Sparse Latent Class Model for Cognitive Diagnosis (SLCM)
Description
Performs the Gibbs sampling routine for a sparse latent class model as described in Chen et al. (2020) <doi: 10.1007/s11336-019-09693-2>
Usage
slcm(
y,
k,
burnin = 1000L,
chain_length = 10000L,
psi_invj = c(1, rep(2, 2^k - 1)),
m0 = 0,
bq = 1
)
Arguments
y
|
Item Matrix |
k
|
Dimension to estimate for Q matrix |
burnin
|
Amount of Draws to Burn |
chain_length
|
Number of Iterations for chain. |
psi_invj, m0, bq
|
Additional tuning parameters. |
Details
The estimates list contains the mean information from the sampling procedure. Meanwhile, the chain list contains full MCMC values. Lastly, the details list provides information regarding the estimation call.
Value
An slcm object containing three named lists:
-
estimates-
beta: Average beta coefficients -
theta: Average theta coefficients -
delta: Average activeness of coefficients -
class: Average class membership -
pi: Average attribute class probability. -
omega: Average omega -
q: Average activeness of Q matrix entries based on heuristic transformation. -
m2ll: Average negative two times log-likelihood
-
-
chain-
theta: theta coefficients iterations -
beta: beta coefficients iterations -
class: class membership iterations -
pi: attribute class probability iterations -
omega: omega iterations -
m2ll: Negative two times log-likelihood iterations
-
-
details-
n: Number of Subjects -
j: Number of Items -
k: Number of Traits -
l1: Slab parameter -
m0,bq: Additional tuning parameters -
burnin: Number of Iterations to discard -
chain_length: Number of Iterations to keep -
runtime: Duration of model run inside of the C++ code. (Does not include summarization of MCMC chain.) -
package_version: Version of the package the SLCM model was fit with. -
date_time: Date and Time the model was fit.
-
Examples
library(slcm)
# Use a demo data set from the paper
data("items_matrix_reasoning", package = "edmdata")
burnin = 50 # Set for demonstration purposes, increase to at least 1,000 in practice.
chain_length = 100 # Set for demonstration purposes, increase to at least 10,000 in practice.
model_reasoning = slcm(items_matrix_reasoning, k = 4,
burnin = burnin, chain_length = chain_length)
print(model_reasoning)
Model Details:
- Observations (n): 400
- Items (j): 25
- Attributes (k): 4
- Runtime: 0.294
- Date: 2024-06-14 01:09:54.345644
- Package Version: 0.1.0
Chain properties:
- Burn in: 50
- Chain Length: 100
- Total Iterations: 150
Hyperparameter Details:
- m0: 400
- bq: 25
- l1:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] 1 2 2 2 2 2 2 2 2 2 2 2
[,13] [,14] [,15] [,16]
[1,] 2 2 2 2
Beta Coefficients:
B_0000 B_0001 B_0010 B_0011 B_0100 B_0101 B_0110
Item1 0.26461 1.85519 0.01551 0.00000 1.30027 0.00000 0.00000
Item2 0.52241 0.94994 0.00911 0.00000 1.24358 0.00000 0.00000
Item3 -0.08369 0.71393 0.01876 0.00000 0.93911 0.00000 0.00000
Item4 -0.95735 1.05575 0.44959 0.62507 0.08793 0.00000 0.00000
Item5 0.09590 0.74075 0.03248 0.00000 0.32075 0.00000 0.00000
Item6 -0.33117 1.14116 0.25630 0.51433 0.32420 0.00000 0.00000
Item7 -1.30225 0.18436 0.20987 0.00000 0.27076 0.29983 0.00000
Item8 -0.81947 0.35760 0.07715 0.00000 0.88605 0.00000 0.00000
