oneplcdm {TDCM}

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)

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.

Value

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

Note

Currently, this model cannot be embedded within the TDCM via the rule argument.

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

## 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)