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Builds a diagnostic classification (cognitive diagnosis) model: several binary latent attributes (latent categorical vertices) govern, through a Q-matrix, the observed item responses at the crossing of person and item plates. Item parameters are fixed unknowns in the item plate. This combines a latent categorical structure with the crossed-plate measurement form, a structure no single classic convention can draw.

Usage

umg_dcm(Q = NULL, attr_cov = TRUE, plate_index = "i = 1, ..., N")

Arguments

Q

A K-by-J 0/1 Q-matrix: rows are attributes, columns are items; Q[k, j] = 1 if item j requires attribute k. Note that this is the transpose of the J-by-K (items-by-attributes) layout used by, for example, the GDINA and CDM packages; a warning is issued when the supplied matrix has at least as many rows as columns, the usual sign of the transposed convention. Because the diagram shows the generic response vertex u_ij rather than per-item vertices, the Q-matrix is collapsed to the attribute level: attribute k points at u when at least one item requires it. Defaults to a 3-attribute, 6-item example.

attr_cov

Logical; draw pairwise covariance edges among the latent attributes (default TRUE), reflecting the saturated (or higher-order) attribute distribution that standard DCMs assume. Set to FALSE to draw independent attributes.

plate_index

Index label for the person plate.

Value

An object of class umg.

Examples

Q <- rbind(c(1,1,0,0,1,0), c(0,1,1,0,0,1), c(0,0,1,1,1,1))
plot(umg_dcm(Q))