# Load necessary libraries
library(TAM)
## Loading required package: CDM
## Loading required package: mvtnorm
## **********************************
## ** CDM 8.2-6 (2022-08-25 15:43:23)
## ** Cognitive Diagnostic Models **
## **********************************
## * TAM 4.2-21 (2024-02-19 18:52:08)
# install.packages("WrightMap")
library("WrightMap")
# Get the directory where the current R script is located
script_dir <- dirname(rstudioapi::getActiveDocumentContext()$path)
# Set the working directory to the script's directory
setwd(script_dir)
# Specify the file name (replace 'your_file_name.extension' with the actual file name)
file_name <- "patternTR.csv"
# Read the file (adjust the function based on the file type, e.g., read.csv, read.table, etc.)
data <- read.csv(file_name, sep=",", stringsAsFactors=FALSE)
# For other file types, use the appropriate function, e.g., read.table, readRDS, etc.
# Display the first few rows of the data
head(data)
## code IDPattern_ABC IDPattern_AABB IDPattern_ABB IDPattern_ABCD IDPattern_ABC2
## 1 1001 0 1 1 1 1
## 2 1002 1 1 1 1 1
## 3 1003 0 0 1 1 1
## 4 1004 0 1 1 1 0
## 5 1005 0 0 1 0 1
## 6 1006 0 1 1 1 1
## Extend_AABB Extend_AB Extend_ABC Extend_ABCD Extend_AAB Extend_AABC
## 1 1 1 1 1 1 1
## 2 1 0 1 0 0 0
## 3 0 1 1 0 1 0
## 4 0 0 0 0 0 1
## 5 1 0 1 1 0 0
## 6 1 1 1 1 1 1
## Extend_AABB2 Abstract_ABB Abstract_AB Abstract_AAB Abstract_AABC
## 1 1 1 1 1 1
## 2 0 0 1 0 0
## 3 0 0 0 0 0
## 4 1 0 1 0 1
## 5 0 1 1 0 0
## 6 0 1 1 0 1
## Abstract.ABCD Abstract_ABB2 Abstract_ABCC
## 1 1 1 1
## 2 1 1 0
## 3 0 1 0
## 4 0 0 0
## 5 1 1 0
## 6 0 1 1
summary(data)
## code IDPattern_ABC IDPattern_AABB IDPattern_ABB
## Min. :1001 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:1030 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:1.0000
## Median :1060 Median :1.0000 Median :1.0000 Median :1.0000
## Mean :1059 Mean :0.6636 Mean :0.7664 Mean :0.7944
## 3rd Qu.:1088 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1115 Max. :1.0000 Max. :1.0000 Max. :1.0000
## IDPattern_ABCD IDPattern_ABC2 Extend_AABB Extend_AB
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.5000 1st Qu.:1.0000 1st Qu.:1.0000
## Median :1.0000 Median :1.0000 Median :1.0000 Median :1.0000
## Mean :0.5981 Mean :0.7477 Mean :0.8411 Mean :0.7664
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## Extend_ABC Extend_ABCD Extend_AAB Extend_AABC
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:0.0000
## Median :1.0000 Median :1.0000 Median :1.000 Median :1.0000
## Mean :0.7383 Mean :0.6075 Mean :0.785 Mean :0.7383
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
## Extend_AABB2 Abstract_ABB Abstract_AB Abstract_AAB
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000
## Median :1.0000 Median :1.0000 Median :1.0000 Median :1.0000
## Mean :0.7944 Mean :0.6636 Mean :0.7664 Mean :0.6542
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## Abstract_AABC Abstract.ABCD Abstract_ABB2 Abstract_ABCC
## Min. :0.000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:0.0000
## Median :1.000 Median :1.0000 Median :1.000 Median :1.0000
## Mean :0.757 Mean :0.7103 Mean :0.757 Mean :0.5794
## 3rd Qu.:1.000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:1.0000
## Max. :1.000 Max. :1.0000 Max. :1.000 Max. :1.0000
# Remove the Student ID and Grade level variables:
data.responses <- subset(data, select = -c(code))
# Compute total score for each participant
TotalScore <- rowSums(data.responses)
# Compute the maximum possible score (all items correct)
MaxScore <- ncol(data.responses)
# Identify participants who did NOT score full marks
filtered_data <- data.responses[TotalScore < MaxScore, ]
# Check the number of participants removed
cat("Number of participants removed due to full scores:", nrow(data.responses) - nrow(filtered_data), "\n")
## Number of participants removed due to full scores: 16
# Update the dataset for analysis
data.responses <- filtered_data
# Running the Dichotomous Rasch Model
dichot.data <- tam(data.responses)
