrix: a data frame specifying the Q-matrix

data.tdcm02 is a simulated dataset with three time points, two attributes, ten items, one group of size 2500, and a single Q-matrix. The format is a list of two:

data: a data frame of binary item responses
q.matrix: a data frame specifying the Q-matrix

data.tdcm03 is a simulated dataset with three time points, two attributes, one group of size 1500, and three different ten-item Q-matrices for each time point. Anchor items are specified as items 1/11/21 and items 14/24. The format is a list of five:

data: a data frame of binary item responses
q.matrix.1: a data frame specifying the Q-matrix for the first time point
q.matrix.2: a data frame specifying the Q-matrix for the second time point
q.matrix.3: a data frame specifying the Q-matrix for the third time point
q.matrix.stacked: data frame specifying the combined Q-matrix for all time points

data.tdcm04 is a simulated dataset with two time points, four attributes, twenty items, two group of size 800 and 900, respectively, and a single Q-matrix. The format is a list of three:

data: a data frame of binary item responses
q.matrix: a data frame specifying the Q-matrix
groups: a vector specifying the examinee group membership

data.tdcm05 is a simulated dataset with one time point, four attributes, and twenty items. For use with the 1-PLCDM. The format is a list of two:

data: a data frame of binary item responses
q.matrix: a data frame specifying the Q-matrix

Examples



#############################
## Example 1: T = 2, A = 4 ##
data(data.tdcm01, package = "TDCM")
data <- data.tdcm01$data
q.matrix <- data.tdcm01$q.matrix
model <- TDCM::tdcm(data, q.matrix, num.time.points = 2)
results <- TDCM::tdcm.summary(model)
results$item.parameters
results$growth.effects

#############################
## Example 3: T = 3, A = 2 ##
data <- data.tdcm03$data
q1 <- data.tdcm03$q.matrix.1
q2 <- data.tdcm03$q.matrix.2
q3 <- data.tdcm03$q.matrix.3
q <- data.tdcm03$q.matrix.stacked

#TDCM with anchor items constrained
m1 <- tdcm(data, q, num.time.points = 3, num.q.matrix = 3,
anchor = c(1,11,1,21,14,24), num.items = c(10,10,10))

#TDCM without anchor items
m2 <- tdcm(data, q, num.time.points = 3, num.q.matrix = 3, num.items = c(10,10,10))

#Compare models to assess measurement invariance
tdcm.compare(m1, m2)

#Summarize model 1
r1 = tdcm.summary(m1, transition.option = 3)
r1$item.parameters
r1$growth
r1$growth.effects

Estimating item influence measures.

Description

Function to estimate estimate item influence measures. Code adapted from (Jurich & Madison, 2023). This function is not available for longitudinal DCMs.

Usage

item.influence(model, data, fullcorrelation = FALSE, progress = TRUE)

Arguments

model

a previously calibrated model; an object of class gdina.

data

a required N \times I matrix. Binary item responses are in the columns.

fullcorrelation

optional logical argument indicating a full or reduced response-classification correlation matrix.

progress

An optional logical indicating whether the function should print the progress of estimation.

Details

For DCMs, item influence quantifies how much an item impacts classifications. Given an estimated DCM and item response data, this function estimates five item influence measures, including item pull, item override, proportion of attribute information, response-classification correlation (corr1), and response-posterior correlation (corr2).

Value

A list containing several item influence measures.

Note

Currently, this function currently only runs on DCMs estimated at a single time point. It will not run properly for TDCM objects.

References

Jurich, D. & Madison, M. J. (2023). Measuring item influence for diagnostic classification models. Educational Assessment.

Examples


## Item influence illustration
#load data (simulated based on Jurich and Bradshaw (2014))
qmatrix <- CDM::data.sda6$q.matrix
responses <- CDM::data.sda6$data

#Estimate the full LCDM
model1 <- CDM::gdina(responses, qmatrix, linkfct = "logit", method = "ML")

#Estimate item influence measures
influence <- TDCM::item.influence(model1, responses)

#Summarize influence statistics
influence$Pull #item pull
influence$Override #item override
influence$Information #proportion of attribute information
influence$Correlation1 #correlation of responses and classifications
influence$Correlation2 #correlation of responses and posterior probabilities

Estimating the multigroup transition diagnostic classification model (TDCM)

Description

mg.tdcm() estimates the Transition Diagnostic Classification Model for scenarios involving multiple groups (e.g., control and treatment group; Madison & Bradshaw, 2018b). Similar to tdcm(), this function supports the estimation of various DCMs by allowing different rule specifications via the rule option and link functions via the linkfct option,with LCDM as the default rule and link function. The rule can be modified to estimate the DINA model, DINO model, CRUM (i.e., ACDM, or main effects model), or reduced interaction versions of the LCDM. Additionally, the link function can be adjusted to specify the GDINA model.

