Responses to Chess Problems and Knowledge Structures

Description

Held, Schrepp and Fries (1995) derive several knowledge structures for the representation of 92 responses to 16 chess problems. See Schrepp, Held and Albert (1999) for a detailed description of these problems.

Usage

data(chess)

Format

A list consisting of five components:

dst1
a state-by-problem indicator matrix representing the knowledge structure DST1.
dst3
the knowledge structure DST3.
dst4
the knowledge structure DST4.
N.R
a named integer vector. The names denote response patterns, the values denote their frequencies.
R
a person-by-problem indicator matrix representing the responses. Column names hdbgXX and grazYY identify responses collected in Heidelberg and Graz, respectively.

Note

The graphs of the precedence relations for DST1 and DST4 in Held et. al (1995) contain mistakes that have been corrected. See examples.

Source

Held, T., Schrepp, M., & Fries, S. (1995). Methoden zur Bestimmung von Wissensstrukturen – eine Vergleichsstudie. Zeitschrift fuer Experimentelle Psychologie, 42(2), 205–236.

References

Schrepp, M., Held, T., & Albert, D. (1999). Component-based construction of surmise relations for chess problems. In D. Albert & J. Lukas (Eds.), Knowledge spaces: Theories, empirical research, and applications (pp. 41–66). Mahwah, NJ: Erlbaum.

Examples

library("pks")