## ....................................................
## Processing Data 2025-02-13 01:26:58.590369
## * Response Data: 91 Persons and 19 Items
## * Numerical integration with 21 nodes
## * Created Design Matrices ( 2025-02-13 01:26:58.592417 )
## * Calculated Sufficient Statistics ( 2025-02-13 01:26:58.60266 )
## ....................................................
## Iteration 1 2025-02-13 01:26:58.604263
## E Step
## M Step Intercepts |---
## Deviance = 2000.527
## Maximum item intercept parameter change: 0.13592
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.097888
## ....................................................
## Iteration 2 2025-02-13 01:26:58.606238
## E Step
## M Step Intercepts |--
## Deviance = 1998.2883 | Absolute change: 2.2387 | Relative change: 0.0011203
## Maximum item intercept parameter change: 0.026118
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.031401
## ....................................................
## Iteration 3 2025-02-13 01:26:58.606696
## E Step
## M Step Intercepts |--
## Deviance = 1997.9378 | Absolute change: 0.3505 | Relative change: 0.00017545
## Maximum item intercept parameter change: 0.018739
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.0139
## ....................................................
## Iteration 4 2025-02-13 01:26:58.607102
## E Step
## M Step Intercepts |--
## Deviance = 1997.7648 | Absolute change: 0.173 | Relative change: 8.66e-05
## Maximum item intercept parameter change: 0.013441
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.005693
## ....................................................
## Iteration 5 2025-02-13 01:26:58.6075
## E Step
## M Step Intercepts |--
## Deviance = 1997.6736 | Absolute change: 0.0912 | Relative change: 4.564e-05
## Maximum item intercept parameter change: 0.00974
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.001829
## ....................................................
## Iteration 6 2025-02-13 01:26:58.607891
## E Step
## M Step Intercepts |--
## Deviance = 1997.6237 | Absolute change: 0.0499 | Relative change: 2.498e-05
## Maximum item intercept parameter change: 0.007128
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 8.6e-05
## ....................................................
## Iteration 7 2025-02-13 01:26:58.608278
## E Step
## M Step Intercepts |--
## Deviance = 1997.5958 | Absolute change: 0.0279 | Relative change: 1.397e-05
## Maximum item intercept parameter change: 0.005391
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000618
## ....................................................
## Iteration 8 2025-02-13 01:26:58.608662
## E Step
## M Step Intercepts |--
## Deviance = 1997.58 | Absolute change: 0.0158 | Relative change: 7.91e-06
## Maximum item intercept parameter change: 0.004098
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000829
## ....................................................
## Iteration 9 2025-02-13 01:26:58.609047
## E Step
## M Step Intercepts |--
## Deviance = 1997.571 | Absolute change: 0.009 | Relative change: 4.5e-06
## Maximum item intercept parameter change: 0.003111
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000817
## ....................................................
## Iteration 10 2025-02-13 01:26:58.609428
## E Step
## M Step Intercepts |--
## Deviance = 1997.5659 | Absolute change: 0.0051 | Relative change: 2.58e-06
## Maximum item intercept parameter change: 0.002362
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000719