Item9 0.41146 0.10650 0.13358 0.00000 0.67930 0.00000 0.23657
Item10 -0.98080 0.22379 0.34943 0.00000 1.16013 0.00000 0.00000
Item11 -0.38404 0.10237 0.06622 0.37789 0.79333 0.27238 0.52411
Item12 -1.13256 1.15886 0.04215 0.40463 0.03892 0.00000 0.00000
Item13 -1.08360 0.33101 0.37732 0.36036 0.16947 0.00000 0.00000
Item14 -1.15924 0.66064 0.43554 0.00000 1.03098 0.00000 0.00000
Item15 -0.90107 0.76546 0.42938 0.00000 1.46054 0.00000 0.00000
Item16 -0.68069 0.81902 0.06212 0.00000 1.88412 0.00000 0.00000
Item17 -1.31510 0.46214 0.70879 0.00000 0.09426 0.00000 0.61828
Item18 -1.96699 0.66817 1.17070 0.00000 0.91820 0.00000 0.00000
Item19 -1.09393 0.19039 0.98152 0.00000 1.17178 0.00000 0.00000
Item20 -1.51430 0.18138 0.68318 0.00000 0.89147 0.00000 0.00000
Item21 -1.63514 0.08250 0.11030 0.20641 0.33172 0.00000 0.00000
Item22 -1.83399 0.13639 0.33481 0.43933 0.19468 0.00000 0.00000
Item23 -1.16816 0.26479 0.11697 0.00000 0.88549 0.00000 0.30526
Item24 -1.31878 0.46969 1.36786 0.00000 0.80982 0.34477 0.00000
Item25 -0.30039 0.11887 0.15991 0.73650 0.69557 0.08755 0.43455
B_0111 B_1000 B_1001 B_1010 B_1011 B_1100 B_1101
Item1 0.00000 0.11702 0.00000 0.00000 0.00000 0.00000 0.00000
Item2 0.00000 0.06114 0.00000 0.00000 0.00000 0.00000 0.00000
Item3 0.00000 0.13846 0.00000 0.00000 0.00000 0.00000 0.00000
Item4 0.00000 0.67110 0.00000 0.00000 0.00000 0.00000 0.00000
Item5 0.00000 0.15448 0.00000 0.00000 0.00000 0.00000 0.00000
Item6 0.00000 0.31951 0.69434 0.30581 0.39519 0.00000 0.00000
Item7 0.00000 0.54547 0.00000 0.00000 0.00000 0.00000 0.00000
Item8 0.00000 1.20160 0.00000 0.00000 0.00000 0.00000 0.00000
Item9 0.00000 0.17019 0.00000 0.57586 0.00000 0.14731 0.00000
Item10 0.00000 0.84085 0.00000 0.00000 0.00000 0.00000 0.00000
Item11 0.38470 0.55809 0.00000 0.00000 0.00000 0.00000 0.00000
Item12 0.00000 1.12502 0.00000 0.00000 0.00000 0.00000 0.00000
Item13 0.00000 0.26543 0.94511 0.43879 0.51062 0.00000 0.00000
Item14 0.00000 0.98425 0.00000 0.00000 0.00000 0.00000 0.00000
Item15 0.00000 0.61470 0.00000 0.00000 0.00000 0.00000 0.00000
Item16 0.00000 0.12871 0.00000 0.00000 0.00000 0.00000 0.00000
Item17 0.00000 0.43279 0.00000 0.00000 0.00000 0.00000 0.00000
Item18 0.00000 0.14441 0.00000 0.00000 0.00000 0.00000 0.00000
Item19 0.00000 0.04506 0.71711 0.00000 0.00000 0.00000 0.00000
Item20 0.00000 0.03934 0.00000 0.00000 0.00000 0.00000 0.00000
Item21 0.00000 0.06780 0.12683 0.16430 0.40293 0.00000 0.00000
Item22 0.00000 0.11764 0.20380 0.43668 0.32933 0.00000 0.00000
Item23 0.00000 0.19111 0.00000 0.51972 0.00000 0.46495 0.00000
Item24 0.00000 0.14193 0.00000 0.00000 0.00000 0.00000 0.00000
Item25 0.15332 0.14647 0.17545 0.54895 0.28199 0.21980 0.01524
B_1110 B_1111
Item1 0.00000 0.00000
Item2 0.00000 0.00000
Item3 0.00000 0.00000
Item4 0.00000 0.00000
Item5 0.00000 0.00000
Item6 0.00000 0.00000
Item7 0.00000 0.00000
Item8 0.00000 0.00000
Item9 0.64524 0.00000
Item10 0.00000 0.00000
Item11 0.00000 0.00000
Item12 0.00000 0.00000
Item13 0.00000 0.00000
Item14 0.00000 0.00000
Item15 0.00000 0.00000
Item16 0.00000 0.00000
Item17 0.00000 0.00000
Item18 0.00000 0.00000
Item19 0.00000 0.00000
Item20 0.00000 0.00000
Item21 0.00000 0.00000
Item22 0.00000 0.00000
Item23 0.46100 0.00000
