#Load library
library(MBESS)
library(lavaan)
library(semPlot)
library(readr)
library(psych)
library(CTT)
library(GPArotation)
library(psychometric)
library(cocron)
library(knitr)
library(ltm)
library(mirt)
library(ggplot2)
library(Hmisc)
#Import data
SCORES <- read_csv("C:/Goran/01 FAKS/4TT/Project/Data/SCORES.csv")
data <- SCORES
#Convert to cathegorical data
data[,c("X1", "X2", "X3", "X4", "X5", "X6", "X7", "X8", "X9", "X10", "X11", "X12", "X13", "X14", "X15", "X16", "X17", "X18", "X19", "X20", "X21", "X22", "X23", "X24", "X25")] <-
lapply(data[,c("X1", "X2", "X3", "X4", "X5", "X6", "X7", "X8", "X9", "X10", "X11", "X12", "X13", "X14", "X15", "X16", "X17", "X18", "X19", "X20", "X21", "X22", "X23", "X24", "X25")],
ordered)
#Import data 2
ctt.data <- read.csv("C:/Goran/01 FAKS/4TT/Project/Data/SCORES.csv", header = TRUE)
#Matrix 2 [,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -18, -19, -20, -21, -23, -24)]
responses <- as.matrix(ctt.data)
#CFA testing
one.model = "model1 =~ X4 + X17 + X2 + X3 + X5 + X6 + X7 + X8 + X9 + X10 + X11 + X12 + X13 + X14 + X15 + X16 + X1 + X18 + X19 + X20 + X21 + X22 + X23 + X24 + X25"
#Run the model
one.fit = cfa(one.model,
data = responses,
estimator = "mlr")
semPaths(one.fit, whatLabels = "std", layout = "tree", intercepts = TRUE, residuals = TRUE)
summary(one.fit, standardized = TRUE, fit.measures = T, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 73 iterations
##
## Number of observations 105
##
## Estimator ML Robust
## Minimum Function Test Statistic 339.180 347.386
## Degrees of freedom 275 275
## P-value (Chi-square) 0.005 0.002
## Scaling correction factor 0.976
## for the Yuan-Bentler correction
##
## Model test baseline model:
##
## Minimum Function Test Statistic 521.769 517.868
## Degrees of freedom 300 300
## P-value 0.000 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.711 0.668
## Tucker-Lewis Index (TLI) 0.684 0.638
##
## Robust Comparative Fit Index (CFI) 0.678
## Robust Tucker-Lewis Index (TLI) 0.649
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1313.466 -1313.466
## Scaling correction factor 1.210
## for the MLR correction
## Loglikelihood unrestricted model (H1) -1143.876 -1143.876
## Scaling correction factor 1.026
## for the MLR correction
##
## Number of free parameters 75 75
## Akaike (AIC) 2776.931 2776.931
## Bayesian (BIC) 2975.978 2975.978
## Sample-size adjusted Bayesian (BIC) 2739.039 2739.039
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.047 0.050
## 90 Percent Confidence Interval 0.027 0.063 0.031 0.066
## P-value RMSEA <= 0.05 0.599 0.486
##
## Robust RMSEA 0.049
## 90 Percent Confidence Interval 0.031 0.065
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.082 0.082
##
## Parameter Estimates:
##
## Information Observed
## Standard Errors Robust.huber.white
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## model1 =~
## X4 1.000 0.242 0.494
## X17 0.951 0.256 3.721 0.000 0.230 0.461
## X2 0.312 0.210 1.488 0.137 0.076 0.285
## X3 0.532 0.203 2.623 0.009 0.129 0.358
## X5 0.511 0.257 1.993 0.046 0.124 0.277
## X6 0.106 0.204 0.522 0.602 0.026 0.066
## X7 0.413 0.248 1.669 0.095 0.100 0.214
## X8 0.844 0.273 3.097 0.002 0.204 0.410
## X9 0.401 0.273 1.470 0.141 0.097 0.203
## X10 0.256 0.258 0.992 0.321 0.062 0.138
## X11 0.954 0.289 3.295 0.001 0.231 0.463
## X12 0.478 0.231 2.064 0.039 0.116 0.322
## X13 0.941 0.332 2.832 0.005 0.228 0.580
## X14 0.111 0.214 0.517 0.605 0.027 0.070
## X15 0.667 0.182 3.668 0.000 0.162 0.365
## X16 0.214 0.244 0.877 0.380 0.052 0.109
## X1 0.344 0.183 1.877 0.061 0.083 0.212
## X18 0.853 0.297 2.878 0.004 0.207 0.467
## X19 0.550 0.257 2.141 0.032 0.133 0.476
## X20 0.313 0.242 1.291 0.197 0.076 0.164
## X21 0.388 0.254 1.527 0.127 0.094 0.441
## X22 0.607 0.175 3.459 0.001 0.147 0.329
## X23 0.639 0.329 1.944 0.052 0.155 0.346
## X24 -0.139 0.246 -0.563 0.573 -0.034 -0.070
## X25 0.837 0.294 2.846 0.004 0.203 0.427
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X4 0.600 0.048 12.550 0.000 0.600 1.225
## .X17 0.476 0.049 9.770 0.000 0.476 0.953
## .X2 0.924 0.026 35.681 0.000 0.924 3.482
## .X3 0.848 0.035 24.167 0.000 0.848 2.358
## .X5 0.724 0.044 16.588 0.000 0.724 1.619
## .X6 0.810 0.038 21.125 0.000 0.810 2.062
## .X7 0.676 0.046 14.808 0.000 0.676 1.445
## .X8 0.543 0.049 11.166 0.000 0.543 1.090
## .X9 0.648 0.047 13.891 0.000 0.648 1.356
## .X10 0.276 0.044 6.330 0.000 0.276 0.618
## .X11 0.533 0.049 10.954 0.000 0.533 1.069
## .X12 0.848 0.035 24.167 0.000 0.848 2.358
## .X13 0.810 0.038 21.125 0.000 0.810 2.062
## .X14 0.819 0.038 21.801 0.000 0.819 2.128
## .X15 0.267 0.043 6.179 0.000 0.267 0.603
## .X16 0.648 0.047 13.891 0.000 0.648 1.356
## .X1 0.810 0.038 21.125 0.000 0.810 2.062
## .X18 0.733 0.043 16.993 0.000 0.733 1.658
## .X19 0.914 0.027 33.466 0.000 0.914 3.266
## .X20 0.695 0.045 15.477 0.000 0.695 1.510
## .X21 0.952 0.021 45.826 0.000 0.952 4.472
## .X22 0.276 0.044 6.330 0.000 0.276 0.618
## .X23 0.724 0.044 16.588 0.000 0.724 1.619
## .X24 0.362 0.047 7.717 0.000 0.362 0.753
## .X25 0.657 0.046 14.186 0.000 0.657 1.384
## model1 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X4 0.181 0.026 7.074 0.000 0.181 0.756
## .X17 0.196 0.021 9.524 0.000 0.196 0.787
## .X2 0.065 0.020 3.304 0.001 0.065 0.919
## .X3 0.113 0.022 5.125 0.000 0.113 0.872
## .X5 0.185 0.022 8.436 0.000 0.185 0.923
## .X6 0.154 0.024 6.501 0.000 0.154 0.996
## .X7 0.209 0.019 11.180 0.000 0.209 0.954
## .X8 0.206 0.023 8.838 0.000 0.206 0.832
## .X9 0.219 0.018 12.388 0.000 0.219 0.959
## .X10 0.196 0.020 9.569 0.000 0.196 0.981
## .X11 0.196 0.023 8.502 0.000 0.196 0.786
## .X12 0.116 0.023 5.124 0.000 0.116 0.896
## .X13 0.102 0.026 3.979 0.000 0.102 0.663
## .X14 0.147 0.024 6.206 0.000 0.147 0.995
## .X15 0.169 0.017 9.898 0.000 0.169 0.867
## .X16 0.226 0.015 15.083 0.000 0.226 0.988
## .X1 0.147 0.023 6.425 0.000 0.147 0.955
## .X18 0.153 0.025 6.028 0.000 0.153 0.782
## .X19 0.061 0.017 3.608 0.000 0.061 0.774
## .X20 0.206 0.019 10.895 0.000 0.206 0.973
## .X21 0.037 0.012 3.102 0.002 0.037 0.805
## .X22 0.178 0.019 9.606 0.000 0.178 0.892
## .X23 0.176 0.024 7.302 0.000 0.176 0.880
## .X24 0.230 0.014 16.793 0.000 0.230 0.995
## .X25 0.184 0.024 7.724 0.000 0.184 0.818
## model1 0.059 0.024 2.448 0.014 1.000 1.000
##
## R-Square:
## Estimate
## X4 0.244
## X17 0.213
## X2 0.081
## X3 0.128
## X5 0.077
## X6 0.004
## X7 0.046
## X8 0.168
## X9 0.041
## X10 0.019
## X11 0.214
## X12 0.104
## X13 0.337
## X14 0.005
## X15 0.133
## X16 0.012
## X1 0.045
## X18 0.218
## X19 0.226
## X20 0.027
## X21 0.195
## X22 0.108
## X23 0.120
## X24 0.005
## X25 0.182
ci.reliability(data = responses, type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.7238847
##
## $se
## [1] 0.03656865
##
## $ci.lower
## [1] 0.6432098
##
## $ci.upper
## [1] 0.7827432
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#test 2
one.model = "model2 =~ X4 + X17 + X3 + X5 + X8 + X11 + X12 + X13 + X15 + X1 + X18 + X19 + X22 + X25"
#Run the model
one.fit = cfa(one.model,
data = responses,
estimator = "mlr")
semPaths(one.fit, whatLabels = "std", layout = "tree", intercepts = TRUE, residuals = TRUE)
summary(one.fit, standardized = TRUE, fit.measures = T, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 47 iterations
##
## Number of observations 105
##
## Estimator ML Robust
## Minimum Function Test Statistic 82.201 81.921
## Degrees of freedom 77 77
## P-value (Chi-square) 0.322 0.329
## Scaling correction factor 1.003
## for the Yuan-Bentler correction
##
## Model test baseline model:
##
## Minimum Function Test Statistic 219.873 212.253
## Degrees of freedom 91 91
## P-value 0.000 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.960 0.959
## Tucker-Lewis Index (TLI) 0.952 0.952
##
## Robust Comparative Fit Index (CFI) 0.961
## Robust Tucker-Lewis Index (TLI) 0.954
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -759.481 -759.481
## Scaling correction factor 1.049
## for the MLR correction
## Loglikelihood unrestricted model (H1) -718.380 -718.380
## Scaling correction factor 1.020
## for the MLR correction
##
## Number of free parameters 42 42
## Akaike (AIC) 1602.961 1602.961
## Bayesian (BIC) 1714.428 1714.428
## Sample-size adjusted Bayesian (BIC) 1581.742 1581.742
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.025 0.025
## 90 Percent Confidence Interval 0.000 0.062 0.000 0.062
## P-value RMSEA <= 0.05 0.837 0.842
##
## Robust RMSEA 0.025
## 90 Percent Confidence Interval 0.000 0.062
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.063 0.063
##
## Parameter Estimates:
##
## Information Observed
## Standard Errors Robust.huber.white
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## model2 =~
## X4 1.000 0.278 0.567
## X17 0.855 0.232 3.679 0.000 0.237 0.475
## X3 0.494 0.180 2.740 0.006 0.137 0.382
## X5 0.523 0.204 2.562 0.010 0.145 0.325
## X8 0.741 0.234 3.172 0.002 0.206 0.413
## X11 0.784 0.228 3.446 0.001 0.218 0.436
## X12 0.390 0.181 2.157 0.031 0.108 0.301
## X13 0.772 0.248 3.111 0.002 0.214 0.546
## X15 0.592 0.170 3.489 0.000 0.164 0.372
## X1 0.349 0.163 2.141 0.032 0.097 0.247
## X18 0.668 0.239 2.800 0.005 0.185 0.419
## X19 0.462 0.184 2.510 0.012 0.128 0.459
## X22 0.556 0.159 3.506 0.000 0.154 0.345
## X25 0.703 0.226 3.115 0.002 0.195 0.411
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X4 0.600 0.048 12.550 0.000 0.600 1.225
