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")