Usage

mg.tdcm(
  data,
  q.matrix,
  num.time.points,
  rule = "LCDM",
  linkfct = "logit",
  groups,
  forget.att = c(),
  group.invariance = TRUE,
  time.invariance = TRUE,
  progress = TRUE
)

Arguments

data

A required N \times T \times I matrix or data.frame where rows correspond to N examinees and columns represent the binary item responses across T time points and I items.

q.matrix

A required I \times A matrix indicating which items measure which attributes. Currently, the function only accepts a single Q-matrix.

num.time.points

A required integer \ge 2 specifying the number of time points (i.e., measurement occasions).

rule

A string or a vector indicating the specific DCM to be employed. A vector of supported rule values is provided by tdcm.rules. Currently accepted values are: "LCDM", "DINA", "DINO", "CRUM", "RRUM", "LCDM1" for the LCDM with only main effects, "LCDM2" for the LCDM with two-way interactions, "LCDM3", and so on. If rule is supplied as a single string, then that DCM will be assumed for each item. If entered as a vector, a rule can be specified for each item. The vector must have length equal to the total number of items across all time points.

linkfct

A string or a vector indicating the LCDM link function. Currently accepts "logit" (default) to estimate the LCDM, "identity" to estimate the GDINA model, and "log" link function to estimate the reduced reparameterized unified model (RRUM). The vector must have length equal to the total number of items across all time points.

groups

A required vector of integer group identifiers for multiple group estimation.

forget.att

An optional vector allowing for constraining of individual attribute proficiency loss, or forgetting. The default allows forgetting for each measured attribute (e.g., P(1 \rightarrow 0) \neq 0). See tdcm for more detailed information.

group.invariance

logical argument. If TRUE (default), item parameters are assumed to be equal for all groups. If FALSE, item parameters are not assumed to be equal for all groups.

time.invariance

logical argument. If TRUE (default), item parameters are assumed to be equal for all time points. If FALSE, item parameters are not assumed to be equal for all time points.

progress

logical argument. If FALSE, the function will print the progress of estimation. If TRUE (default), no progress information is printed.

Details

Multigroup Transition Diagnostic Classification Model (Multigroup TDCM)

Multigroup TDCM is a confirmatory latent transition model that measures examinees' growth or decline in attribute mastery over time among groups (Madison & Bradshaw, 2018b). In this model, the probability of the item response vector X_e is conditioned on observed groups membership G:

P(X_e = x_e|G=g) = \sum_{c_1=1}^{C} \sum_{c_2=1}^{C} \cdots \sum_{c_T=1}^{C} v_{c_1|g} \tau_{c_2 | c_{1},g} \tau_{c_3 | c_{2},g} \cdots \tau_{c_T | c_{T-1},g} \prod_{t=1}^{T} \prod_{i=1}^{I} \pi_{i c_{t,g}}^{x_{eit}} (1 - \pi_{i c_{t,g}})^{1 - x_{eit}},

where:

v_{c_1|g} represents the probability of belonging to attribute profile c at time 1 given the observed group g.
\tau_{c_t | c_{T-1},g} represents the probability of transitioning attribute profiles from time point t-1 to time point t.
\pi_{ic_{t,g}} is the item response function, which models the probability of answering item i correctly at time t given attribute profile c and observed group g.

Therefore, if the study purpose is to assess growth between a treatment and control group in a pre- and post-test design, the probability of the item response vector reduces to:

P(X_e = x_e|G=g) = \sum_{c_1=1}^{C} \sum_{c_2=1}^{C} v_{c_1|g} \tau_{c_2 | c_{1,g}} \prod_{t=1}^{2} \prod_{i=1}^{I} \pi_{i c_{t,g}}^{x_{eit}} (1 - \pi_{i c_{t,g}})^{1 - x_{eit}}.

Accounting for Measurement Invariance

Measurement invariance indicates whether the item response function remains constant over time points (time invariance) or across groups (group invariance). Note that regardless of the assumed invariance, attribute mastery transitions can still be compared across time and groups.

Depending on the assumed constrained, one of the four measurement invariance conditions can be applied:

Consider an experiment design with a treatment and control group.

a) No time Invariance across time or group invariance assumed

If neither time nor group invariance is assumed, each item has a different response function over time and across groups. Thus, the probability of the item response function remains unchanged.

P(X_e = x_e|G=g) = \sum_{c_1=1}^{C} \sum_{c_2=1}^{C} v_{c_1|g} \tau_{c_2 | c_{1}, g} \prod_{t=1}^{2} \prod_{i=1}^{I} \pi_{i c_{t,g}}^{x_{eit}} (1 - \pi_{i c_{t,g}})^{1 - x_{eit}}.

b) No time Invariance across time assumed but group invariance assumed

If time invariance is not assumed but group invariance is, each item has a different response function over time. Thus, the probability of the item response function only depends on t.

P(X_e = x_e|G=g) = \sum_{c_1=1}^{C} \sum_{c_2=1}^{C} v_{c_1|g} \tau_{c_2 | c_{1}, g} \prod_{t=1}^{2} \prod_{i=1}^{I} \pi_{i c_{t}}^{x_{eit}} (1 - \pi_{i c_{t}})^{1 - x_{eit}}.

c) Time Invariance across time assumed but not group invariance

If time invariance is assumed but group invariance is not, each item has a different response function across groups. Thus, the probability of the item response function only depends on g.

P(X_e = x_e|G=g) = \sum_{c_1=1}^{C} \sum_{c_2=1}^{C} v_{c_1|g} \tau_{c_2 | c_{1}, g} \prod_{t=1}^{2} \prod_{i=1}^{I} \pi_{i c_{g}}^{x_{eit}} (1 - \pi_{i c_{g}})^{1 - x_{eit}}.

d) Time Invariance across time and group invariance assumed

Finally, when time and group invariance are assumed, each item has the same item response function over time and groups, reducing the measurement model to an LCDM.

P(X_e = x_e|G=g) = \sum_{c_1=1}^{C} \sum_{c_2=1}^{C} v_{c_1|g} \tau_{c_2 | c_{1,g}} \prod_{t=1}^{2} \prod_{i=1}^{I} \pi_{i c}^{x_{eit}} (1 - \pi_{i c})^{1 - x_{eit}}.

Value

An object of class gdina with entries as indicated in the CDM package. For the TDCM-specific results (e.g., growth, transitions), use TDCM::mg.tdcm.summary().