## .X17 0.476 0.049 9.770 0.000 0.476 0.953
## .X3 0.848 0.035 24.167 0.000 0.848 2.358
## .X5 0.724 0.044 16.588 0.000 0.724 1.619
## .X8 0.543 0.049 11.166 0.000 0.543 1.090
## .X11 0.533 0.049 10.954 0.000 0.533 1.069
## .X12 0.848 0.035 24.167 0.000 0.848 2.358
## .X13 0.810 0.038 21.125 0.000 0.810 2.062
## .X15 0.267 0.043 6.179 0.000 0.267 0.603
## .X1 0.810 0.038 21.125 0.000 0.810 2.062
## .X18 0.733 0.043 16.993 0.000 0.733 1.658
## .X19 0.914 0.027 33.466 0.000 0.914 3.266
## .X22 0.276 0.044 6.330 0.000 0.276 0.618
## .X25 0.657 0.046 14.186 0.000 0.657 1.384
## model2 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X4 0.163 0.027 6.123 0.000 0.163 0.679
## .X17 0.193 0.022 8.722 0.000 0.193 0.774
## .X3 0.110 0.021 5.173 0.000 0.110 0.854
## .X5 0.179 0.022 8.285 0.000 0.179 0.895
## .X8 0.206 0.024 8.582 0.000 0.206 0.829
## .X11 0.201 0.022 9.267 0.000 0.201 0.809
## .X12 0.117 0.023 5.212 0.000 0.117 0.909
## .X13 0.108 0.022 4.839 0.000 0.108 0.702
## .X15 0.169 0.018 9.257 0.000 0.169 0.862
## .X1 0.145 0.022 6.466 0.000 0.145 0.939
## .X18 0.161 0.025 6.573 0.000 0.161 0.824
## .X19 0.062 0.016 3.890 0.000 0.062 0.790
## .X22 0.176 0.018 9.735 0.000 0.176 0.881
## .X25 0.187 0.023 8.086 0.000 0.187 0.831
## model2 0.077 0.025 3.042 0.002 1.000 1.000
##
## R-Square:
## Estimate
## X4 0.321
## X17 0.226
## X3 0.146
## X5 0.105
## X8 0.171
## X11 0.191
## X12 0.091
## X13 0.298
## X15 0.138
## X1 0.061
## X18 0.176
## X19 0.210
## X22 0.119
## X25 0.169
ci.reliability(data = responses[,c( -2, -6, -7, -9, -10, -14, -16, -20, -21, -23, -24)], type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.7327189
##
## $se
## [1] 0.03466816
##
## $ci.lower
## [1] 0.6617799
##
## $ci.upper
## [1] 0.7965369
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#test 3
one.model = "model3 =~ X19 + X4 + X17 + X3 + X5 + X8 + X11 + X12 + X13 + X15 + X1 + X18 + X22 + X25"
#Run the model
one.fit = cfa(one.model,
data = data,
estimator = "wlsmv")
semPaths(one.fit, whatLabels = "std", layout = "tree", intercepts = TRUE, residuals = TRUE)
summary(one.fit, standardized = TRUE, fit.measures = T, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 18 iterations
##
## Number of observations 105
##
## Estimator DWLS Robust
## Minimum Function Test Statistic 50.580 71.771
## Degrees of freedom 77 77
## P-value (Chi-square) 0.991 0.647
## Scaling correction factor 1.079
## Shift parameter 24.916
## for simple second-order correction (Mplus variant)
##
## Model test baseline model:
##
## Minimum Function Test Statistic 409.067 284.767
## Degrees of freedom 91 91
## P-value 0.000 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.098 1.032
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.000
## 90 Percent Confidence Interval 0.000 0.000 0.000 0.048
## P-value RMSEA <= 0.05 1.000 0.961
##
## Robust RMSEA NA
## 90 Percent Confidence Interval 0.000 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.117 0.117
##
## Weighted Root Mean Square Residual:
##
## WRMR 0.694 0.694
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Robust.sem
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## model3 =~
## X19 1.000 0.771 0.771
## X4 0.956 0.234 4.085 0.000 0.737 0.737
## X17 0.812 0.209 3.883 0.000 0.626 0.626
## X3 0.711 0.238 2.994 0.003 0.548 0.548
## X5 0.574 0.220 2.609 0.009 0.442 0.442
## X8 0.688 0.228 3.013 0.003 0.530 0.530
## X11 0.718 0.199 3.612 0.000 0.554 0.554
## X12 0.595 0.232 2.559 0.010 0.459 0.459
## X13 0.965 0.249 3.880 0.000 0.744 0.744
## X15 0.677 0.206 3.279 0.001 0.522 0.522
## X1 0.476 0.203 2.346 0.019 0.367 0.367
## X18 0.713 0.204 3.503 0.000 0.550 0.550
## X22 0.650 0.195 3.339 0.001 0.501 0.501
## X25 0.700 0.209 3.350 0.001 0.540 0.540
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X19 0.000 0.000 0.000
## .X4 0.000 0.000 0.000
## .X17 0.000 0.000 0.000
## .X3 0.000 0.000 0.000
## .X5 0.000 0.000 0.000
## .X8 0.000 0.000 0.000
## .X11 0.000 0.000 0.000
## .X12 0.000 0.000 0.000
## .X13 0.000 0.000 0.000
## .X15 0.000 0.000 0.000
## .X1 0.000 0.000 0.000
## .X18 0.000 0.000 0.000
## .X22 0.000 0.000 0.000
## .X25 0.000 0.000 0.000
## model3 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X19|t1 -1.368 0.175 -7.801 0.000 -1.368 -1.368
## X4|t1 -0.253 0.124 -2.038 0.042 -0.253 -0.253
## X17|t1 0.060 0.123 0.486 0.627 0.060 0.060
## X3|t1 -1.026 0.150 -6.861 0.000 -1.026 -1.026
## X5|t1 -0.594 0.131 -4.532 0.000 -0.594 -0.594
## X8|t1 -0.108 0.123 -0.874 0.382 -0.108 -0.108
## X11|t1 -0.084 0.123 -0.680 0.497 -0.084 -0.084
## X12|t1 -1.026 0.150 -6.861 0.000 -1.026 -1.026
## X13|t1 -0.876 0.142 -6.184 0.000 -0.876 -0.876
## X15|t1 0.623 0.132 4.720 0.000 0.623 0.623
## X1|t1 -0.876 0.142 -6.184 0.000 -0.876 -0.876
## X18|t1 -0.623 0.132 -4.720 0.000 -0.623 -0.623
## X22|t1 0.594 0.131 4.532 0.000 0.594 0.594
## X25|t1 -0.405 0.127 -3.196 0.001 -0.405 -0.405
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X19 0.405 0.405 0.405
## .X4 0.457 0.457 0.457
## .X17 0.608 0.608 0.608
## .X3 0.699 0.699 0.699
## .X5 0.804 0.804 0.804
## .X8 0.719 0.719 0.719
## .X11 0.693 0.693 0.693
## .X12 0.790 0.790 0.790
## .X13 0.447 0.447 0.447
## .X15 0.728 0.728 0.728
## .X1 0.865 0.865 0.865
## .X18 0.698 0.698 0.698
## .X22 0.749 0.749 0.749
## .X25 0.709 0.709 0.709
## model3 0.595 0.252 2.356 0.018 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X19 1.000 1.000 1.000
## X4 1.000 1.000 1.000
## X17 1.000 1.000 1.000
## X3 1.000 1.000 1.000
## X5 1.000 1.000 1.000
## X8 1.000 1.000 1.000
## X11 1.000 1.000 1.000
## X12 1.000 1.000 1.000
## X13 1.000 1.000 1.000
## X15 1.000 1.000 1.000
## X1 1.000 1.000 1.000
## X18 1.000 1.000 1.000
## X22 1.000 1.000 1.000
## X25 1.000 1.000 1.000
##
## R-Square:
## Estimate
## X19 0.595
## X4 0.543
## X17 0.392
## X3 0.301
## X5 0.196
## X8 0.281
## X11 0.307
## X12 0.210
## X13 0.553
## X15 0.272
## X1 0.135
## X18 0.302
## X22 0.251
## X25 0.291
ci.reliability(data = responses[,c( -2, -6, -7, -9, -10, -14, -16, -20, -21, -23, -24)], type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.7327189
##
## $se
## [1] 0.03492094
##
## $ci.lower
## [1] 0.6586863
##
## $ci.upper
## [1] 0.7933485
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#Test 4
one.model = "science =~ X4 + X17 + X3 + X5 + X8 + X11 + X12 + X13 + X15 + X1 + X18 + X22 + X25"
#Run the model
one.fit = cfa(one.model,
data = data,
estimator = "wlsmv")
semPaths(one.fit, whatLabels = "std", layout = "tree", intercepts = TRUE, residuals = TRUE)
summary(one.fit, standardized = TRUE, fit.measures = T, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 19 iterations
##
## Number of observations 105
##
## Estimator DWLS Robust
## Minimum Function Test Statistic 43.101 61.022
## Degrees of freedom 65 65
## P-value (Chi-square) 0.983 0.617
## Scaling correction factor 1.043
## Shift parameter 19.686
## for simple second-order correction (Mplus variant)
##
## Model test baseline model:
##
## Minimum Function Test Statistic 335.008 243.611
## Degrees of freedom 78 78
## P-value 0.000 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.102 1.029
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.000
## 90 Percent Confidence Interval 0.000 0.000 0.000 0.052
## P-value RMSEA <= 0.05 1.000 0.942
##
## Robust RMSEA NA
## 90 Percent Confidence Interval 0.000 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.111 0.111
##
## Weighted Root Mean Square Residual:
##
## WRMR 0.688 0.688
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Robust.sem
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## science =~
## X4 1.000 0.717 0.717
## X17 0.857 0.194 4.418 0.000 0.615 0.615
## X3 0.780 0.216 3.609 0.000 0.560 0.560
## X5 0.656 0.210 3.130 0.002 0.471 0.471
## X8 0.781 0.211 3.703 0.000 0.560 0.560
## X11 0.775 0.204 3.796 0.000 0.556 0.556
## X12 0.644 0.257 2.508 0.012 0.462 0.462
## X13 0.996 0.222 4.493 0.000 0.715 0.715
## X15 0.718 0.207 3.471 0.001 0.515 0.515
## X1 0.542 0.195 2.772 0.006 0.389 0.389
## X18 0.736 0.220 3.355 0.001 0.528 0.528
## X22 0.686 0.163 4.200 0.000 0.492 0.492
## X25 0.796 0.198 4.018 0.000 0.571 0.571
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X4 0.000 0.000 0.000
## .X17 0.000 0.000 0.000
## .X3 0.000 0.000 0.000
## .X5 0.000 0.000 0.000
## .X8 0.000 0.000 0.000
## .X11 0.000 0.000 0.000
## .X12 0.000 0.000 0.000
## .X13 0.000 0.000 0.000
## .X15 0.000 0.000 0.000
## .X1 0.000 0.000 0.000
## .X18 0.000 0.000 0.000
## .X22 0.000 0.000 0.000
## .X25 0.000 0.000 0.000
## science 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X4|t1 -0.253 0.124 -2.038 0.042 -0.253 -0.253
## X17|t1 0.060 0.123 0.486 0.627 0.060 0.060
## X3|t1 -1.026 0.150 -6.861 0.000 -1.026 -1.026
## X5|t1 -0.594 0.131 -4.532 0.000 -0.594 -0.594
## X8|t1 -0.108 0.123 -0.874 0.382 -0.108 -0.108
## X11|t1 -0.084 0.123 -0.680 0.497 -0.084 -0.084
## X12|t1 -1.026 0.150 -6.861 0.000 -1.026 -1.026
## X13|t1 -0.876 0.142 -6.184 0.000 -0.876 -0.876
## X15|t1 0.623 0.132 4.720 0.000 0.623 0.623
## X1|t1 -0.876 0.142 -6.184 0.000 -0.876 -0.876
## X18|t1 -0.623 0.132 -4.720 0.000 -0.623 -0.623
## X22|t1 0.594 0.131 4.532 0.000 0.594 0.594
## X25|t1 -0.405 0.127 -3.196 0.001 -0.405 -0.405
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X4 0.485 0.485 0.485