Item24 0.00000 0.00000
Item25 0.24957 0.07856
Delta activeness:
D_0000 D_0001 D_0010 D_0011 D_0100 D_0101 D_0110 D_0111 D_1000
Item1 1.00 1.00 0.09 0.00 1.00 0.00 0.00 0.00 0.34
Item2 1.00 1.00 0.11 0.00 1.00 0.00 0.00 0.00 0.17
Item3 1.00 0.91 0.05 0.00 0.97 0.00 0.00 0.00 0.22
Item4 1.00 1.00 0.17 1.00 0.10 0.00 0.00 0.00 0.37
Item5 1.00 1.00 0.12 0.00 0.76 0.00 0.00 0.00 0.31
Item6 1.00 1.00 0.08 1.00 0.32 0.00 0.00 0.00 0.07
Item7 1.00 0.03 0.00 0.00 0.02 1.00 0.00 0.00 1.00
Item8 1.00 0.76 0.22 0.00 1.00 0.00 0.00 0.00 1.00
Item9 1.00 0.00 1.00 0.00 0.00 0.00 1.00 0.00 0.00
Item10 1.00 0.55 0.55 0.00 1.00 0.00 0.00 0.00 0.87
Item11 1.00 0.14 0.13 1.00 1.00 1.00 1.00 1.00 0.72
Item12 1.00 1.00 0.20 1.00 0.19 0.00 0.00 0.00 1.00
Item13 1.00 0.35 0.12 1.00 0.02 0.00 0.00 0.00 0.68
Item14 1.00 0.98 0.76 0.00 1.00 0.00 0.00 0.00 1.00
Item15 1.00 1.00 0.50 0.00 1.00 0.00 0.00 0.00 0.84
Item16 1.00 1.00 0.22 0.00 1.00 0.00 0.00 0.00 0.30
Item17 1.00 0.61 0.34 0.00 0.09 0.00 1.00 0.00 0.78
Item18 1.00 0.91 0.98 0.00 1.00 0.00 0.00 0.00 0.36
Item19 1.00 0.41 1.00 0.00 1.00 0.00 0.00 0.00 0.16
Item20 1.00 0.48 0.93 0.00 1.00 0.00 0.00 0.00 0.14
Item21 1.00 0.40 0.04 1.00 0.64 0.00 0.00 0.00 0.01
Item22 1.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00
Item23 1.00 0.47 0.08 0.00 1.00 0.00 1.00 0.00 0.15
Item24 1.00 0.77 1.00 0.00 1.00 1.00 0.00 0.00 0.35
Item25 1.00 0.13 0.06 1.00 1.00 1.00 1.00 1.00 0.05
D_1001 D_1010 D_1011 D_1100 D_1101 D_1110 D_1111
Item1 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item2 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item3 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item4 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item5 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item6 1.00 1.00 1.00 0.00 0.00 0.00 0.00
Item7 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item8 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item9 0.00 1.00 0.00 1.00 0.00 1.00 0.00
Item10 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item11 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item12 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item13 1.00 1.00 1.00 0.00 0.00 0.00 0.00
Item14 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item15 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item16 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item17 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item18 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item19 1.00 0.00 0.00 0.00 0.00 0.00 0.00
Item20 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item21 1.00 1.00 1.00 0.00 0.00 0.00 0.00
Item22 1.00 1.00 1.00 0.00 0.00 0.00 0.00
Item23 0.00 1.00 0.00 1.00 0.00 1.00 0.00
Item24 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Item25 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Q matrix:
Q_1 Q_2 Q_3 Q_4
Item1 0 1 0 1
Item2 0 1 0 1
Item3 0 1 0 1
Item4 0 0 1 1
Item5 0 0 0 1
Item6 1 0 1 1
Item7 1 1 0 1
Item8 1 1 0 0
Item9 1 1 1 0
Item10 1 1 0 0
Item11 0 1 1 1
Item12 1 0 0 1
Item13 1 0 1 1
Item14 1 1 0 1
Item15 0 1 0 1
Item16 0 1 0 0
Item17 0 1 1 0
Item18 0 1 1 1
Item19 1 1 1 1
Item20 0 1 1 0
Item21 1 0 1 1
Item22 1 0 1 1
Item23 1 1 1 0
Item24 0 1 1 1
Item25 1 1 1 1