data(chess)
chess$dst1  # knowledge structure DST1
      s gs egs eegs cs gcs ts ges f gf gff ggff ggf ff tf tff
 [1,] 0  0   0    0  0   0  0   0 0  0   0    0   0  0  0   0
 [2,] 0  0   0    0  0   0  0   0 1  0   0    0   0  0  0   0
 [3,] 1  0   0    0  0   0  0   0 1  0   0    0   0  0  0   0
 [4,] 0  0   0    0  1   0  0   0 1  0   0    0   0  0  0   0
 [5,] 0  0   0    0  0   0  0   0 1  0   0    0   0  1  0   0
 [6,] 0  0   0    0  0   0  0   0 1  0   0    0   0  0  1   0
 [7,] 1  0   0    0  1   0  0   0 1  0   0    0   0  0  0   0
 [8,] 1  0   0    0  0   0  0   0 1  0   0    0   0  1  0   0
 [9,] 1  0   0    0  0   0  0   0 1  0   0    0   0  0  1   0
[10,] 0  0   0    0  1   0  0   0 1  0   0    0   0  1  0   0
[11,] 0  0   0    0  1   0  0   0 1  0   0    0   0  0  1   0
[12,] 0  0   0    0  0   0  0   0 1  0   0    0   0  1  1   0
[13,] 1  0   0    0  1   0  0   0 1  0   0    0   0  1  0   0
[14,] 1  0   0    0  1   0  0   0 1  0   0    0   0  0  1   0
[15,] 1  0   0    0  0   0  0   0 1  0   0    0   0  1  1   0
[16,] 0  0   0    0  1   0  0   0 1  0   0    0   0  1  1   0
[17,] 1  0   0    0  1   0  0   0 1  0   0    0   0  1  1   0
[18,] 1  0   0    0  0   0  1   0 1  0   0    0   0  1  1   0
[19,] 1  0   0    0  0   0  0   0 1  1   0    0   0  1  1   0
[20,] 1  0   0    0  0   0  0   0 1  0   0    0   0  1  1   1
[21,] 1  1   0    0  0   0  0   0 1  1   0    0   0  1  1   0
[22,] 1  0   0    0  1   0  1   0 1  0   0    0   0  1  1   0
[23,] 1  0   0    0  1   0  0   0 1  1   0    0   0  1  1   0
[24,] 1  0   0    0  1   0  0   0 1  0   0    0   0  1  1   1
[25,] 1  0   0    0  0   0  1   0 1  1   0    0   0  1  1   0
[26,] 1  0   0    0  0   0  1   0 1  0   0    0   0  1  1   1
[27,] 1  0   0    0  0   0  0   0 1  1   0    0   0  1  1   1
[28,] 1  1   0    0  1   0  0   0 1  1   0    0   0  1  1   0
[29,] 1  1   0    0  0   0  1   0 1  1   0    0   0  1  1   0
[30,] 1  1   0    0  0   0  0   0 1  1   0    0   0  1  1   1
[31,] 1  0   0    0  1   0  1   0 1  1   0    0   0  1  1   0
[32,] 1  0   0    0  1   0  1   0 1  0   0    0   0  1  1   1
[33,] 1  0   0    0  1   0  0   0 1  1   0    0   0  1  1   1
[34,] 1  0   0    0  0   0  1   0 1  1   0    0   0  1  1   1
[35,] 1  1   0    0  1   0  1   0 1  1   0    0   0  1  1   0
[36,] 1  1   0    0  1   0  0   0 1  1   0    0   0  1  1   1
[37,] 1  1   0    0  0   0  1   0 1  1   0    0   0  1  1   1
[38,] 1  0   0    0  1   0  1   0 1  1   0    0   0  1  1   1
[39,] 1  1   0    0  1   0  1   0 1  1   0    0   0  1  1   1
[40,] 1  1   0    0  0   0  1   1 1  1   0    0   0  1  1   1
[41,] 1  1   0    0  0   0  1   0 1  1   1    0   0  1  1   1
[42,] 1  1   0    0  1   0  1   1 1  1   0    0   0  1  1   1
[43,] 1  1   0    0  1   0  1   0 1  1   1    0   0  1  1   1
[44,] 1  1   0    0  0   0  1   1 1  1   1    0   0  1  1   1
[45,] 1  1   0    0  1   0  1   1 1  1   1    0   0  1  1   1
[46,] 1  1   1    1  0   0  1   1 1  1   1    0   0  1  1   1
[47,] 1  1   1    1  1   0  1   1 1  1   1    0   0  1  1   1
[48,] 1  1   1    1  0   0  1   1 1  1   1    1   0  1  1   1
[49,] 1  1   1    1  0   0  1   1 1  1   1    0   1  1  1   1
[50,] 1  1   1    1  1   1  1   1 1  1   1    0   0  1  1   1
[51,] 1  1   1    1  1   0  1   1 1  1   1    1   0  1  1   1
[52,] 1  1   1    1  1   0  1   1 1  1   1    0   1  1  1   1
[53,] 1  1   1    1  0   0  1   1 1  1   1    1   1  1  1   1
[54,] 1  1   1    1  1   1  1   1 1  1   1    1   0  1  1   1
[55,] 1  1   1    1  1   1  1   1 1  1   1    0   1  1  1   1
[56,] 1  1   1    1  1   0  1   1 1  1   1    1   1  1  1   1
[57,] 1  1   1    1  1   1  1   1 1  1   1    1   1  1  1   1
## Precedence relation (Held et al., 1995, p. 215) and knowledge space
P <- as.binmat(c("1111011101111001",   # s
               # "0100000000000000",   # gs   mistake in Abb. 3
                 "0111010100111000",   # gs   correction
                 "0011010000011000",   # egs
                 "0011010000011000",   # eegs
                 "0000110000000000",   # cs
                 "0000010000000000",   # gcs
                 "0011011100111000",   # ts
                 "0011010100011000",   # ges
                 "1111111111111111",   # f
                 "0111010101111000",   # gf
                 "0011010000111000",   # gff
                 "0000000000010000",   # ggff
                 "0000000000001000",   # ggf
                 "0111011101111101",   # ff
                 "0111011101111011",   # tf
                 "0011010100111001"),  # tff
               as.logical = TRUE)
dimnames(P) <- list("<" = colnames(chess$R), ">" = colnames(chess$R))
K <- rbind(0L, binary_closure(t(P)))
identical(sort(as.pattern(K)),
          sort(as.pattern(chess$dst1)))
[1] TRUE
blim(chess$dst1, chess$N.R)  # Tab. 1

Basic local independence models (BLIMs)

Number of knowledge states: 57
Number of response patterns: 69
Number of respondents: 92

Method: Minimum discrepancy
Number of iterations: 1
Goodness of fit (2 log likelihood ratio):
    G2(4) = 401.39, p = 0

Minimum discrepancy distribution (mean = 0.83696)
 0  1  2  3  4 
43 30 11  7  1 

Mean number of errors (total = 0.83696)
careless error    lucky guess 
      0.422102       0.414856 

Error and guessing parameters
         beta      eta
s    0.035971 0.044444
gs   0.056604 0.029412
egs  0.020134 0.024814
eegs 0.194631 0.044665
cs   0.044776 0.000001
gcs  0.000001 0.070968
ts   0.065217 0.086957
ges  0.101695 0.104000
f    0.049724 0.000001
gf   0.033473 0.009585
gff  0.098266 0.094987
ggff 0.000001 0.049107
ggf  0.000001 0.027027
ff   0.052239 0.020000
tf   0.092683 0.000001
tff  0.073469 0.042345