## ....................................................
## Iteration 11 2025-02-13 01:26:58.609808
## E Step
## M Step Intercepts |--
## Deviance = 1997.5629 | Absolute change: 0.003 | Relative change: 1.48e-06
## Maximum item intercept parameter change: 0.001792
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000597
## ....................................................
## Iteration 12 2025-02-13 01:26:58.610187
## E Step
## M Step Intercepts |--
## Deviance = 1997.5612 | Absolute change: 0.0017 | Relative change: 8.5e-07
## Maximum item intercept parameter change: 0.00136
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000479
## ....................................................
## Iteration 13 2025-02-13 01:26:58.610582
## E Step
## M Step Intercepts |--
## Deviance = 1997.5602 | Absolute change: 0.001 | Relative change: 4.9e-07
## Maximum item intercept parameter change: 0.001032
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000378
## ....................................................
## Iteration 14 2025-02-13 01:26:58.610957
## E Step
## M Step Intercepts |--
## Deviance = 1997.5597 | Absolute change: 6e-04 | Relative change: 2.8e-07
## Maximum item intercept parameter change: 0.000783
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000294
## ....................................................
## Iteration 15 2025-02-13 01:26:58.611347
## E Step
## M Step Intercepts |--
## Deviance = 1997.5594 | Absolute change: 3e-04 | Relative change: 1.6e-07
## Maximum item intercept parameter change: 0.000594
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000227
## ....................................................
## Iteration 16 2025-02-13 01:26:58.611732
## E Step
## M Step Intercepts |--
## Deviance = 1997.5592 | Absolute change: 2e-04 | Relative change: 9e-08
## Maximum item intercept parameter change: 0.000451
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000174
## ....................................................
## Iteration 17 2025-02-13 01:26:58.612111
## E Step
## M Step Intercepts |--
## Deviance = 1997.5591 | Absolute change: 1e-04 | Relative change: 5e-08
## Maximum item intercept parameter change: 0.000342
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000133
## ....................................................
## Iteration 18 2025-02-13 01:26:58.612494
## E Step
## M Step Intercepts |--
## Deviance = 1997.559 | Absolute change: 1e-04 | Relative change: 3e-08
## Maximum item intercept parameter change: 0.00026
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000101
## ....................................................
## Iteration 19 2025-02-13 01:26:58.612875
## E Step
## M Step Intercepts |--
## Deviance = 1997.559 | Absolute change: 0 | Relative change: 2e-08
## Maximum item intercept parameter change: 0.000197
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 7.7e-05
## ....................................................
## Iteration 20 2025-02-13 01:26:58.61327
## E Step
## M Step Intercepts |--
## Deviance = 1997.5589 | Absolute change: 0 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.00015
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 5.9e-05
## ....................................................
## Iteration 21 2025-02-13 01:26:58.613652
## E Step
## M Step Intercepts |--
## Deviance = 1997.5589 | Absolute change: 0 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000114
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 4.5e-05