## .X17 0.622 0.622 0.622
## .X3 0.687 0.687 0.687
## .X5 0.778 0.778 0.778
## .X8 0.686 0.686 0.686
## .X11 0.691 0.691 0.691
## .X12 0.787 0.787 0.787
## .X13 0.489 0.489 0.489
## .X15 0.735 0.735 0.735
## .X1 0.849 0.849 0.849
## .X18 0.721 0.721 0.721
## .X22 0.758 0.758 0.758
## .X25 0.674 0.674 0.674
## science 0.515 0.149 3.463 0.001 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X4 1.000 1.000 1.000
## X17 1.000 1.000 1.000
## X3 1.000 1.000 1.000
## X5 1.000 1.000 1.000
## X8 1.000 1.000 1.000
## X11 1.000 1.000 1.000
## X12 1.000 1.000 1.000
## X13 1.000 1.000 1.000
## X15 1.000 1.000 1.000
## X1 1.000 1.000 1.000
## X18 1.000 1.000 1.000
## X22 1.000 1.000 1.000
## X25 1.000 1.000 1.000
##
## R-Square:
## Estimate
## X4 0.515
## X17 0.378
## X3 0.313
## X5 0.222
## X8 0.314
## X11 0.309
## X12 0.213
## X13 0.511
## X15 0.265
## X1 0.151
## X18 0.279
## X22 0.242
## X25 0.326
#Reliability
ci.reliability(data = responses[,c( -1, -2, -6, -7, -9, -10, -14, -16, -19, -20, -21, -23, -24)], type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.7173688
##
## $se
## [1] 0.03631823
##
## $ci.lower
## [1] 0.6360684
##
## $ci.upper
## [1] 0.7804222
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#test 4
one.model = "science =~ X13 + X4 + X17 + X3 + X5 + X8 + X11 + X15 + X18 + X25"
#Run the model
one.fit = cfa(one.model,
data = data,
estimator = "wlsmv")
semPaths(one.fit, whatLabels = "std", layout = "tree", intercepts = TRUE, residuals = TRUE)
summary(one.fit, standardized = TRUE, fit.measures = T, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 17 iterations
##
## Number of observations 105
##
## Estimator DWLS Robust
## Minimum Function Test Statistic 19.319 29.678
## Degrees of freedom 35 35
## P-value (Chi-square) 0.985 0.723
## Scaling correction factor 0.847
## Shift parameter 6.875
## for simple second-order correction (Mplus variant)
##
## Model test baseline model:
##
## Minimum Function Test Statistic 241.782 187.314
## Degrees of freedom 45 45
## P-value 0.000 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.102 1.048
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.000
## 90 Percent Confidence Interval 0.000 0.000 0.000 0.054
## P-value RMSEA <= 0.05 0.999 0.934
##
## Robust RMSEA NA
## 90 Percent Confidence Interval 0.000 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.094 0.094
##
## Weighted Root Mean Square Residual:
##
## WRMR 0.593 0.593
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Robust.sem
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## science =~
## X13 1.000 0.732 0.732
## X4 0.904 0.225 4.017 0.000 0.662 0.662
## X17 0.782 0.208 3.763 0.000 0.572 0.572
## X3 0.829 0.209 3.959 0.000 0.607 0.607
## X5 0.707 0.241 2.930 0.003 0.517 0.517
## X8 0.814 0.238 3.415 0.001 0.596 0.596
## X11 0.791 0.201 3.934 0.000 0.579 0.579
## X15 0.721 0.221 3.262 0.001 0.528 0.528
## X18 0.780 0.242 3.218 0.001 0.571 0.571
## X25 0.678 0.212 3.200 0.001 0.496 0.496
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X13 0.000 0.000 0.000
## .X4 0.000 0.000 0.000
## .X17 0.000 0.000 0.000
## .X3 0.000 0.000 0.000
## .X5 0.000 0.000 0.000
## .X8 0.000 0.000 0.000
## .X11 0.000 0.000 0.000
## .X15 0.000 0.000 0.000
## .X18 0.000 0.000 0.000
## .X25 0.000 0.000 0.000
## science 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X13|t1 -0.876 0.142 -6.184 0.000 -0.876 -0.876
## X4|t1 -0.253 0.124 -2.038 0.042 -0.253 -0.253
## X17|t1 0.060 0.123 0.486 0.627 0.060 0.060
## X3|t1 -1.026 0.150 -6.861 0.000 -1.026 -1.026
## X5|t1 -0.594 0.131 -4.532 0.000 -0.594 -0.594
## X8|t1 -0.108 0.123 -0.874 0.382 -0.108 -0.108
## X11|t1 -0.084 0.123 -0.680 0.497 -0.084 -0.084
## X15|t1 0.623 0.132 4.720 0.000 0.623 0.623
## X18|t1 -0.623 0.132 -4.720 0.000 -0.623 -0.623
## X25|t1 -0.405 0.127 -3.196 0.001 -0.405 -0.405
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X13 0.464 0.464 0.464
## .X4 0.562 0.562 0.562
## .X17 0.672 0.672 0.672
## .X3 0.631 0.631 0.631
## .X5 0.732 0.732 0.732
## .X8 0.645 0.645 0.645
## .X11 0.665 0.665 0.665
## .X15 0.721 0.721 0.721
## .X18 0.674 0.674 0.674
## .X25 0.754 0.754 0.754
## science 0.536 0.185 2.899 0.004 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X13 1.000 1.000 1.000
## X4 1.000 1.000 1.000
## X17 1.000 1.000 1.000
## X3 1.000 1.000 1.000
## X5 1.000 1.000 1.000
## X8 1.000 1.000 1.000
## X11 1.000 1.000 1.000
## X15 1.000 1.000 1.000
## X18 1.000 1.000 1.000
## X25 1.000 1.000 1.000
##
## R-Square:
## Estimate
## X13 0.536
## X4 0.438
## X17 0.328
## X3 0.369
## X5 0.268
## X8 0.355
## X11 0.335
## X15 0.279
## X18 0.326
## X25 0.246
#Test 5
one.model = "science =~ X13 + X4 + X8 + X11 + X15 + X17 + X18 + X25"
#Run the model
one.fit = cfa(one.model,
data = data,
estimator = "wlsmv")
lavInspect(one.fit, "zero.cell.tables")
## (There are no tables with empty cells for this fitted model)
semPaths(one.fit, whatLabels = "std", layout = "tree", intercepts = TRUE, residuals = TRUE)
summary(one.fit, standardized = TRUE, fit.measures = T, rsquare = TRUE)
## lavaan (0.5-23.1097) converged normally after 18 iterations
##
## Number of observations 105
##
## Estimator DWLS Robust
## Minimum Function Test Statistic 8.897 14.259
## Degrees of freedom 20 20
## P-value (Chi-square) 0.984 0.817
## Scaling correction factor 0.744
## Shift parameter 2.305
## for simple second-order correction (Mplus variant)
##
## Model test baseline model:
##
## Minimum Function Test Statistic 163.980 135.304
## Degrees of freedom 28 28
## P-value 0.000 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.114 1.075
##
## Robust Comparative Fit Index (CFI) NA
## Robust Tucker-Lewis Index (TLI) NA
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.000
## 90 Percent Confidence Interval 0.000 0.000 0.000 0.053
## P-value RMSEA <= 0.05 0.997 0.941
##
## Robust RMSEA NA
## 90 Percent Confidence Interval 0.000 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.074 0.074
##
## Weighted Root Mean Square Residual:
##
## WRMR 0.497 0.497
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Robust.sem
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## science =~
## X13 1.000 0.737 0.737
## X4 0.796 0.246 3.236 0.001 0.587 0.587
## X8 0.793 0.252 3.152 0.002 0.585 0.585
## X11 0.754 0.221 3.411 0.001 0.556 0.556
## X15 0.767 0.235 3.265 0.001 0.565 0.565
## X17 0.848 0.244 3.477 0.001 0.625 0.625
## X18 0.817 0.272 3.008 0.003 0.602 0.602
## X25 0.692 0.237 2.921 0.003 0.510 0.510
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X13 0.000 0.000 0.000
## .X4 0.000 0.000 0.000
## .X8 0.000 0.000 0.000
## .X11 0.000 0.000 0.000
## .X15 0.000 0.000 0.000
## .X17 0.000 0.000 0.000
## .X18 0.000 0.000 0.000
## .X25 0.000 0.000 0.000
## science 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X13|t1 -0.876 0.142 -6.184 0.000 -0.876 -0.876
## X4|t1 -0.253 0.124 -2.038 0.042 -0.253 -0.253
## X8|t1 -0.108 0.123 -0.874 0.382 -0.108 -0.108
## X11|t1 -0.084 0.123 -0.680 0.497 -0.084 -0.084
## X15|t1 0.623 0.132 4.720 0.000 0.623 0.623
## X17|t1 0.060 0.123 0.486 0.627 0.060 0.060
## X18|t1 -0.623 0.132 -4.720 0.000 -0.623 -0.623
## X25|t1 -0.405 0.127 -3.196 0.001 -0.405 -0.405
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X13 0.457 0.457 0.457
## .X4 0.656 0.656 0.656
## .X8 0.658 0.658 0.658
## .X11 0.691 0.691 0.691
## .X15 0.680 0.680 0.680
## .X17 0.609 0.609 0.609
## .X18 0.637 0.637 0.637
## .X25 0.740 0.740 0.740
## science 0.543 0.228 2.386 0.017 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X13 1.000 1.000 1.000
## X4 1.000 1.000 1.000
## X8 1.000 1.000 1.000
## X11 1.000 1.000 1.000
## X15 1.000 1.000 1.000
## X17 1.000 1.000 1.000
## X18 1.000 1.000 1.000
## X25 1.000 1.000 1.000
##
## R-Square:
## Estimate
## X13 0.543
## X4 0.344
## X8 0.342
## X11 0.309
## X15 0.320
## X17 0.391
## X18 0.363
## X25 0.260
ci.reliability(data = responses[,c( -1, -2, -3, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)], type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.6730051
##
## $se
## [1] 0.04915866
##
## $ci.lower
## [1] 0.5587039
##
## $ci.upper
## [1] 0.74821
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#IRT
#2PL model
IRTmodel = ltm(ctt.data[,c( -1, -2, -3, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)] ~z1, IRT.param = TRUE)
summary(IRTmodel)
