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)
oneplcdm(data, q.matrix, progress = TRUE)
Arguments
data |
a required N×I matrix. Binary item responses are in the columns.
|
q.matrix |
a required I×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. (2024).
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., Wind, S., Maas, L., Yamaguchi, K. & Haab, S. (2024). A one-parameter diagnostic
classification model with familiar measurement properties. Journal of Educational Measurement.
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)
data(data.tdcm05)
dat5 <- data.tdcm05$data
qmat5 <- data.tdcm05$q.matrix
m1 <- CDM::gdina(dat5, qmat5, linkfct = "logit", method = "ML")
m2 <- TDCM::oneplcdm(dat5, qmat5)
summary(m2)
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])
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)
,
Sergio Haab [aut],
Minjeong Jeon [aut, cph],
Michael E. Cotterell [aut, cre, cph]