## ....................................................
## Iteration 22 2025-02-13 01:26:58.61404
## E Step
## M Step Intercepts |-
## Deviance = 1997.5589 | Absolute change: 0 | Relative change: 0
## Maximum item intercept parameter change: 8.6e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 3.4e-05
## ....................................................
## Item Parameters
## xsi.index xsi.label est
## 1 1 IDPattern_ABC -0.5038
## 2 2 IDPattern_AABB -1.1443
## 3 3 IDPattern_ABB -1.3427
## 4 4 IDPattern_ABCD -0.1315
## 5 5 IDPattern_ABC2 -1.0194
## 6 6 Extend_AABB -1.7148
## 7 7 Extend_AB -1.1443
## 8 8 Extend_ABC -0.9587
## 9 9 Extend_ABCD -0.1840
## 10 10 Extend_AAB -1.2749
## 11 11 Extend_AABC -0.9587
## 12 12 Extend_AABB2 -1.3427
## 13 13 Abstract_ABB -0.5038
## 14 14 Abstract_AB -1.1443
## 15 15 Abstract_AAB -0.4497
## 16 16 Abstract_AABC -1.0812
## 17 17 Abstract.ABCD -0.7826
## 18 18 Abstract_ABB2 -1.0812
## 19 19 Abstract_ABCC -0.0267
## ...................................
## Regression Coefficients
## [,1]
## [1,] 0
##
## Variance:
## [,1]
## [1,] 0.8548
##
##
## EAP Reliability:
## [1] 0.735
##
## -----------------------------
## Start: 2025-02-13 01:26:58.589836
## End: 2025-02-13 01:26:58.621954
## Time difference of 0.03211808 secs
# Request a summary of the model results
summary(dichot.data)
## ------------------------------------------------------------
## TAM 4.2-21 (2024-02-19 18:52:08)
## R version 4.4.2 (2024-10-31) aarch64, darwin20 | nodename=unknown1a5b05895e03.home | login=root
##
## Date of Analysis: 2025-02-13 01:26:58.621954
## Time difference of 0.03211808 secs
## Computation time: 0.03211808
##
## Multidimensional Item Response Model in TAM
##
## IRT Model: 1PL
## Call:
## tam.mml(resp = resp)
##
## ------------------------------------------------------------
## Number of iterations = 22
## Numeric integration with 21 integration points
##
## Deviance = 1997.56
## Log likelihood = -998.78
## Number of persons = 91
## Number of persons used = 91
## Number of items = 19
## Number of estimated parameters = 20
## Item threshold parameters = 19
## Item slope parameters = 0
## Regression parameters = 0
## Variance/covariance parameters = 1
##
## AIC = 2038 | penalty=40 | AIC=-2*LL + 2*p
## AIC3 = 2058 | penalty=60 | AIC3=-2*LL + 3*p
## BIC = 2088 | penalty=90.22 | BIC=-2*LL + log(n)*p
## aBIC = 2024 | penalty=26.21 | aBIC=-2*LL + log((n-2)/24)*p (adjusted BIC)
## CAIC = 2108 | penalty=110.22 | CAIC=-2*LL + [log(n)+1]*p (consistent AIC)
## AICc = 2050 | penalty=52 | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1) (bias corrected AIC)
## GHP = 0.58923 | GHP=( -LL + p ) / (#Persons * #Items) (Gilula-Haberman log penalty)
##
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.735
## ------------------------------------------------------------
## Covariances and Variances
## [,1]
## [1,] 0.855
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