##
## Call:
## ltm(formula = ctt.data[, c(-1, -2, -3, -5, -6, -7, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)] ~ z1, IRT.param = TRUE)
##
## Model Summary:
## log.Lik AIC BIC
## -491.1438 1014.288 1056.751
##
## Coefficients:
## value std.err z.vals
## Dffclt.X4 -0.4314 0.2375 -1.8159
## Dffclt.X8 -0.1908 0.2332 -0.8181
## Dffclt.X11 -0.1449 0.2286 -0.6340
## Dffclt.X13 -1.2381 0.2961 -4.1811
## Dffclt.X15 1.0464 0.3343 3.1299
## Dffclt.X17 0.1054 0.1918 0.5499
## Dffclt.X18 -1.0831 0.3410 -3.1767
## Dffclt.X25 -0.7916 0.3266 -2.4237
## Dscrmn.X4 1.1740 0.3955 2.9680
## Dscrmn.X8 1.0646 0.3783 2.8142
## Dscrmn.X11 1.0779 0.3766 2.8622
## Dscrmn.X13 1.7310 0.6037 2.8672
## Dscrmn.X15 1.2587 0.4899 2.5691
## Dscrmn.X17 1.3977 0.4707 2.9692
## Dscrmn.X18 1.1757 0.4067 2.8909
## Dscrmn.X25 0.9769 0.3524 2.7722
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Convergence: 0
## max(|grad|): <1e-06
## quasi-Newton: BFGS
item.fit(IRTmodel) #we want the chi^2 to be NON-SIGNIFICANT! But depends on sample size
##
## Item-Fit Statistics and P-values
##
## Call:
## ltm(formula = ctt.data[, c(-1, -2, -3, -5, -6, -7, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)] ~ z1, IRT.param = TRUE)
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## X4 8.5255 0.3839
## X8 16.9856 0.0303
## X11 14.7289 0.0646
## X13 10.0286 0.263
## X15 15.0775 0.0577
## X17 27.3406 0.0006
## X18 9.3359 0.3148
## X25 12.3213 0.1374
#3PL model
IRTmodel2 = tpm(data = ctt.data[,c( -1, -2, -3, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)],
type = "latent.trait", IRT.param = TRUE)
summary(IRTmodel2)
##
## Call:
## tpm(data = ctt.data[, c(-1, -2, -3, -5, -6, -7, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)], type = "latent.trait",
## IRT.param = TRUE)
##
## Model Summary:
## log.Lik AIC BIC
## -490.6555 1029.311 1093.006
##
## Coefficients:
## value std.err z.vals
## Gussng.X4 0.2792 0.1747 1.5986
## Gussng.X8 0.0000 0.0027 0.0084
## Gussng.X11 0.0001 0.0040 0.0124
## Gussng.X13 0.0020 0.0432 0.0472
## Gussng.X15 0.0000 0.0010 0.0049
## Gussng.X17 0.0827 0.2306 0.3587
## Gussng.X18 0.0009 0.0233 0.0385
## Gussng.X25 0.2285 0.4172 0.5476
## Dffclt.X4 0.1980 0.3980 0.4974
## Dffclt.X8 -0.1873 0.2332 -0.8031
## Dffclt.X11 -0.1457 0.2336 -0.6237
## Dffclt.X13 -1.2280 0.2988 -4.1095
## Dffclt.X15 1.0213 0.3146 3.2461
## Dffclt.X17 0.2718 0.4718 0.5762
## Dffclt.X18 -1.0476 0.3255 -3.2183
## Dffclt.X25 -0.2137 1.1162 -0.1914
## Dscrmn.X4 2.3637 2.0506 1.1527
## Dscrmn.X8 1.0653 0.3706 2.8745
## Dscrmn.X11 1.0475 0.3705 2.8277
## Dscrmn.X13 1.7487 0.6076 2.8778
## Dscrmn.X15 1.3123 0.4942 2.6555
## Dscrmn.X17 1.6982 1.3495 1.2584
## Dscrmn.X18 1.2316 0.4153 2.9659
## Dscrmn.X25 1.2984 1.0722 1.2110
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Optimizer: optim (BFGS)
## Convergence: 0
## max(|grad|): 0.019
item.fit(IRTmodel2) #we want the chi^2 to be NON-SIGNIFICANT! But depends on sample size
##
## Item-Fit Statistics and P-values
##
## Call:
## tpm(data = ctt.data[, c(-1, -2, -3, -5, -6, -7, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)], type = "latent.trait",
## IRT.param = TRUE)
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## X4 15.5121 0.03
## X8 15.6803 0.0282
## X11 14.6777 0.0404
## X13 13.1008 0.0697
## X15 8.1619 0.3185
## X17 15.8600 0.0264
## X18 12.1948 0.0943
## X25 10.4904 0.1624
#Mirt 2PL
mirtmodel2PL = mirt(data = ctt.data[,c( -1, -2, -3, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)],
model = 1,
itemtype = "2PL")
##
Iteration: 1, Log-Lik: -495.436, Max-Change: 0.38303
Iteration: 2, Log-Lik: -492.314, Max-Change: 0.21613
Iteration: 3, Log-Lik: -491.488, Max-Change: 0.12017
Iteration: 4, Log-Lik: -491.220, Max-Change: 0.05603
Iteration: 5, Log-Lik: -491.170, Max-Change: 0.03216
Iteration: 6, Log-Lik: -491.153, Max-Change: 0.01817
Iteration: 7, Log-Lik: -491.146, Max-Change: 0.00834
Iteration: 8, Log-Lik: -491.145, Max-Change: 0.00553
Iteration: 9, Log-Lik: -491.144, Max-Change: 0.00252
Iteration: 10, Log-Lik: -491.144, Max-Change: 0.00123
Iteration: 11, Log-Lik: -491.144, Max-Change: 0.00088
Iteration: 12, Log-Lik: -491.144, Max-Change: 0.00103
Iteration: 13, Log-Lik: -491.144, Max-Change: 0.00060
Iteration: 14, Log-Lik: -491.144, Max-Change: 0.00012
Iteration: 15, Log-Lik: -491.144, Max-Change: 0.00009
summary(mirtmodel2PL)
## F1 h2
## X4 0.568 0.322
## X8 0.530 0.281
## X11 0.535 0.286
## X13 0.713 0.508
## X15 0.595 0.354
## X17 0.635 0.403
## X18 0.568 0.323
## X25 0.498 0.248
##
## SS loadings: 2.725
## Proportion Var: 0.341
##
## Factor correlations:
##
## F1
## F1 1
itemfit(mirtmodel2PL) #item fit statistics
## item S_X2 df.S_X2 p.S_X2
## 1 X4 4.579 4 0.333
## 2 X8 11.403 4 0.022
## 3 X11 6.764 4 0.149
## 4 X13 1.765 3 0.623
## 5 X15 3.379 3 0.337
## 6 X17 3.581 4 0.466
## 7 X18 6.477 4 0.166
## 8 X25 2.149 5 0.828
#Mirt 3PL
mirtmodel3PL = mirt(data = ctt.data[,c( -1, -2, -3, -5, -6, -7, -8, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)],
model = 1,
itemtype = "3PL")
##
Iteration: 1, Log-Lik: -439.020, Max-Change: 1.97634
Iteration: 2, Log-Lik: -428.751, Max-Change: 0.68169
Iteration: 3, Log-Lik: -426.287, Max-Change: 0.32360
Iteration: 4, Log-Lik: -425.409, Max-Change: 1.20602
Iteration: 5, Log-Lik: -425.142, Max-Change: 8.95683
Iteration: 6, Log-Lik: -425.020, Max-Change: 0.12767
Iteration: 7, Log-Lik: -425.019, Max-Change: 0.12727
Iteration: 8, Log-Lik: -424.974, Max-Change: 0.10903
Iteration: 9, Log-Lik: -424.948, Max-Change: 0.09775
Iteration: 10, Log-Lik: -424.918, Max-Change: 0.03685
Iteration: 11, Log-Lik: -424.903, Max-Change: 0.02437
Iteration: 12, Log-Lik: -424.901, Max-Change: 0.02087
Iteration: 13, Log-Lik: -424.900, Max-Change: 0.01340
Iteration: 14, Log-Lik: -424.900, Max-Change: 0.00242
Iteration: 15, Log-Lik: -424.900, Max-Change: 0.01014
Iteration: 16, Log-Lik: -424.899, Max-Change: 0.00898
Iteration: 17, Log-Lik: -424.899, Max-Change: 0.00240
Iteration: 18, Log-Lik: -424.899, Max-Change: 0.00142
Iteration: 19, Log-Lik: -424.899, Max-Change: 0.00715
Iteration: 20, Log-Lik: -424.899, Max-Change: 0.00119
Iteration: 21, Log-Lik: -424.899, Max-Change: 0.00049
Iteration: 22, Log-Lik: -424.899, Max-Change: 0.00035
Iteration: 23, Log-Lik: -424.899, Max-Change: 0.00101
Iteration: 24, Log-Lik: -424.899, Max-Change: 0.00099
Iteration: 25, Log-Lik: -424.899, Max-Change: 0.00182
Iteration: 26, Log-Lik: -424.899, Max-Change: 0.00023
Iteration: 27, Log-Lik: -424.899, Max-Change: 0.00087
Iteration: 28, Log-Lik: -424.899, Max-Change: 0.00025
Iteration: 29, Log-Lik: -424.899, Max-Change: 0.00080
Iteration: 30, Log-Lik: -424.899, Max-Change: 0.00019
Iteration: 31, Log-Lik: -424.899, Max-Change: 0.00085
Iteration: 32, Log-Lik: -424.899, Max-Change: 0.00028
Iteration: 33, Log-Lik: -424.899, Max-Change: 0.00084
Iteration: 34, Log-Lik: -424.899, Max-Change: 0.00123
Iteration: 35, Log-Lik: -424.899, Max-Change: 0.00019
Iteration: 36, Log-Lik: -424.899, Max-Change: 0.00073
Iteration: 37, Log-Lik: -424.899, Max-Change: 0.00020
Iteration: 38, Log-Lik: -424.899, Max-Change: 0.00070
Iteration: 39, Log-Lik: -424.899, Max-Change: 0.00017
Iteration: 40, Log-Lik: -424.899, Max-Change: 0.00016
Iteration: 41, Log-Lik: -424.899, Max-Change: 0.00062
Iteration: 42, Log-Lik: -424.899, Max-Change: 0.00068
Iteration: 43, Log-Lik: -424.899, Max-Change: 0.00018
Iteration: 44, Log-Lik: -424.899, Max-Change: 0.00064
Iteration: 45, Log-Lik: -424.899, Max-Change: 0.00014
Iteration: 46, Log-Lik: -424.899, Max-Change: 0.00013
Iteration: 47, Log-Lik: -424.899, Max-Change: 0.00063
Iteration: 48, Log-Lik: -424.899, Max-Change: 0.00065
Iteration: 49, Log-Lik: -424.899, Max-Change: 0.00017
Iteration: 50, Log-Lik: -424.899, Max-Change: 0.00061
Iteration: 51, Log-Lik: -424.899, Max-Change: 0.00014
Iteration: 52, Log-Lik: -424.899, Max-Change: 0.00013
Iteration: 53, Log-Lik: -424.899, Max-Change: 0.00055
Iteration: 54, Log-Lik: -424.899, Max-Change: 0.00059
Iteration: 55, Log-Lik: -424.899, Max-Change: 0.00018
Iteration: 56, Log-Lik: -424.899, Max-Change: 0.00053
Iteration: 57, Log-Lik: -424.899, Max-Change: 0.00013
Iteration: 58, Log-Lik: -424.899, Max-Change: 0.00011
Iteration: 59, Log-Lik: -424.899, Max-Change: 0.00055
Iteration: 60, Log-Lik: -424.899, Max-Change: 0.00053
Iteration: 61, Log-Lik: -424.899, Max-Change: 0.00019
Iteration: 62, Log-Lik: -424.899, Max-Change: 0.00053
Iteration: 63, Log-Lik: -424.899, Max-Change: 0.00014
Iteration: 64, Log-Lik: -424.899, Max-Change: 0.00011
Iteration: 65, Log-Lik: -424.899, Max-Change: 0.00049
Iteration: 66, Log-Lik: -424.899, Max-Change: 0.00051
Iteration: 67, Log-Lik: -424.899, Max-Change: 0.00020
Iteration: 68, Log-Lik: -424.899, Max-Change: 0.00047
Iteration: 69, Log-Lik: -424.899, Max-Change: 0.00014
Iteration: 70, Log-Lik: -424.899, Max-Change: 0.00011
Iteration: 71, Log-Lik: -424.899, Max-Change: 0.00048
Iteration: 72, Log-Lik: -424.899, Max-Change: 0.00045
Iteration: 73, Log-Lik: -424.899, Max-Change: 0.00020
Iteration: 74, Log-Lik: -424.899, Max-Change: 0.00046
Iteration: 75, Log-Lik: -424.899, Max-Change: 0.00015
Iteration: 76, Log-Lik: -424.899, Max-Change: 0.00012
Iteration: 77, Log-Lik: -424.899, Max-Change: 0.00044
Iteration: 78, Log-Lik: -424.899, Max-Change: 0.00009
itemfit(mirtmodel3PL) #item fit statistics
## item S_X2 df.S_X2 p.S_X2
## 1 X4 3.744 3 0.291
## 2 X11 2.111 2 0.348
## 3 X13 0.171 1 0.679
## 4 X15 0.303 1 0.582
## 5 X17 2.235 2 0.327
## 6 X18 6.701 2 0.035
## 7 X25 0.715 3 0.870
#compare models & get model fit statistics, the function anova is ment only for model comparrsion!
