TDCM (version 0.1.0)

oneplcdm: One-parameter log-linear cognitive diagnosis model.

Description

Function to estimate the 1-PLCDM (Madison et al., 2023; Maas et al., 2023).

Usage

oneplcdm(data, q.matrix, progress = TRUE)

Value

An object of class gdina with entries as indicated in the CDM package.

Arguments

data

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

q.matrix

a required \(I \times A\) matrix indicating which items measure which attributes.

progress

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

Details

Estimates the single-attribute and multi-attribute 1-PLCDM described in Madison et al. (2023). Example shows that attribute subscores are sufficient statistics for classifications.

References

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.

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.

Madison, M.J., Chung, S., Kim, J., & Bradshaw, L. (2023). Approaches to estimating longitudinal diagnostic classification models. Behaviormetrika.

Madison, M.J., Wind, S., Maas, L., Yamaguchi, K. & Haab, S. (2023). A one-parameter diagnostic classification model with familiar measurement properties. Arxiv.

Maas, L., Madison, M. J., & Brinkhuis, M. J. (2024). Properties and performance of the one-parameter log-linear cognitive diagnosis model. Frontiers.

Examples

# \donttest{
## Example 1: A = 4
data(data.tdcm05)
dat5 <- data.tdcm05$data
qmat5 <- data.tdcm05$q.matrix

# calibrate LCDM
m1 <- CDM::gdina(dat5, qmat5, linkfct = "logit", method = "ML")

# calibrate 1-PLCDM
m2 <- TDCM::oneplcdm(dat5, qmat5)
summary(m2)
#demonstrate 1-PLCDM sum score sufficiency for each attribute
subscores <- cbind(rowSums(dat5[, 1:5]), rowSums(dat5[, 6:10]),
rowSums(dat5[, 11:15]), rowSums(dat5[, 16:20]))
colnames(subscores) <- c("Att1", "Att2", "Att3", "Att4")
proficiency <- cbind(m2$pattern[, 6] > .50, m2$pattern[, 7] > .50,
m2$pattern[, 8] > .50, m2$pattern[, 9] > .5) * 1
table(subscores[, 1], proficiency[, 1])
table(subscores[, 2], proficiency[, 2])
table(subscores[, 3], proficiency[, 3])
table(subscores[, 4], proficiency[, 4])

#plot sum score sufficiency for each attribute
posterior1pl <- m2$pattern[, 6:9]
posteriorlcdm <- m1$pattern[, 6:9]
oldpar <- par(mfrow = c(2, 2))
for (i in 1:4) {
 plot(subscores[, i], posteriorlcdm[, i], pch = 19,las = 1, cex.lab = 1.5,
 xlab = "Sum Scores", ylab = "P(proficiency)",
 cex.main = 1.5, col = "grey", xaxt = "n", yaxt = "n", cex = 1.2,
 main = paste("Attribute ", i, sep = ""))
 graphics::axis(side = 1, at = c(0, 1, 2, 3, 4, 5), )
 graphics::axis(side = 2, at = c(0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.0), las = 1)
 graphics::points(subscores[, i], posterior1pl[, i], col = "black", pch = 18, cex = 1.5)
 graphics::abline(a = .50, b = 0, col = "red")
 graphics::legend("bottomright", c("1-PLCDM", "LCDM"), col = c("black", "grey"),
 pch = c(18 ,19), box.lwd = 0, box.col = "white", bty = 'n')
}
par(oldpar)
# }