## [,1]
## [1,] 0.925
## ------------------------------------------------------------
## Regression Coefficients
## [,1]
## [1,] 0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
## 1 IDPattern_ABC 91 0.604 -0.504 -0.504 1
## 2 IDPattern_AABB 91 0.725 -1.144 -1.144 1
## 3 IDPattern_ABB 91 0.758 -1.343 -1.343 1
## 4 IDPattern_ABCD 91 0.527 -0.131 -0.131 1
## 5 IDPattern_ABC2 91 0.703 -1.019 -1.019 1
## 6 Extend_AABB 91 0.813 -1.715 -1.715 1
## 7 Extend_AB 91 0.725 -1.144 -1.144 1
## 8 Extend_ABC 91 0.692 -0.959 -0.959 1
## 9 Extend_ABCD 91 0.538 -0.184 -0.184 1
## 10 Extend_AAB 91 0.747 -1.275 -1.275 1
## 11 Extend_AABC 91 0.692 -0.959 -0.959 1
## 12 Extend_AABB2 91 0.758 -1.343 -1.343 1
## 13 Abstract_ABB 91 0.604 -0.504 -0.504 1
## 14 Abstract_AB 91 0.725 -1.144 -1.144 1
## 15 Abstract_AAB 91 0.593 -0.450 -0.450 1
## 16 Abstract_AABC 91 0.714 -1.081 -1.081 1
## 17 Abstract.ABCD 91 0.659 -0.783 -0.783 1
## 18 Abstract_ABB2 91 0.714 -1.081 -1.081 1
## 19 Abstract_ABCC 91 0.505 -0.027 -0.027 1
##
## Item Parameters in IRT parameterization
## item alpha beta
## 1 IDPattern_ABC 1 -0.504
## 2 IDPattern_AABB 1 -1.144
## 3 IDPattern_ABB 1 -1.343
## 4 IDPattern_ABCD 1 -0.131
## 5 IDPattern_ABC2 1 -1.019
## 6 Extend_AABB 1 -1.715
## 7 Extend_AB 1 -1.144
## 8 Extend_ABC 1 -0.959
## 9 Extend_ABCD 1 -0.184
## 10 Extend_AAB 1 -1.275
## 11 Extend_AABC 1 -0.959
## 12 Extend_AABB2 1 -1.343
## 13 Abstract_ABB 1 -0.504
## 14 Abstract_AB 1 -1.144
## 15 Abstract_AAB 1 -0.450
## 16 Abstract_AABC 1 -1.081
## 17 Abstract.ABCD 1 -0.783
## 18 Abstract_ABB2 1 -1.081
## 19 Abstract_ABCC 1 -0.027
# Plot the Wright Map
IRT.WrightMap(dichot.data, show.thr.lab=FALSE, main.title = "Patterning Wright Map")
difficulty <- dichot.data$xsi
summary(difficulty)
## xsi se.xsi
## Min. :-1.71483 Min. :0.2287
## 1st Qu.:-1.14431 1st Qu.:0.2331
## Median :-1.01935 Median :0.2475
## Mean :-0.88364 Mean :0.2468
## 3rd Qu.:-0.50383 3rd Qu.:0.2526
## Max. :-0.02674 Max. :0.2852
sd(difficulty$xsi)
## [1] 0.4626988
sd(difficulty$se.xsi)
## [1] 0.01452339
hist(difficulty$xsi, main = "Histogram of Item Difficulty Estimates for the Patterning TR Data",
xlab = "Item Difficulty Estimates in Logits")
item.fit <- tam.fit(dichot.data)
## Item fit calculation based on 100 simulations
## |**********|
## |----------|
item.fit <- as.data.frame(item.fit$itemfit)
summary(item.fit)
## parameter Outfit Outfit_t Outfit_p
## Length:19 Min. :0.7719 Min. :-2.3035 Min. :0.0000
## Class :character 1st Qu.:0.8434 1st Qu.:-1.3608 1st Qu.:0.0631
## Mode :character Median :0.8920 Median :-0.9137 Median :0.1651
## Mean :0.9866 Mean :-0.0990 Mean :0.2000
## 3rd Qu.:1.1331 3rd Qu.: 1.4228 3rd Qu.:0.2925
## Max. :1.5250 Max. : 5.4786 Max. :0.6026
## Outfit_pholm Infit Infit_t Infit_p
## Min. :0.0000008 Min. :0.8620 Min. :-1.46123 Min. :0.0000092
## 1st Qu.:0.9044535 1st Qu.:0.8970 1st Qu.:-0.92772 1st Qu.:0.1717641
## Median :1.0000000 Median :0.9452 Median :-0.44586 Median :0.3655766
## Mean :0.8659853 Mean :0.9984 Mean : 0.03083 Mean :0.3719531
## 3rd Qu.:1.0000000 3rd Qu.:1.0837 3rd Qu.: 0.83085 3rd Qu.:0.5061732
## Max. :1.0000000 Max. :1.4119 Max. : 4.43436 Max. :0.8766593
## Infit_pholm
## Min. :0.0001755
## 1st Qu.:1.0000000
## Median :1.0000000
## Mean :0.9473777
## 3rd Qu.:1.0000000
## Max. :1.0000000
achievement <- as.data.frame(tam.wle(dichot.data))
## Iteration in WLE/MLE estimation 1 | Maximal change 0.9945
## Iteration in WLE/MLE estimation 2 | Maximal change 0.2444
## Iteration in WLE/MLE estimation 3 | Maximal change 0.0074
## Iteration in WLE/MLE estimation 4 | Maximal change 4e-04
## Iteration in WLE/MLE estimation 5 | Maximal change 0
## ----
## WLE Reliability= 0.671
summary(achievement)