anova(mirtmodel2PL, mirtmodel3PL)
##
## Model 1: mirt(data = ctt.data[, c(-1, -2, -3, -5, -6, -7, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)], model = 1, itemtype = "2PL")
## Model 2: mirt(data = ctt.data[, c(-1, -2, -3, -5, -6, -7, -8, -9, -10,
## -12, -14, -16, -19, -20, -21, -22, -23, -24)], model = 1,
## itemtype = "3PL")
## AIC AICc SABIC BIC logLik X2 df p
## 1 1014.288 1020.469 1006.204 1056.751 -491.144 NaN NaN NaN
## 2 891.798 902.931 881.188 947.531 -424.899 132.489 133 0.496
#2PL model2
IRTmodel = ltm(ctt.data[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)] ~z1, IRT.param = TRUE)
summary(IRTmodel)
##
## Call:
## ltm(formula = ctt.data[, c(-1, -2, -5, -6, -7, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)] ~ z1, IRT.param = TRUE)
##
## Model Summary:
## log.Lik AIC BIC
## -530.7005 1097.401 1145.172
##
## Coefficients:
## value std.err z.vals
## Dffclt.X3 -1.7661 0.5142 -3.4349
## Dffclt.X4 -0.4065 0.2198 -1.8490
## Dffclt.X8 -0.1993 0.2405 -0.8286
## Dffclt.X11 -0.1528 0.2369 -0.6450
## Dffclt.X13 -1.1737 0.2652 -4.4257
## Dffclt.X15 1.0405 0.3261 3.1910
## Dffclt.X17 0.1079 0.2040 0.5291
## Dffclt.X18 -1.1370 0.3664 -3.1032
## Dffclt.X25 -0.7946 0.3242 -2.4511
## Dscrmn.X3 1.2285 0.4743 2.5903
## Dscrmn.X4 1.2973 0.4222 3.0730
## Dscrmn.X8 1.0177 0.3590 2.8346
## Dscrmn.X11 1.0228 0.3566 2.8683
## Dscrmn.X13 1.9609 0.6981 2.8090
## Dscrmn.X15 1.2706 0.4802 2.6462
## Dscrmn.X17 1.2602 0.4172 3.0202
## Dscrmn.X18 1.0954 0.3826 2.8630
## Dscrmn.X25 0.9747 0.3448 2.8266
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Convergence: 0
## max(|grad|): 1.1e-06
## quasi-Newton: BFGS
knitr::kable(coef(IRTmodel),
align = "c",
caption = "")
| X3 |
-1.7661474 |
1.2284639 |
| X4 |
-0.4064987 |
1.2972918 |
| X8 |
-0.1992840 |
1.0176513 |
| X11 |
-0.1528179 |
1.0228019 |
| X13 |
-1.1737363 |
1.9608996 |
| X15 |
1.0404783 |
1.2706484 |
| X17 |
0.1079196 |
1.2601894 |
| X18 |
-1.1370237 |
1.0953515 |
| X25 |
-0.7946384 |
0.9746607 |
plot(IRTmodel, type = "ICC") #add argument items = ... for plot one item at a time
plot(IRTmodel, type = "IIC", items = 0) #test information function
#person.fit(IRTmodel)
item.fit(IRTmodel) #we want the chi^2 to be NON-SIGNIFICANT! But depends on sample size
##
## Item-Fit Statistics and P-values
##
## Call:
## ltm(formula = ctt.data[, c(-1, -2, -5, -6, -7, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)] ~ z1, IRT.param = TRUE)
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## X3 8.4967 0.3865
## X4 11.6202 0.169
## X8 10.4632 0.234
## X11 24.9142 0.0016
## X13 10.2793 0.246
## X15 12.1137 0.1462
## X17 15.6537 0.0476
## X18 6.6198 0.5782
## X25 5.0104 0.7565
#3PL model2
IRTmodel2 = tpm(data = ctt.data[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)],
type = "latent.trait", IRT.param = TRUE)
summary(IRTmodel2) #the summary is EFA
##
## Call:
## tpm(data = ctt.data[, c(-1, -2, -5, -6, -7, -9, -10, -12, -14,
## -16, -19, -20, -21, -22, -23, -24)], type = "latent.trait",
## IRT.param = TRUE)
##
## Model Summary:
## log.Lik AIC BIC
## -530.2731 1114.546 1186.203
##
## Coefficients:
## value std.err z.vals
## Gussng.X3 0.5849 0.2163 2.7039
## Gussng.X4 0.2294 0.2106 1.0895
## Gussng.X8 0.0000 0.0003 0.0008
## Gussng.X11 0.0000 0.0006 0.0019
## Gussng.X13 0.0009 0.0415 0.0228
## Gussng.X15 0.0000 0.0001 0.0002
## Gussng.X17 0.0101 NaN NaN
## Gussng.X18 0.0003 0.0155 0.0216
## Gussng.X25 0.2061 0.4543 0.4536
## Dffclt.X3 -0.3830 0.7117 -0.5382
## Dffclt.X4 0.0839 0.4700 0.1785
## Dffclt.X8 -0.1960 0.2407 -0.8141
## Dffclt.X11 -0.1499 0.2374 -0.6312
## Dffclt.X13 -1.1339 0.2623 -4.3220
## Dffclt.X15 1.0228 0.3129 3.2686
## Dffclt.X17 0.1339 NaN NaN
## Dffclt.X18 -1.1065 0.3508 -3.1540
## Dffclt.X25 -0.2787 1.2250 -0.2275
## Dscrmn.X3 2.6375 2.8048 0.9404
## Dscrmn.X4 2.0721 1.6706 1.2404
## Dscrmn.X8 1.0173 0.3560 2.8577
## Dscrmn.X11 1.0196 0.3482 2.9283
## Dscrmn.X13 2.1105 0.7956 2.6526
## Dscrmn.X15 1.3077 0.4823 2.7113
## Dscrmn.X17 1.2540 NaN NaN
## Dscrmn.X18 1.1352 0.3846 2.9519
## Dscrmn.X25 1.2207 1.0156 1.2019
##
## Integration:
## method: Gauss-Hermite
## quadrature points: 21
##
## Optimization:
## Optimizer: optim (BFGS)
## Convergence: 0
## max(|grad|): 0.0074
knitr::kable(coef(IRTmodel2),
align = "c",
caption = "")
| X3 |
0.5848557 |
-0.3830114 |
2.637543 |
| X4 |
0.2294450 |
0.0838892 |
2.072131 |
| X8 |
0.0000003 |
-0.1960008 |
1.017329 |
| X11 |
0.0000012 |
-0.1498838 |
1.019645 |
| X13 |
0.0009450 |
-1.1338687 |
2.110485 |
| X15 |
0.0000000 |
1.0228345 |
1.307739 |
| X17 |
0.0100587 |
0.1339429 |
1.254030 |
| X18 |
0.0003351 |
-1.1064647 |
1.135187 |
| X25 |
0.2060903 |
-0.2786587 |
1.220691 |
plot(IRTmodel2, type = "ICC")
plot(IRTmodel2, type = "IIC", items = 0) #test information function
#person.fit(IRTmodel2) #check for outliers in the model
item.fit(IRTmodel2) #we want the chi^2 to be NON-SIGNIFICANT! But depends on sample size
##
## Item-Fit Statistics and P-values
##
## Call:
## tpm(data = ctt.data[, c(-1, -2, -5, -6, -7, -9, -10, -12, -14,
## -16, -19, -20, -21, -22, -23, -24)], type = "latent.trait",
## IRT.param = TRUE)
##
## Alternative: Items do not fit the model
## Ability Categories: 10
##
## X^2 Pr(>X^2)
## X3 11.9780 0.1013
## X4 9.8336 0.1982
## X8 9.7231 0.2048
## X11 21.5158 0.0031
## X13 9.2195 0.2373
## X15 8.8556 0.2632
## X17 13.9501 0.0521
## X18 9.9985 0.1887
## X25 4.5557 0.714
#Mirt 2PL "2"
mirtmodel2PL2 = mirt(data = ctt.data[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -20, -21, -22, -23, -24)],
model = 1,
itemtype = "2PL")
##
Iteration: 1, Log-Lik: -560.916, Max-Change: 0.51792
Iteration: 2, Log-Lik: -555.560, Max-Change: 0.30790
Iteration: 3, Log-Lik: -554.165, Max-Change: 0.17614
Iteration: 4, Log-Lik: -553.680, Max-Change: 0.08927
Iteration: 5, Log-Lik: -553.575, Max-Change: 0.05189
Iteration: 6, Log-Lik: -553.537, Max-Change: 0.03062
Iteration: 7, Log-Lik: -553.519, Max-Change: 0.00991
Iteration: 8, Log-Lik: -553.516, Max-Change: 0.01401
Iteration: 9, Log-Lik: -553.514, Max-Change: 0.00485
Iteration: 10, Log-Lik: -553.514, Max-Change: 0.00454
Iteration: 11, Log-Lik: -553.513, Max-Change: 0.00553
Iteration: 12, Log-Lik: -553.513, Max-Change: 0.00120
Iteration: 13, Log-Lik: -553.513, Max-Change: 0.00106
Iteration: 14, Log-Lik: -553.513, Max-Change: 0.00075
Iteration: 15, Log-Lik: -553.513, Max-Change: 0.00057
Iteration: 16, Log-Lik: -553.513, Max-Change: 0.00010
# -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -20, -21, -22, -23, -24
reliability(responses[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -20, -21, -22, -23, -24)])
##
## Number of Items
## 10
##
## Number of Examinees
## 105
##
## Coefficient Alpha
## 0.707
summary(mirtmodel2PL2)
## F1 h2
## X3 0.558 0.312
## X4 0.635 0.404
## X8 0.469 0.220
## X11 0.511 0.261
## X13 0.765 0.585
## X15 0.637 0.405
## X17 0.614 0.377
## X18 0.549 0.302
## X19 0.776 0.602
## X25 0.464 0.215
##
## SS loadings: 3.682
## Proportion Var: 0.368
##
## Factor correlations:
##
## F1
## F1 1
coef(mirtmodel2PL2, IRTpars = T) #coefficiants
## $X3
## a b g u
## par 1.146 -1.846 0 1
##
## $X4
## a b g u
## par 1.4 -0.384 0 1
##
## $X8
## a b g u
## par 0.903 -0.217 0 1
##
## $X11
## a b g u
## par 1.011 -0.152 0 1
##
## $X13
## a b g u
## par 2.02 -1.151 0 1
##
## $X15
## a b g u
## par 1.405 0.98 0 1
##
## $X17
## a b g u
## par 1.324 0.108 0 1
##
## $X18
## a b g u
## par 1.119 -1.117 0 1
##
## $X19
## a b g u
## par 2.095 -1.811 0 1
##
## $X25
## a b g u
## par 0.892 -0.846 0 1
##
## $GroupPars
## MEAN_1 COV_11
## par 0 1
plot(mirtmodel2PL2, type = "trace") #curves for all items
plot(mirtmodel2PL2, type = "info") # test information curve, optimal information is around 10
plot(mirtmodel2PL2) #expected total score
itemfit(mirtmodel2PL2) #item fit statistics
## item S_X2 df.S_X2 p.S_X2
## 1 X3 3.916 5 0.562
## 2 X4 4.502 4 0.342
## 3 X8 9.452 5 0.092
## 4 X11 4.871 5 0.432
## 5 X13 4.696 3 0.195
## 6 X15 2.152 3 0.542
## 7 X17 6.463 4 0.167
## 8 X18 7.299 5 0.199
## 9 X19 2.651 1 0.103
## 10 X25 11.222 6 0.082
M2(mirtmodel2PL2, residmat = TRUE) #model fit statistics
## X3 X4 X8 X11 X13
## X3 NA NA NA NA NA
## X4 0.117765686 NA NA NA NA
## X8 0.006720220 0.067684037 NA NA NA
## X11 -0.012586639 -0.004659849 0.1296609453 NA NA
## X13 0.110943428 -0.082859907 -0.0161902426 0.006228264 NA
## X15 -0.005200261 0.042429551 -0.0579038255 -0.062650517 -0.02088310
## X17 -0.083442996 -0.061136324 -0.0449770401 0.070463527 0.01513583
## X18 -0.055685971 -0.047764488 0.1525376935 -0.045533730 0.06829452
## X19 -0.041835114 0.088638932 -0.0976506697 0.021305890 0.07418675
## X25 0.003788198 -0.002120361 0.0006134005 -0.025577498 0.05686918
## X15 X17 X18 X19 X25
## X3 NA NA NA NA NA
## X4 NA NA NA NA NA
## X8 NA NA NA NA NA
## X11 NA NA NA NA NA
## X13 NA NA NA NA NA
## X15 NA NA NA NA NA
## X17 0.006227021 NA NA NA NA
## X18 -0.054891440 0.02843321 NA NA NA
## X19 0.042322293 0.03585802 0.077025773 NA NA
## X25 0.044706136 0.02437605 -0.001698038 -0.09986365 NA
#Mirt 3PL 2
mirtmodel3PL2 = mirt(data = ctt.data[,c( -1, -2, -5, -6, -7, -8, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)],
model = 1,
itemtype = "3PL")
##
Iteration: 1, Log-Lik: -479.402, Max-Change: 1.72924
Iteration: 2, Log-Lik: -468.248, Max-Change: 0.83988
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summary(mirtmodel3PL2)
