Responses and Knowledge Structures from Heller and Wickelmaier (2013)

Knowledge structures and 200 artificial responses to four problems are used to illustrate parameter estimation in Heller and Wickelmaier (2013).

data(endm)

Format

A list consisting of three components:

K

a state-by-problem indicator matrix representing the true knowledge structure that underlies the model that generated the data.

K2

a slightly misspecified knowledge structure.

N.R

a named numeric vector. The names denote response patterns, the values denote their frequencies.

Source

Heller, J., & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42, 49–56. doi:10.1016/j.endm.2013.05.145

Examples

data(endm)
endm$K    # true knowledge structure
#>      a b c d
#> 0000 0 0 0 0
#> 0110 0 1 1 0
#> 0101 0 1 0 1
#> 1110 1 1 1 0
#> 1101 1 1 0 1
#> 1011 1 0 1 1
#> 1111 1 1 1 1
endm$K2   # misspecified knowledge structure
#>      a b c d
#> 0000 0 0 0 0
#> 0110 0 1 1 0
#> 1110 1 1 1 0
#> 1101 1 1 0 1
#> 1011 1 0 1 1
#> 1111 1 1 1 1
endm$N.R  # response patterns
#> 0000 1000 0100 0010 0001 1100 1010 1001 0110 0101 0011 1110 1101 1011 0111 1111 
#>   15    4    6    4    5    2    3    4   18   22    2   39   37   12    7   20 

## Generate data from BLIM based on K
blim0 <- list(
     P.K = setNames(c(.1, .15, .15, .2, .2, .1, .1), as.pattern(endm$K)),
    beta = rep(.1, 4),
     eta = rep(.1, 4),
       K = endm$K,
  ntotal = 200)
class(blim0) <- "blim"
simulate(blim0)
#> 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 
#>   13    3    6    4    6   23   18    7    3    2    8   12    8   33   32   22 

## Fit BLIM based on K2
blim1 <- blim(endm$K2, endm$N.R, "MD")