## pid N.items PersonScores PersonMax theta
## Min. : 1.0 Min. :19 Min. : 3.0 Min. :19 Min. :-2.5039
## 1st Qu.:23.5 1st Qu.:19 1st Qu.:10.0 1st Qu.:19 1st Qu.:-0.7815
## Median :46.0 Median :19 Median :13.0 Median :19 Median :-0.1167
## Mean :46.0 Mean :19 Mean :12.8 Mean :19 Mean :-0.0194
## 3rd Qu.:68.5 3rd Qu.:19 3rd Qu.:16.0 3rd Qu.:19 3rd Qu.: 0.7393
## Max. :91.0 Max. :19 Max. :18.0 Max. :19 Max. : 1.7266
## error WLE.rel
## Min. :0.4705 Min. :0.6706
## 1st Qu.:0.4844 1st Qu.:0.6706
## Median :0.5013 Median :0.6706
## Mean :0.5705 Mean :0.6706
## 3rd Qu.:0.6148 3rd Qu.:0.6706
## Max. :0.8815 Max. :0.6706
hist(achievement$theta, main = "Histogram of Person Achievement Estimates \nfor the Patterning TR Data",
xlab = "Person Achievement Estimates in Logits")
person.fit <- tam.personfit(dichot.data)
summary(person.fit)
## outfitPerson outfitPerson_t infitPerson infitPerson_t
## Min. :0.3765 Min. :-1.30060 Min. :0.6451 Min. :-1.16583
## 1st Qu.:0.8044 1st Qu.:-0.50064 1st Qu.:0.8460 1st Qu.:-0.28291
## Median :0.9597 Median :-0.05992 Median :0.9532 Median :-0.09401
## Mean :0.9100 Mean :-0.04553 Mean :0.9398 Mean : 0.00029
## 3rd Qu.:1.0273 3rd Qu.: 0.24468 3rd Qu.:1.0126 3rd Qu.: 0.15923
## Max. :1.3254 Max. : 2.54319 Max. :1.2666 Max. : 2.49697
summary.table.statistics <- c("Logit Scale Location Mean",
"Logit Scale Location SD",
"Standard Error Mean",
"Standard Error SD",
"Outfit MSE Mean",
"Outfit MSE SD",
"Infit MSE Mean",
"Infit MSE SD",
"Std. Outfit Mean",
"Std. Outfit SD",
"Std. Infit Mean",
"Std. Infit SD",
"Reliability of Separation")
item.summary.results <- rbind(mean(difficulty$xsi),
sd(difficulty$xsi),
mean(difficulty$se.xsi),
sd(difficulty$se.xsi),
mean(item.fit$Outfit),
sd(item.fit$Outfit),
mean(item.fit$Infit),
sd(item.fit$Infit),
mean(item.fit$Outfit_t),
sd(item.fit$Outfit_t),
mean(item.fit$Infit_t),
sd(item.fit$Infit_t),
dichot.data$EAP.rel)
person.summary.results <- rbind(mean(achievement$theta),
sd(achievement$theta),
mean(achievement$error),
sd(achievement$error),
mean(person.fit$outfitPerson),
sd(person.fit$outfitPerson),
mean(person.fit$infitPerson),
sd(person.fit$infitPerson),
mean(person.fit$outfitPerson_t),
sd(person.fit$outfitPerson_t),
mean(person.fit$infitPerson_t),
sd(person.fit$infitPerson_t),
mean(achievement$WLE.rel))
# Round the values for presentation in a table:
item.summary.results_rounded <- round(item.summary.results, digits = 2)
person.summary.results_rounded <- round(person.summary.results, digits = 2)
Table1 <- cbind.data.frame(summary.table.statistics,
item.summary.results_rounded,
person.summary.results_rounded)
# add descriptive column labels:
names(Table1) <- c("Statistic", "Items", "Persons")
# Calculate the proportion correct for each task:
TaskCorrect <- apply(data.responses, 2, sum)
PropCorrect <- (TaskCorrect/nrow(data.responses))
SD_PropCorrect <- sqrt((PropCorrect * (1 - PropCorrect)) / nrow(data.responses))
# Compute Item-Trait Correlation (correlation of each item with person ability estimates)
ItemTraitCorrelation <- cor(data.responses, achievement$theta, use = "complete.obs")
# Compute Item-Total Correlation (correlation of each item with total test scores)
TotalScore <- rowSums(data.responses) # Compute total score for each student
ItemTotalCorrelation <- sapply(1:ncol(data.responses), function(i) {
cor(data.responses[, i], TotalScore - data.responses[, i], use = "complete.obs")
})
# Combine item statistics into Table2
Table2 <- cbind.data.frame(item.fit$parameter,
PropCorrect,
SD_PropCorrect,
difficulty$xsi,
difficulty$se.xsi,
item.fit$Outfit,
item.fit$Outfit_t,
item.fit$Infit,
item.fit$Infit_t,
ItemTraitCorrelation, # 🔹 Added Item-Trait Correlation