## F1 h2
## X3 0.824 0.679
## X4 0.573 0.329
## X11 0.474 0.224
## X13 0.837 0.700
## X15 0.689 0.475
## X17 0.631 0.398
## X18 0.498 0.248
## X25 0.585 0.342
##
## SS loadings: 3.395
## Proportion Var: 0.424
##
## Factor correlations:
##
## F1
## F1 1
coef(mirtmodel3PL2, IRTpars = T) #coefficiants
## $X3
## a b g u
## par 2.476 -0.595 0.51 1
##
## $X4
## a b g u
## par 1.191 -0.428 0.003 1
##
## $X11
## a b g u
## par 0.915 -0.17 0 1
##
## $X13
## a b g u
## par 2.603 -1.051 0 1
##
## $X15
## a b g u
## par 1.619 1.018 0.033 1
##
## $X17
## a b g u
## par 1.383 0.162 0.031 1
##
## $X18
## a b g u
## par 0.977 -1.231 0 1
##
## $X25
## a b g u
## par 1.227 -0.377 0.166 1
##
## $GroupPars
## MEAN_1 COV_11
## par 0 1
plot(mirtmodel3PL2, type = "trace") #curves for all items
plot(mirtmodel3PL2, type = "info") # test information curve
plot(mirtmodel3PL2) #expected total score
itemfit(mirtmodel3PL2) #item fit statistics
## item S_X2 df.S_X2 p.S_X2
## 1 X3 1.758 2 0.415
## 2 X4 5.629 3 0.131
## 3 X11 3.903 3 0.272
## 4 X13 3.111 1 0.078
## 5 X15 0.029 1 0.865
## 6 X17 1.347 2 0.510
## 7 X18 4.395 2 0.111
## 8 X25 0.662 3 0.882
M2(mirtmodel3PL2)
## M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR TLI
## stats 7.510697 12 0.8221048 0 0 0.06118191 0.04937744 1.104076
## CFI
## stats 1
#compare models & model fit statistics
anova(mirtmodel2PL2, mirtmodel3PL2)
##
## Model 1: mirt(data = ctt.data[, c(-1, -2, -5, -6, -7, -9, -10, -12, -14,
## -16, -20, -21, -22, -23, -24)], model = 1, itemtype = "2PL")
## Model 2: mirt(data = ctt.data[, c(-1, -2, -5, -6, -7, -8, -9, -10, -12,
## -14, -16, -19, -20, -21, -22, -23, -24)], model = 1, itemtype = "3PL")
## AIC AICc SABIC BIC logLik X2 df p
## 1 1147.026 1157.026 1136.921 1200.105 -553.513 NaN NaN NaN
## 2 976.561 991.561 964.436 1040.256 -464.281 178.464 772 1
#item analysis
responses <- as.matrix(ctt.data[,c( -1, -2, -3, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)])
dimnames(responses) <- NULL
(N <- dim(responses) [2])
## [1] 8
(K <- dim(responses) [1])
## [1] 105
#Histogram
Summed <- data.frame(rowSums(responses))
colnames(Summed) <- c("Total")
cleanup = theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_blank(),
axis.line.y = element_line(color = "black"),
axis.line.x = element_line(color = "black"))
Histogram1 = ggplot(data = Summed, aes(Total))
Histogram1 + #Don't add TITLE (APA)
geom_histogram(binwidth = .5, #change the binwidh to adjust the columns
color = "black", #Google hex color picker
fill = "black") +
xlab("Total Score") +
ylab("Freqency") +
cleanup #You can choose other themes with theme_
#Descriptives
#Percentiles and Z values
#X<=Score Probability
scale(Summed)
## Total
## [1,] -2.2236228
## [2,] 1.6276002
## [3,] 1.1461973
## [4,] 1.1461973
## [5,] -0.7794142
## [6,] 1.1461973
## [7,] 0.1833916
## [8,] 0.1833916
## [9,] -0.7794142
## [10,] -0.7794142
## [11,] 0.6647944
## [12,] -1.2608170
## [13,] 0.1833916
## [14,] 0.1833916
## [15,] 0.1833916
## [16,] -0.7794142
## [17,] 0.1833916
## [18,] -1.2608170
## [19,] 0.1833916
## [20,] 0.1833916
## [21,] 1.1461973
## [22,] 0.1833916
## [23,] 1.1461973
## [24,] 1.1461973
## [25,] 0.1833916
## [26,] 0.6647944
## [27,] 0.6647944
## [28,] -0.2980113
## [29,] -1.7422199
## [30,] 1.6276002
## [31,] 0.1833916
## [32,] -1.7422199
## [33,] 1.1461973
## [34,] -0.2980113
## [35,] -1.2608170
## [36,] 0.6647944
## [37,] 0.1833916
## [38,] 1.6276002
## [39,] -0.2980113
## [40,] -0.2980113
## [41,] 0.1833916
## [42,] -1.7422199
## [43,] -0.2980113
## [44,] -0.2980113
## [45,] -1.2608170
## [46,] -1.7422199
## [47,] 1.1461973
## [48,] 1.1461973
## [49,] -1.7422199
## [50,] -0.2980113
## [51,] 1.1461973
## [52,] 0.1833916
## [53,] 0.6647944
## [54,] -1.2608170
## [55,] -1.7422199
## [56,] -1.2608170
## [57,] 0.1833916
## [58,] 0.1833916
## [59,] 0.1833916
## [60,] -2.2236228
## [61,] -0.2980113
## [62,] -0.7794142
## [63,] 0.6647944
## [64,] -1.2608170
## [65,] 1.1461973
## [66,] 0.6647944
## [67,] -0.7794142
## [68,] 0.6647944
## [69,] -0.7794142
## [70,] 1.1461973
## [71,] 0.6647944
## [72,] 0.6647944
## [73,] 0.6647944
## [74,] 1.1461973
## [75,] 1.1461973
## [76,] 0.1833916
## [77,] 0.6647944
## [78,] 0.6647944
## [79,] 1.1461973
## [80,] -2.2236228
## [81,] 1.1461973
## [82,] 1.1461973
## [83,] -0.2980113
## [84,] 1.6276002
## [85,] -0.2980113
## [86,] 0.6647944
## [87,] -0.2980113
## [88,] 0.1833916
## [89,] -0.7794142
## [90,] 1.1461973
## [91,] 0.6647944
## [92,] -1.7422199
## [93,] -0.2980113
## [94,] 0.6647944
## [95,] 0.6647944
## [96,] -0.2980113
## [97,] -0.2980113
## [98,] -0.7794142
## [99,] -1.2608170
## [100,] -1.7422199
## [101,] 1.1461973
## [102,] -1.2608170
## [103,] -0.2980113
## [104,] 0.1833916
## [105,] 0.1833916
## attr(,"scaled:center")
## Total
## 4.619048
## attr(,"scaled:scale")
## Total
## 2.077262
#cumulative percent
pnorm(q = 0, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.01308768
pnorm(q = 1, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.04073697
pnorm(q = 2, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.1036915
pnorm(q = 3, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.2178746
pnorm(q = 4, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.382856
pnorm(q = 5, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.5727636
pnorm(q = 6, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.7469164
pnorm(q = 7, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.874148
pnorm(q = 8, mean = 4.619, sd = 2.077262, lower.tail = T)
## [1] 0.9481976
#Zscores
qnorm(p = pnorm(q = 0, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] -2.2236
qnorm(p = pnorm(q = 1, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] -1.742197
qnorm(p = pnorm(q = 2, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] -1.260794
qnorm(p = pnorm(q = 3, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] -0.7793913
qnorm(p = pnorm(q = 4, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] -0.2979884
qnorm(p = pnorm(q = 5, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] 0.1834145
qnorm(p = pnorm(q = 6, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] 0.6648174
qnorm(p = pnorm(q = 7, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] 1.14622
qnorm(p = pnorm(q = 8, mean = 4.619, sd = 2.077262, lower.tail = T))
## [1] 1.627623
#Probability density function
Score <- seq(from=0, to=8, by=0.04)
probability_density <- dnorm(Score, mean = 4.619, sd = 2.077262)
plot(Score, probability_density, type = "l")
#Alpha Ver. 1
cronbachs.alpha <-
function(X){
X <- data.matrix(responses)
n <- ncol(X) #number of items
k <- nrow(X) #number of examinees
#formula
alphaC <- (n/(n - 1))*(1 - sum(apply(
X, 2, var))/var(rowSums(X)))
return(list("Cronbach's alpha" = alphaC,
"Number of items" = n,
"Number of examinees" = k))
}
dump("cronbachs.alpha", file = "cronbachs.alpha.R")
#Alpha Ver. 2
cronbachs.alpha(responses)
## $`Cronbach's alpha`
## [1] 0.6730051
##
## $`Number of items`
## [1] 8
##
## $`Number of examinees`
## [1] 105
#KR-20
KR20 <-
function(X){
X <- data.matrix(X)
k <- ncol(X)
# Person total score variances
SX <- var(rowSums(X))
# item means
IM <- colMeans(X)
return(((k/(k - 1))*((SX - sum(IM*(1 - IM)))/SX)))
}
dump("KR20", file = "KR20.R")
KR20(responses)
## [1] 0.6774799
# Kuder-Richardson formula 21
KR21 <-
function(X){
X <- data.matrix(X)
n <- ncol(X)
return((n/(n-1))*((var(rowSums(X)) - n*(sum(colMeans(X))/n) *
(1-(sum(colMeans(X))/n))))/var(rowSums(X)))
}
dump("KR21", file = "KR21.R")
KR21(responses)
## [1] 0.625833
#Covariances
covar = cov(responses, method = "pearson")
covar
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.24230769 0.06538462 0.05192308 0.03846154 0.05961538 0.04807692
## [2,] 0.06538462 0.25054945 0.07307692 0.03708791 0.02692308 0.03708791
## [3,] 0.05192308 0.07307692 0.25128205 0.04487179 0.02948718 0.07051282
## [4,] 0.03846154 0.03708791 0.04487179 0.15567766 0.03205128 0.05311355
## [5,] 0.05961538 0.02692308 0.02948718 0.03205128 0.19743590 0.05448718
## [6,] 0.04807692 0.03708791 0.07051282 0.05311355 0.05448718 0.25183150
## [7,] 0.03653846 0.06923077 0.02820513 0.05448718 0.02371795 0.05128205
## [8,] 0.04423077 0.03406593 0.03076923 0.04945055 0.04423077 0.04945055
## [,7] [,8]
## [1,] 0.03653846 0.04423077
## [2,] 0.06923077 0.03406593
## [3,] 0.02820513 0.03076923
## [4,] 0.05448718 0.04945055
## [5,] 0.02371795 0.04423077
## [6,] 0.05128205 0.04945055
## [7,] 0.19743590 0.03269231
## [8,] 0.03269231 0.22747253
#the problem with corr tables is that they dont have a cutoff value. We could risk it and declare 0.1 and lower as being a bad value
#Correlation
cor(x = responses, method = "pearson")
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1.0000000 0.2653660 0.2104244 0.1980295 0.2725597 0.1946247 0.1670527
## [2,] 0.2653660 1.0000000 0.2912412 0.1877900 0.1210500 0.1476490 0.3112715
## [3,] 0.2104244 0.2912412 1.0000000 0.2268713 0.1323852 0.2803060 0.1266293
## [4,] 0.1980295 0.1877900 0.2268713 1.0000000 0.1828181 0.2682484 0.3107908
## [5,] 0.2725597 0.1210500 0.1323852 0.1828181 1.0000000 0.2443578 0.1201299
## [6,] 0.1946247 0.1476490 0.2803060 0.2682484 0.2443578 1.0000000 0.2299838
## [7,] 0.1670527 0.3112715 0.1266293 0.3107908 0.1201299 0.2299838 1.0000000
## [8,] 0.1883981 0.1426951 0.1286979 0.2627807 0.2087118 0.2066101 0.1542652
## [,8]
## [1,] 0.1883981
## [2,] 0.1426951
## [3,] 0.1286979
## [4,] 0.2627807
## [5,] 0.2087118
## [6,] 0.2066101
## [7,] 0.1542652
## [8,] 1.0000000
#CTT
#Reliability
str(reliability(responses, itemal=TRUE), vec.len = 25) #vec.len numeric (>= 0) indicating how many 'first few' elements are displayed of each vector.
