This function can be used to generate hierarchical attributes structures, and to provide prior joint attribute distribution with hierarchical structures.
att.structure(hierarchy.list = NULL, K, Q, att.prob = "uniform")a list specifying the hierarchical structure between attributes. Each
element in this list specifies a DIRECT prerequisite relation between two or more attributes.
See example for more information.
the number of attributes involved in the assessment
Q-matrix
How are the probabilities for latent classes simulated? It can be "random" or "uniform".
att.str reduced latent classes under the specified hierarchical structure
impossible.latentclass impossible latent classes under the specified hierarchical structure
att.prob probabilities for all latent classes; 0 for impossible latent classes
if (FALSE) {
#################
#
# Leighton et al. (2004, p.210)
#
##################
# linear structure A1->A2->A3->A4->A5->A6
K <- 6
linear=list(c(1,2),c(2,3),c(3,4),c(4,5),c(5,6))
att.structure(linear,K)
# convergent structure A1->A2->A3->A5->A6;A1->A2->A4->A5->A6
K <- 6
converg <- list(c(1,2),c(2,3),c(2,4),
c(3,4,5), #this is how to show that either A3 or A4 is a prerequisite to A5
c(5,6))
att.structure(converg,K)
# convergent structure [the difference between this one and the previous one is that
# A3 and A4 are both needed in order to master A5]
K <- 6
converg2 <- list(c(1,2),c(2,3),c(2,4),
c(3,5), #this is how to specify that both A3 and A4 are needed for A5
c(4,5), #this is how to specify that both A3 and A4 are needed for A5
c(5,6))
att.structure(converg2,K)
# divergent structure A1->A2->A3;A1->A4->A5;A1->A4->A6
diverg <- list(c(1,2),
c(2,3),
c(1,4),
c(4,5),
c(4,6))
att.structure(diverg,K)
# unstructured A1->A2;A1->A3;A1->A4;A1->A5;A1->A6
unstru <- list(c(1,2),c(1,3),c(1,4),c(1,5),c(1,6))
att.structure(unstru,K)
## See Example 4 and 5 in GDINA function
}