ItemTotalCorrelation) # 🔹 Added Item-Total Correlation
# Rename columns to include new statistics
names(Table2) <- c("Task ID", "Proportion Correct", "Proportion Correct SD",
"Item Location", "Item SE", "Outfit MSE", "Std. Outfit",
"Infit MSE", "Std. Infit", "Item-Trait Correlation", "Item-Total Correlation")
# Sort Table2 by Item difficulty
Table2 <- Table2[order(-Table2$`Item Location`),]
# Round the numeric values (all columns except the first one) to 2 digits
Table2[, -1] <- round(Table2[, -1], digits = 2)
# Display Table2
print(Table2)
## Task ID Proportion Correct Proportion Correct SD
## Abstract_ABCC Abstract_ABCC 0.51 0.05
## IDPattern_ABCD IDPattern_ABCD 0.53 0.05
## Extend_ABCD Extend_ABCD 0.54 0.05
## Abstract_AAB Abstract_AAB 0.59 0.05
## IDPattern_ABC IDPattern_ABC 0.60 0.05
## Abstract_ABB Abstract_ABB 0.60 0.05
## Abstract.ABCD Abstract.ABCD 0.66 0.05
## Extend_ABC Extend_ABC 0.69 0.05
## Extend_AABC Extend_AABC 0.69 0.05
## IDPattern_ABC2 IDPattern_ABC2 0.70 0.05
## Abstract_AABC Abstract_AABC 0.71 0.05
## Abstract_ABB2 Abstract_ABB2 0.71 0.05
## IDPattern_AABB IDPattern_AABB 0.73 0.05
## Extend_AB Extend_AB 0.73 0.05
## Abstract_AB Abstract_AB 0.73 0.05
## Extend_AAB Extend_AAB 0.75 0.05
## IDPattern_ABB IDPattern_ABB 0.76 0.04
## Extend_AABB2 Extend_AABB2 0.76 0.04
## Extend_AABB Extend_AABB 0.81 0.04
## Item Location Item SE Outfit MSE Std. Outfit Infit MSE
## Abstract_ABCC -0.03 0.23 0.87 -1.65 0.88
## IDPattern_ABCD -0.13 0.23 1.52 5.48 1.41
## Extend_ABCD -0.18 0.23 1.16 1.80 1.11
## Abstract_AAB -0.45 0.23 0.83 -2.00 0.88
## IDPattern_ABC -0.50 0.23 1.11 1.19 1.08
## Abstract_ABB -0.50 0.23 0.84 -1.93 0.88
## Abstract.ABCD -0.78 0.24 1.23 2.15 1.16
## Extend_ABC -0.96 0.25 1.19 1.66 1.14
## Extend_AABC -0.96 0.25 0.77 -2.30 0.86
## IDPattern_ABC2 -1.02 0.25 1.20 1.66 1.08
## Abstract_AABC -1.08 0.25 1.06 0.52 1.09
## Abstract_ABB2 -1.08 0.25 0.85 -1.39 0.91
## IDPattern_AABB -1.14 0.25 0.89 -0.95 0.95
## Extend_AB -1.14 0.25 0.87 -1.17 0.91
## Abstract_AB -1.14 0.25 0.90 -0.91 0.95
## Extend_AAB -1.27 0.26 0.89 -0.89 0.87
## IDPattern_ABB -1.34 0.26 0.92 -0.58 0.98
## Extend_AABB2 -1.34 0.26 0.83 -1.33 0.91
## Extend_AABB -1.71 0.29 0.81 -1.23 0.93
## Std. Infit Item-Trait Correlation Item-Total Correlation
## Abstract_ABCC -1.46 0.60 0.50
## IDPattern_ABCD 4.43 -0.03 -0.17
## Extend_ABCD 1.25 0.34 0.20
## Abstract_AAB -1.40 0.60 0.51
## IDPattern_ABC 0.90 0.35 0.22
## Abstract_ABB -1.44 0.61 0.52
## Abstract.ABCD 1.58 0.25 0.12
## Extend_ABC 1.26 0.26 0.14
## Extend_AABC -1.33 0.60 0.53
## IDPattern_ABC2 0.69 0.30 0.20
## Abstract_AABC 0.76 0.34 0.21
## Abstract_ABB2 -0.79 0.53 0.45
## IDPattern_AABB -0.45 0.48 0.40
## Extend_AB -0.73 0.51 0.44
## Abstract_AB -0.45 0.49 0.40
## Extend_AAB -1.07 0.53 0.49
## IDPattern_ABB -0.16 0.43 0.34
## Extend_AABB2 -0.64 0.51 0.44
## Extend_AABB -0.38 0.46 0.40
# Calculate proportion correct for persons:
PersonPropCorrect <- achievement$PersonScores / achievement$PersonMax
# Combine person calibration results in a table:
Table3 <- cbind.data.frame(achievement$pid,
PersonPropCorrect,
achievement$theta,
achievement$error,
person.fit$outfitPerson,
person.fit$outfitPerson_t,
person.fit$infitPerson,
person.fit$infitPerson_t)
names(Table3) <- c("Person ID", "Proportion Correct", "Person Location","Person SE","Outfit MSE","Std. Outfit", "Infit MSE","Std. Infit")
# Round the numeric values (all columns except the first one) to 2 digits:
Table3[, -1] <- round(Table3[,-1], digits = 2)