## List of 9
## $ nItem : int 8
## $ nPerson : int 105
## $ alpha : num 0.673
## $ scaleMean : num 4.62
## $ scaleSD : num 2.08
## $ alphaIfDeleted: num [1:8(1d)] 0.639 0.641 0.645 0.633 0.652 0.634 0.645 0.654
## $ pBis : num [1:8(1d)] 0.38 0.373 0.355 0.417 0.322 0.397 0.355 0.318
## $ bis : num [1:8(1d)] 0.461 0.449 0.436 0.537 0.476 0.494 0.436 0.392
## $ itemMean : num [1:8] 0.6 0.543 0.533 0.81 0.267 0.476 0.733 0.657
## - attr(*, "class")= chr "reliability"
#CI for discrimination. package psychometric
CIr(r = 0.380, n = 105, level = 0.9)
## [1] 0.2328444 0.5101440
CIr(r = 0.373, n = 105, level = 0.9)
## [1] 0.2251159 0.5040854
CIr(r = 0.355, n = 105, level = 0.9)
## [1] 0.2053277 0.4884465
CIr(r = 0.417, n = 105, level = 0.9)
## [1] 0.2740063 0.5419552
CIr(r = 0.322, n = 105, level = 0.9)
## [1] 0.1693643 0.4595508
CIr(r = 0.397, n = 105, level = 0.9)
## [1] 0.2516914 0.5248043
CIr(r = 0.355, n = 105, level = 0.9)
## [1] 0.2053277 0.4884465
CIr(r = 0.318, n = 105, level = 0.9)
## [1] 0.1650325 0.4560284
#Alpha and Omega
ci.reliability(data = responses, type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.6730051
##
## $se
## [1] 0.04823633
##
## $ci.lower
## [1] 0.5736695
##
## $ci.upper
## [1] 0.756275
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#Item analysis
knitr::kable(item.exam(responses, y = NULL, discrim = TRUE),
align = "c",
caption = "Item Analysis")
Item Analysis
| 0.4922476 |
0.5736164 |
0.3801324 |
0.6000000 |
0.6857143 |
NA |
0.2810135 |
0.1862261 |
NA |
| 0.5005491 |
0.5707085 |
0.3726389 |
0.5428571 |
0.6857143 |
NA |
0.2843041 |
0.1856337 |
NA |
| 0.5012804 |
0.5571241 |
0.3554569 |
0.5333333 |
0.5714286 |
NA |
0.2779423 |
0.1773330 |
NA |
| 0.3945601 |
0.5675925 |
0.4169282 |
0.8095238 |
0.4000000 |
NA |
0.2228803 |
0.1637180 |
NA |
| 0.4443376 |
0.5069836 |
0.3219158 |
0.2666667 |
0.5142857 |
NA |
0.2241966 |
0.1423565 |
NA |
| 0.5018282 |
0.5907766 |
0.3971923 |
0.4761905 |
0.6285714 |
NA |
0.2950532 |
0.1983709 |
NA |
| 0.4443376 |
0.5347635 |
0.3549832 |
0.7333333 |
0.4857143 |
NA |
0.2364813 |
0.1569795 |
NA |
| 0.4769408 |
0.5171561 |
0.3184780 |
0.6571429 |
0.6000000 |
NA |
0.2454755 |
0.1511701 |
NA |
#Sample.SD = Standard deviation of the item
#Item.total = Correlation of the item with the total test score
#Item.Tot.woi = Correlation of item with total test score (scored without item)
#Difficulty = Mean of the item (p)
#Discrimination = Discrimination of the item (u-l)/n
#Item.Criterion = Correlation of the item with the Criterion (y)
#Item.Reliab = Item reliability index
#Item.Rel.woi = Item reliability index (scored without item)
#Item.Validity = Item validity index
#Spearman.brown
#If n.or.r="n", the function will return a new reliability; if n.or.r="r", the function
#will return the factor by which the test length must change to achieve a desired level of reliability.
#(input) The new test length or a desired level of reliability, depending on n.or.r
cronbach.alpha(responses, standardized = TRUE)
##
## Standardized Cronbach's alpha for the 'responses' data-set
##
## Items: 8
## Sample units: 105
## alpha: 0.676
H <- cronbach.alpha(responses, standardized = TRUE)
spearman.brown(H$alpha, input = 0.95, n.or.r = "r")
## $n.new
## [1] 9.126731
rel95 <- spearman.brown(H$alpha, input = 0.95, n.or.r = "r") #returns number of items neede to attain 0.95 reliability
rel.Factor <- rel95$n.new*11 #11=number of items in the model
round(rel.Factor)
## [1] 100
#Splithalf coeff.
splitHalf(responses, raw = FALSE, brute = FALSE, n.sample = 1000, covar = FALSE, check.keys = FALSE, key = NULL, use = "complete") # at use = complete/pairwise
## Split half reliabilities
## Call: splitHalf(r = responses, raw = FALSE, brute = FALSE, n.sample = 1000,
## covar = FALSE, check.keys = FALSE, key = NULL, use = "complete")
##
## Maximum split half reliability (lambda 4) = 0.75
## Guttman lambda 6 = 0.66
## Average split half reliability = 0.66
## Guttman lambda 3 (alpha) = 0.68
## Minimum split half reliability (beta) = 0.62
#Striatums H-index
H #standardised alpha
##
## Standardized Cronbach's alpha for the 'responses' data-set
##
## Items: 8
## Sample units: 105
## alpha: 0.676
G <- sqrt(H$alpha/(1-H$alpha))
G
## [1] 1.442843
Striatums = (4*G+1)/3
Striatums
## [1] 2.257124
round(Striatums)
## [1] 2
#Split items
SPLIT.ITEMS <-
function(X, seed = NULL){
# optional fixed seed
if (!is.null(seed)) {set.seed(seed)}
X <- as.matrix(responses)
# if n = 2x, then lengths Y1 = Y2
# if n = 2x+1, then lenths Y1 = Y2+1
n <- ncol(responses)
index <- sample(1:n, ceiling(n/2))
Y1 <- X[, index ]
Y2 <- X[, -index]
return(list(Y1, Y2))
}
dump("SPLIT.ITEMS", file = "SPLIT.ITEMS.R")
#Computes a bootstrapped (1,000 replicates) Pearson product-moment correlation coefficient between two random subsets of examinees.
