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Getting Started with exametrika

Source: vignettes/getting-started.Rmd
getting-started.Rmd

Overview

The exametrika package provides comprehensive Test Data Engineering tools for analyzing educational test data. Based on the methods described in Shojima (2022), this package enables researchers and practitioners to:

  • Analyze test response patterns and item characteristics
  • Classify respondents using various psychometric models
  • Investigate latent structures in test data
  • Examine local dependencies between items
  • Perform network analysis of item relationships

Installation 

# Install from CRAN
install.packages("exametrika")

# Or install the development version from GitHub
if (!require("devtools")) install.packages("devtools")
devtools::install_github("kosugitti/exametrika")

Data Format

Data Requirements

Exametrika accepts both binary and polytomous response data:

  • Binary data (0/1): 0 = incorrect, 1 = correct
  • Polytomous data: ordinal response categories or multiple score levels
  • Missing values: NA values supported; custom missing value codes can be specified

Data Formatting

The dataFormat() function processes input data before analysis:

# Format raw data for analysis
data <- dataFormat(J15S500)
str(data)
#> List of 7
#>  $ ID           : chr [1:500] "Student001" "Student002" "Student003" "Student004" ...
#>  $ ItemLabel    : chr [1:15] "Item01" "Item02" "Item03" "Item04" ...
#>  $ Z            : num [1:500, 1:15] 1 1 1 1 1 1 1 1 1 1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:15] "Item01" "Item02" "Item03" "Item04" ...
#>  $ w            : num [1:15] 1 1 1 1 1 1 1 1 1 1 ...
#>  $ response.type: chr "binary"
#>  $ categories   : Named int [1:15] 2 2 2 2 2 2 2 2 2 2 ...
#>   ..- attr(*, "names")= chr [1:15] "Item01" "Item02" "Item03" "Item04" ...
#>  $ U            : num [1:500, 1:15] 0 1 1 1 1 1 0 0 1 1 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:15] "Item01" "Item02" "Item03" "Item04" ...
#>  - attr(*, "class")= chr [1:2] "exametrika" "exametrikaData"

Sample Datasets

The package includes sample datasets from Shojima (2022). The naming convention is JxxSxxx where J = number of items and S = sample size.

Dataset Items Examinees Type Use Case
J5S10 5 10 Binary Quick testing
J5S1000 5 1,000 Ordinal GRM examples
J12S5000 12 5,000 Binary LDLRA examples
J15S500 15 500 Binary IRT, LCA examples
J15S3810 15 3,810 Ordinal (4-point) Ordinal LRA
J20S400 20 400 Binary BNM examples
J20S600 20 600 Nominal (4-cat) Nominal Biclustering
J35S500 35 500 Ordinal (5-cat) Ordinal Biclustering
J35S515 35 515 Binary Biclustering, network models
J35S5000 35 5,000 Multiple-choice Nominal LRA
J50S100 50 100 Binary Small sample testing

Basic Statistics

Test Statistics 

TestStatistics(J15S500)
#> Test Statistics
#>                   value
#> TestLength   15.0000000
#> SampleSize  500.0000000
#> Mean          9.6640000
#> SEofMean      0.1190738
#> Variance      7.0892826
#> SD            2.6625707
#> Skewness     -0.4116220
#> Kurtosis     -0.4471624
#> Min           2.0000000
#> Max          15.0000000
#> Range        13.0000000
#> Q1.25%        8.0000000
#> Median.50%   10.0000000
#> Q3.75%       12.0000000
#> IQR           4.0000000
#> Stanine.4%    5.0000000
#> Stanine.11%   6.0000000
#> Stanine.23%   7.0000000
#> Stanine.40%   9.0000000
#> Stanine.60%  11.0000000
#> Stanine.77%  12.0000000
#> Stanine.89%  13.0000000
#> Stanine.96%  14.0000000

Item Statistics 

ItemStatistics(J15S500)
#> Item Statistics
#>    ItemLabel  NR   CRR  ODDs Threshold Entropy ITCrr
#> 1     Item01 500 0.746 2.937    -0.662   0.818 0.375
#> 2     Item02 500 0.754 3.065    -0.687   0.805 0.393
#> 3     Item03 500 0.726 2.650    -0.601   0.847 0.321
#> 4     Item04 500 0.776 3.464    -0.759   0.767 0.503
#> 5     Item05 500 0.804 4.102    -0.856   0.714 0.329
#> 6     Item06 500 0.864 6.353    -1.098   0.574 0.377
#> 7     Item07 500 0.716 2.521    -0.571   0.861 0.483
#> 8     Item08 500 0.588 1.427    -0.222   0.978 0.405
#> 9     Item09 500 0.364 0.572     0.348   0.946 0.225
#> 10    Item10 500 0.662 1.959    -0.418   0.923 0.314
#> 11    Item11 500 0.286 0.401     0.565   0.863 0.455
#> 12    Item12 500 0.274 0.377     0.601   0.847 0.468
#> 13    Item13 500 0.634 1.732    -0.342   0.948 0.471
#> 14    Item14 500 0.764 3.237    -0.719   0.788 0.485
#> 15    Item15 500 0.706 2.401    -0.542   0.874 0.413

Classical Test Theory 

CTT(J15S500)
#> Realiability
#>                 name value
#> 1  Alpha(Covariance) 0.625
#> 2         Alpha(Phi) 0.630
#> 3 Alpha(Tetrachoric) 0.771
#> 4  Omega(Covariance) 0.632
#> 5         Omega(Phi) 0.637
#> 6 Omega(Tetrachoric) 0.779
#> 
#> Reliability Excluding Item
#>    IfDeleted Alpha.Covariance Alpha.Phi Alpha.Tetrachoric
#> 1     Item01            0.613     0.618             0.762
#> 2     Item02            0.609     0.615             0.759
#> 3     Item03            0.622     0.628             0.770
#> 4     Item04            0.590     0.595             0.742
#> 5     Item05            0.617     0.624             0.766
#> 6     Item06            0.608     0.613             0.754
#> 7     Item07            0.594     0.600             0.748
#> 8     Item08            0.611     0.616             0.762
#> 9     Item09            0.642     0.645             0.785
#> 10    Item10            0.626     0.630             0.773
#> 11    Item11            0.599     0.606             0.751
#> 12    Item12            0.597     0.603             0.748
#> 13    Item13            0.597     0.604             0.753
#> 14    Item14            0.593     0.598             0.745
#> 15    Item15            0.607     0.612             0.759

Next Steps

Reference

Shojima, Kojiro (2022) Test Data Engineering: Latent Rank Analysis, Biclustering, and Bayesian Network (Behaviormetrics: Quantitative Approaches to Human Behavior, 13), Springer.