# Print Table 1:
knitr::kable(
Table1, booktabs = TRUE,
caption = 'Model Summary Table'
)
Model Summary Table
| Logit Scale Location Mean |
-0.88 |
-0.02 |
| Logit Scale Location SD |
0.46 |
1.02 |
| Standard Error Mean |
0.25 |
0.57 |
| Standard Error SD |
0.01 |
0.12 |
| Outfit MSE Mean |
0.99 |
0.91 |
| Outfit MSE SD |
0.20 |
0.20 |
| Infit MSE Mean |
1.00 |
0.94 |
| Infit MSE SD |
0.14 |
0.13 |
| Std. Outfit Mean |
-0.10 |
-0.05 |
| Std. Outfit SD |
1.97 |
0.63 |
| Std. Infit Mean |
0.03 |
0.00 |
| Std. Infit SD |
1.46 |
0.57 |
| Reliability of Separation |
0.74 |
0.67 |
# Print Table 2:
knitr::kable(
Table2, booktabs = TRUE,
caption = 'Item Calibration'
)
Item Calibration
| Abstract_ABCC |
Abstract_ABCC |
0.51 |
0.05 |
-0.03 |
0.23 |
0.87 |
-1.65 |
0.88 |
-1.46 |
0.60 |
0.50 |
| IDPattern_ABCD |
IDPattern_ABCD |
0.53 |
0.05 |
-0.13 |
0.23 |
1.52 |
5.48 |
1.41 |
4.43 |
-0.03 |
-0.17 |
| Extend_ABCD |
Extend_ABCD |
0.54 |
0.05 |
-0.18 |
0.23 |
1.16 |
1.80 |
1.11 |
1.25 |
0.34 |
0.20 |
| Abstract_AAB |
Abstract_AAB |
0.59 |
0.05 |
-0.45 |
0.23 |
0.83 |
-2.00 |
0.88 |
-1.40 |
0.60 |
0.51 |
| IDPattern_ABC |
IDPattern_ABC |
0.60 |
0.05 |
-0.50 |
0.23 |
1.11 |
1.19 |
1.08 |
0.90 |
0.35 |
0.22 |
| Abstract_ABB |
Abstract_ABB |
0.60 |
0.05 |
-0.50 |
0.23 |
0.84 |
-1.93 |
0.88 |
-1.44 |
0.61 |
0.52 |
| Abstract.ABCD |
Abstract.ABCD |
0.66 |
0.05 |
-0.78 |
0.24 |
1.23 |
2.15 |
1.16 |
1.58 |
0.25 |
0.12 |
| Extend_ABC |
Extend_ABC |
0.69 |
0.05 |
-0.96 |
0.25 |
1.19 |
1.66 |
1.14 |
1.26 |
0.26 |
0.14 |
| Extend_AABC |
Extend_AABC |
0.69 |
0.05 |
-0.96 |
0.25 |
0.77 |
-2.30 |
0.86 |
-1.33 |
0.60 |
0.53 |
| IDPattern_ABC2 |
IDPattern_ABC2 |
0.70 |
0.05 |
-1.02 |
0.25 |
1.20 |
1.66 |
1.08 |
0.69 |
0.30 |
0.20 |
| Abstract_AABC |
Abstract_AABC |
0.71 |
0.05 |
-1.08 |
0.25 |
1.06 |
0.52 |
1.09 |
0.76 |
0.34 |
0.21 |
| Abstract_ABB2 |
Abstract_ABB2 |
0.71 |
0.05 |
-1.08 |
0.25 |
0.85 |
-1.39 |
0.91 |
-0.79 |
0.53 |
0.45 |
| IDPattern_AABB |
IDPattern_AABB |
0.73 |
0.05 |
-1.14 |
0.25 |
0.89 |
-0.95 |
0.95 |
-0.45 |
0.48 |
0.40 |
| Extend_AB |
Extend_AB |
0.73 |
0.05 |
-1.14 |
0.25 |
0.87 |
-1.17 |
0.91 |
-0.73 |
0.51 |
0.44 |
| Abstract_AB |
Abstract_AB |
0.73 |
0.05 |
-1.14 |
0.25 |
0.90 |
-0.91 |
0.95 |
-0.45 |
0.49 |
0.40 |
| Extend_AAB |
Extend_AAB |
0.75 |
0.05 |
-1.27 |
0.26 |
0.89 |
-0.89 |
0.87 |
-1.07 |
0.53 |
0.49 |
| IDPattern_ABB |
IDPattern_ABB |
0.76 |
0.04 |
-1.34 |
0.26 |
0.92 |
-0.58 |
0.98 |
-0.16 |
0.43 |
0.34 |
| Extend_AABB2 |
Extend_AABB2 |
0.76 |
0.04 |
-1.34 |
0.26 |
0.83 |
-1.33 |
0.91 |
-0.64 |
0.51 |
0.44 |
| Extend_AABB |
Extend_AABB |
0.81 |
0.04 |
-1.71 |
0.29 |
0.81 |
-1.23 |
0.93 |
-0.38 |
0.46 |
0.40 |
# Print Table 3 in a neat way:
knitr::kable(
head(Table3,10), booktabs = TRUE,
caption = 'Person Calibration'
)
Person Calibration
| 1 |
0.95 |
1.73 |
0.88 |
0.57 |
-0.35 |
0.72 |
-0.18 |
| 2 |
0.53 |
-0.78 |
0.47 |
0.99 |
-0.05 |
0.99 |
-0.02 |
| 3 |
0.37 |
-1.42 |
0.48 |
1.00 |
0.07 |
1.00 |
0.07 |
| 4 |
0.37 |
-1.42 |
0.48 |
0.98 |
-0.05 |
0.98 |
-0.09 |
| 5 |
0.47 |
-0.99 |
0.47 |
1.01 |
0.14 |
1.02 |
0.21 |
| 6 |
0.79 |
0.41 |
0.56 |
0.97 |
0.03 |
0.99 |
0.07 |
| 7 |
0.63 |
-0.35 |
0.49 |
1.10 |
0.65 |
1.11 |
0.78 |
| 8 |
0.79 |
0.41 |
0.56 |
0.92 |
-0.13 |
0.94 |
-0.11 |
| 9 |
0.53 |
-0.78 |
0.47 |
0.92 |
-0.76 |
0.92 |
-0.74 |
| 10 |
0.58 |
-0.57 |
0.48 |
0.96 |
-0.23 |
0.97 |
-0.22 |
# Plot the variable-Map
IRT.WrightMap(dichot.data,show.thr.lab=FALSE)