pearson <-
function(X, seed = NULL, n = NULL){
source("SPLIT.ITEMS.R")
# optional fixed seed
if (!is.null(seed)) {set.seed(seed)}
# the number of bootstrap replicates
if (is.null(n)) {n <- 1e3}
X <- as.matrix(X)
r <- rep(NA, n)
for (i in 1:n) {
# split items
Y <- SPLIT.ITEMS(X)
# total scores
S1 <- as.matrix(rowSums(Y[[1]]))
S2 <- as.matrix(rowSums(Y[[2]]))
# residual scores
R1 <- S1 - mean(S1)
R2 <- S2 - mean(S2)
# Pearson product-moment correlation coefficient
r[i] <- (t(R1) %*% R2) / (sqrt((t(R1) %*% R1)) * sqrt((t(R2) %*% R2)))
}
return(mean(r))
}
dump("pearson", file = "pearson.R")
#Compute the Pearson product-moment correlation coefficient
pearson(responses, seed = 456, n = 1)
## [1] 0.5218566
# compare
# split items
set.seed(456)
Y <- SPLIT.ITEMS(responses)
# Total scores
S1 <- as.matrix(rowSums(Y[[1]]))
S2 <- as.matrix(rowSums(Y[[2]]))
cor(S1, S2)
## [,1]
## [1,] 0.5218566
#Standard Error of measurement
SEM <-
function(X){
source("cronbachs.alpha.R")
X <- data.matrix(responses)
return(sd(rowSums(responses)) * sqrt(1 - cronbachs.alpha(responses)[[1]]))
}
SEM(responses)
## [1] 1.187851
# 90% confidence interval for the true score
knitr::kable(head(cbind(lower_bound = round(rowSums(responses)-1.65* sd(rowSums(responses))*
sqrt(1-KR20(responses)), 2), observed = rowSums(responses),
upper_bound = round(rowSums(responses)+1.65* sd(rowSums(responses))*
sqrt(1-KR20(responses)), 2)), 105),
align = "c",
caption = "Item Scores")
Item Scores
| -1.95 |
0 |
1.95 |
| 6.05 |
8 |
9.95 |
| 5.05 |
7 |
8.95 |
| 5.05 |
7 |
8.95 |
| 1.05 |
3 |
4.95 |
| 5.05 |
7 |
8.95 |
| 3.05 |
5 |
6.95 |
| 3.05 |
5 |
6.95 |
| 1.05 |
3 |
4.95 |
| 1.05 |
3 |
4.95 |
| 4.05 |
6 |
7.95 |
| 0.05 |
2 |
3.95 |
| 3.05 |
5 |
6.95 |
| 3.05 |
5 |
6.95 |
| 3.05 |
5 |
6.95 |
| 1.05 |
3 |
4.95 |
| 3.05 |
5 |
6.95 |
| 0.05 |
2 |
3.95 |
| 3.05 |
5 |
6.95 |
| 3.05 |
5 |
6.95 |
| 5.05 |
7 |
8.95 |
| 3.05 |
5 |
6.95 |
| 5.05 |
7 |
8.95 |
| 5.05 |
7 |
8.95 |
| 3.05 |
5 |
6.95 |
| 4.05 |
6 |
7.95 |
| 4.05 |
6 |
7.95 |
| 2.05 |
4 |
5.95 |
| -0.95 |
1 |
2.95 |
| 6.05 |
8 |
9.95 |
| 3.05 |
5 |
6.95 |
| -0.95 |
1 |
2.95 |
| 5.05 |
7 |
8.95 |
| 2.05 |
4 |
5.95 |
| 0.05 |
2 |
3.95 |
| 4.05 |
6 |
7.95 |
| 3.05 |
5 |
6.95 |
| 6.05 |
8 |
9.95 |
| 2.05 |
4 |
5.95 |
| 2.05 |
4 |
5.95 |
| 3.05 |
5 |
6.95 |
| -0.95 |
1 |
2.95 |
| 2.05 |
4 |
5.95 |
| 2.05 |
4 |
5.95 |
| 0.05 |
2 |
3.95 |
| -0.95 |
1 |
2.95 |
| 5.05 |
7 |
8.95 |
| 5.05 |
7 |
8.95 |
| -0.95 |
1 |
2.95 |
| 2.05 |
4 |
5.95 |
| 5.05 |
7 |
8.95 |
| 3.05 |
5 |
6.95 |
| 4.05 |
6 |
7.95 |
| 0.05 |
2 |
3.95 |
| -0.95 |
1 |
2.95 |
| 0.05 |
2 |
3.95 |
| 3.05 |
5 |
6.95 |
| 3.05 |
5 |
6.95 |
| 3.05 |
5 |
6.95 |
| -1.95 |
0 |
1.95 |
| 2.05 |
4 |
5.95 |
| 1.05 |
3 |
4.95 |
| 4.05 |
6 |
7.95 |
| 0.05 |
2 |
3.95 |
| 5.05 |
7 |
8.95 |
| 4.05 |
6 |
7.95 |
| 1.05 |
3 |
4.95 |
| 4.05 |
6 |
7.95 |
| 1.05 |
3 |
4.95 |
| 5.05 |
7 |
8.95 |
| 4.05 |
6 |
7.95 |
| 4.05 |
6 |
7.95 |
| 4.05 |
6 |
7.95 |
| 5.05 |
7 |
8.95 |
| 5.05 |
7 |
8.95 |
| 3.05 |
5 |
6.95 |
| 4.05 |
6 |
7.95 |
| 4.05 |
6 |
7.95 |
| 5.05 |
7 |
8.95 |
| -1.95 |
0 |
1.95 |
| 5.05 |
7 |
8.95 |
| 5.05 |
7 |
8.95 |
| 2.05 |
4 |
5.95 |
| 6.05 |
8 |
9.95 |
| 2.05 |
4 |
5.95 |
| 4.05 |
6 |
7.95 |
| 2.05 |
4 |
5.95 |
| 3.05 |
5 |
6.95 |
| 1.05 |
3 |
4.95 |
| 5.05 |
7 |
8.95 |
| 4.05 |
6 |
7.95 |
| -0.95 |
1 |
2.95 |
| 2.05 |
4 |
5.95 |
| 4.05 |
6 |
7.95 |
| 4.05 |
6 |
7.95 |
| 2.05 |
4 |
5.95 |
| 2.05 |
4 |
5.95 |
| 1.05 |
3 |
4.95 |
| 0.05 |
2 |
3.95 |
| -0.95 |
1 |
2.95 |
| 5.05 |
7 |
8.95 |
| 0.05 |
2 |
3.95 |
| 2.05 |
4 |
5.95 |
| 3.05 |
5 |
6.95 |
| 3.05 |
5 |
6.95 |
#Item analysis
item.analysis <-
function(responses){
# CRITICAL VALUES
cvpb = 0.20
cvdl = 0.15
cvdu = 0.85
require(CTT, warn.conflicts = FALSE, quietly = TRUE)
(ctt.analysis <- CTT::reliability(responses, itemal = TRUE, NA.Delete = TRUE))
# Mark items that are potentially problematic
item.analysis <- data.frame(item = seq(1:ctt.analysis$nItem),
r.pbis = ctt.analysis$pBis,
bis = ctt.analysis$bis,
item.mean = ctt.analysis$itemMean,
alpha.del = ctt.analysis$alphaIfDeleted)
# code provided by Dr. Gordon Brooks
if (TRUE) {
item.analysis$check <-
ifelse(item.analysis$r.pbis < cvpb |
item.analysis$item.mean < cvdl |
item.analysis$item.mean > cvdu, "???", "")
}
return(item.analysis)
}
dump("item.analysis", file = "item.analysis.R")
knitr::kable(item.analysis(responses),
align = "c",
caption = "Item Analysis")
Item Analysis
| 1 |
0.3801324 |
0.4605445 |
0.6000000 |
0.6386423 |
|
| 2 |
0.3726389 |
0.4486398 |
0.5428571 |
0.6406295 |
|
| 3 |
0.3554569 |
0.4359285 |
0.5333333 |
0.6450951 |
|
| 4 |
0.4169282 |
0.5367995 |
0.8095238 |
0.6333678 |
|
| 5 |
0.3219158 |
0.4758539 |
0.2666667 |
0.6523966 |
|
| 6 |
0.3971923 |
0.4943629 |
0.4761905 |
0.6342028 |
|
| 7 |
0.3549832 |
0.4358341 |
0.7333333 |
0.6449155 |
|
| 8 |
0.3184780 |
0.3924045 |
0.6571429 |
0.6537634 |
|
#Item Difficulty
item.difficulty <-
function(responses){
# CRITICAL VALUES
cvpb = 0.20
cvdl = 0.15
cvdu = 0.85
require(CTT, warn.conflicts = FALSE, quietly = TRUE)
ctt.analysis <- CTT::reliability(responses, itemal = TRUE, NA.Delete = TRUE)
test_difficulty <- data.frame(item = 1:ctt.analysis$nItem ,
difficulty = ctt.analysis$itemMean)
plot(test_difficulty,
main = "Test Item Difficulty",
type = "p",
pch = 1,
cex = 2.8,
col = "purple",
ylab = "Item Mean (Difficulty)",
xlab = "Item Number",
ylim = c(0, 1),
xlim = c(0, ctt.analysis$nItem))
abline(h = cvdl, col = "tomato")
abline(h = cvdu, col = "tomato")
abline(h = .3, col = "dodgerblue")
abline(h = .7, col = "dodgerblue")
text(diff(range(test_difficulty[, 1]))/2, 0.7,
"maximum information range",
col = "dodger blue",
pos = 3)
text(diff(range(test_difficulty[, 1]))/2, cvdu,
"rule of thumb acceptable range",
col = "tomato",
pos = 3)
outlier2 <- data.matrix(subset(cbind(test_difficulty[, 1],
test_difficulty[, 2]),
subset = ((test_difficulty[, 2] > cvdl &
test_difficulty[, 2] < .3) |
(test_difficulty[, 2] < cvdu &
test_difficulty[, 2] > .7))))
text(outlier2, paste("i", outlier2[,1], sep = ""),
col = "dodgerblue",
cex = .7)
return(test_difficulty[order(test_difficulty$difficulty),])
}
dump("item.difficulty", file = "item.difficulty.R")
knitr::kable(item.difficulty(responses),
align = "c",
caption = "Difficulty")
Difficulty
| 5 |
5 |
0.2666667 |
| 6 |
6 |
0.4761905 |
| 3 |
3 |
0.5333333 |
| 2 |
2 |
0.5428571 |
| 1 |
1 |
0.6000000 |
| 8 |
8 |
0.6571429 |
| 7 |
7 |
0.7333333 |
| 4 |
4 |
0.8095238 |
#Item discrimination
item.discrimination <-
function(responses){
# CRITICAL VALUES
cvpb = 0.30
cvdl = 0.20
cvdu = 0.85
require(CTT, warn.conflicts = FALSE, quietly = TRUE)
ctt.analysis <- CTT::reliability(responses, itemal = TRUE, NA.Delete = TRUE)
item.discrimination <- data.frame(item = 1:ctt.analysis$nItem ,
discrimination = ctt.analysis$pBis)
plot(item.discrimination,
type = "p",
pch = 1,
cex = 3,
col = "purple",
ylab = "Item-Total Correlation",
xlab = "Item Number",
ylim = c(0, 1),
main = "Test Item Discriminations")
abline(h = cvpb, col = "green")
abline(h = cvdl, col = "red")
return(item.discrimination[order(item.discrimination$discrimination),])
}
dump("item.discrimination", file = "item.discrimination.R")
knitr::kable(item.discrimination(responses),
align = "c",
caption = "Item Discrimination")
Item Discrimination
| 8 |
8 |
0.3184780 |
| 5 |
5 |
0.3219158 |
| 7 |
7 |
0.3549832 |
| 3 |
3 |
0.3554569 |
| 2 |
2 |
0.3726389 |
| 1 |
1 |
0.3801324 |
| 6 |
6 |
0.3971923 |
| 4 |
4 |
0.4169282 |
#CI for discrimination. package psychometric
# Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum. p45-46
CIr(r = 0.380, n = 105, level = 0.9)
## [1] 0.2328444 0.5101440
CIr(r = 0.373, n = 105, level = 0.9)
## [1] 0.2251159 0.5040854
CIr(r = 0.355, n = 105, level = 0.9)
## [1] 0.2053277 0.4884465
CIr(r = 0.417, n = 105, level = 0.9)
## [1] 0.2740063 0.5419552
CIr(r = 0.322, n = 105, level = 0.9)
## [1] 0.1693643 0.4595508
CIr(r = 0.397, n = 105, level = 0.9)
## [1] 0.2516914 0.5248043
CIr(r = 0.355, n = 105, level = 0.9)
## [1] 0.2053277 0.4884465
CIr(r = 0.318, n = 105, level = 0.9)
## [1] 0.1650325 0.4560284
# CI for Z scores
CIz(z = -2.223622797, n = 105, level = 0.95)
## [1] -2.417688 -2.029557
CIz(z = -1.742219923, n = 105, level = 0.95)
## [1] -1.936285 -1.548155
CIz(z = -1.26081705, n = 105, level = 0.95)
## [1] -1.454882 -1.066752
CIz(z = -0.779414176, n = 105, level = 0.95)
## [1] -0.9734795 -0.5853488
CIz(z = -0.298011303, n = 105, level = 0.95)
## [1] -0.4920767 -0.1039460
CIz(z = 0.183391571, n = 105, level = 0.95)
## [1] -0.01067378 0.37745692
CIz(z = 0.664794444, n = 105, level = 0.95)
## [1] 0.4707291 0.8588598
CIz(z = 1.146197318, n = 105, level = 0.95)
## [1] 0.952132 1.340263
CIz(z = 1.627600192, n = 105, level = 0.95)
## [1] 1.433535 1.821666
#Item total correlation
test_item.total <-
function(responses){
# CRITICAL VALUES
cvpb = 0.20
cvdl = 0.40
cvdu = 0.85
require(CTT, warn.conflicts = FALSE, quietly = TRUE)
ctt.analysis <- CTT::reliability(responses, itemal = TRUE, NA.Delete = TRUE)
test_item.total <- data.frame(item = 1:ctt.analysis$nItem ,
biserial = ctt.analysis$bis)
plot(test_item.total,
main = "Test Item-Total Correlation",
type = "p",
pch = 1,
cex = 2.8,
col = "purple",
ylab = "Item-Total Correlation",
xlab = "Item Number",
ylim = c(0, 1),
xlim = c(0, ctt.analysis$nItem))
abline(h = cvpb, col = "red")
abline(h = cvdl, col = "green")
return(test_item.total[order(test_item.total$biserial),])
}
dump("test_item.total", file = "test_item.total.R")
knitr::kable(test_item.total(responses),
align = "c",
caption = "Item Total Correlation")
Item Total Correlation
| 8 |
8 |
0.3924045 |
| 7 |
7 |
0.4358341 |
| 3 |
3 |
0.4359285 |
| 2 |
2 |
0.4486398 |
| 1 |
1 |
0.4605445 |
| 5 |
5 |
0.4758539 |
| 6 |
6 |
0.4943629 |
| 4 |
4 |
0.5367995 |