#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)
#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] 0.03567848
##
## $ci.lower
## [1] 0.6470804
##
## $ci.upper
## [1] 0.7837675
##
## $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] 0.03585624
##
## $ci.lower
## [1] 0.65363
##
## $ci.upper
## [1] 0.7889003
##
## $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] 0.03524142
##
## $ci.lower
## [1] 0.6567089
##
## $ci.upper
## [1] 0.7895437
##
## $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( -2, -6, -7, -9, -10, -14, -16, -19, -20, -21, -23, -24)], type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.7195339
##
## $se
## [1] 0.0348314
##
## $ci.lower
## [1] 0.6454797
##
## $ci.upper
## [1] 0.7792268
##
## $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
#Reliability
ci.reliability(data = responses[,c( -1, -2, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)], type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.7042403
##
## $se
## [1] 0.03641389
##
## $ci.lower
## [1] 0.6236427
##
## $ci.upper
## [1] 0.7681296
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#Test 5
one.model = "science =~ X13 + X4 + X17 + 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 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
## X17 0.848 0.244 3.477 0.001 0.625 0.625
## 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
## 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
## .X17 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
## 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 0.457 0.457 0.457
## .X4 0.656 0.656 0.656
## .X17 0.609 0.609 0.609
## .X8 0.658 0.658 0.658
## .X11 0.691 0.691 0.691
## .X15 0.680 0.680 0.680
## .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
## X17 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 0.543
## X4 0.344
## X17 0.391
## X8 0.342
## X11 0.309
## X15 0.320
## X18 0.363
## X25 0.260
ci.reliability(data = responses[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)], type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.6882234
##
## $se
## [1] 0.04338226
##
## $ci.lower
## [1] 0.5995929
##
## $ci.upper
## [1] 0.7642254
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
#IRT
#2PL model
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 model
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)
##
## 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
#Compare models
anova(IRTmodel, IRTmodel2) # p=1, but I get an error
##
## Likelihood Ratio Table
## AIC BIC log.Lik LRT df p.value
## IRTmodel 1097.40 1145.17 -530.70
## IRTmodel2 1114.55 1186.20 -530.27 0.85 9 1
#If the P-value is non-sig, then the models are the same, thus it is better to use the simpler (2PL model)
#Mirt 2PL
mirtmodel2PL = mirt(data = ctt.data[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)],
model = 1,
itemtype = "2PL")
##
Iteration: 1, Log-Lik: -535.669, Max-Change: 0.46682
Iteration: 2, Log-Lik: -532.037, Max-Change: 0.26243
Iteration: 3, Log-Lik: -531.106, Max-Change: 0.15055
Iteration: 4, Log-Lik: -530.792, Max-Change: 0.07360
Iteration: 5, Log-Lik: -530.733, Max-Change: 0.04584
Iteration: 6, Log-Lik: -530.713, Max-Change: 0.02503
Iteration: 7, Log-Lik: -530.704, Max-Change: 0.01523
Iteration: 8, Log-Lik: -530.702, Max-Change: 0.00995
Iteration: 9, Log-Lik: -530.701, Max-Change: 0.00669
Iteration: 10, Log-Lik: -530.700, Max-Change: 0.00209
Iteration: 11, Log-Lik: -530.700, Max-Change: 0.00178
Iteration: 12, Log-Lik: -530.700, Max-Change: 0.00026
Iteration: 13, Log-Lik: -530.700, Max-Change: 0.00026
Iteration: 14, Log-Lik: -530.700, Max-Change: 0.00024
Iteration: 15, Log-Lik: -530.700, Max-Change: 0.00022
Iteration: 16, Log-Lik: -530.700, Max-Change: 0.00062
Iteration: 17, Log-Lik: -530.700, Max-Change: 0.00039
Iteration: 18, Log-Lik: -530.700, Max-Change: 0.00009
summary(mirtmodel2PL)
## F1 h2
## X3 0.585 0.343
## X4 0.606 0.368
## X8 0.513 0.263
## X11 0.515 0.265
## X13 0.755 0.570
## X15 0.598 0.358
## X17 0.595 0.354
## X18 0.541 0.293
## X25 0.497 0.247
##
## SS loadings: 3.061
## Proportion Var: 0.34
##
## Factor correlations:
##
## F1
## F1 1
coef(mirtmodel2PL, IRTpars = T) #coefficiants
## $X3
## a b g u
## par 1.228 -1.766 0 1
##
## $X4
## a b g u
## par 1.297 -0.406 0 1
##
## $X8
## a b g u
## par 1.018 -0.199 0 1
##
## $X11
## a b g u
## par 1.023 -0.153 0 1
##
## $X13
## a b g u
## par 1.96 -1.174 0 1
##
## $X15
## a b g u
## par 1.271 1.04 0 1
##
## $X17
## a b g u
## par 1.26 0.108 0 1
##
## $X18
## a b g u
## par 1.095 -1.137 0 1
##
## $X25
## a b g u
## par 0.975 -0.795 0 1
##
## $GroupPars
## MEAN_1 COV_11
## par 0 1
plot(mirtmodel2PL, type = "trace") #curves for all items
plot(mirtmodel2PL, type = "info") # test information curve
plot(mirtmodel2PL) #expected total score
itemfit(mirtmodel2PL) #item fit statistics
## item S_X2 df.S_X2 p.S_X2
## 1 X3 2.535 4 0.638
## 2 X4 5.628 5 0.344
## 3 X8 10.033 5 0.074
## 4 X11 5.843 5 0.322
## 5 X13 3.954 3 0.266
## 6 X15 2.437 3 0.487
## 7 X17 5.390 4 0.250
## 8 X18 6.898 4 0.141
## 9 X25 2.844 5 0.724
#Mirt 3PL
mirtmodel3PL = mirt(data = ctt.data[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)],
model = 1,
itemtype = "3PL")
##
Iteration: 1, Log-Lik: -546.002, Max-Change: 1.94463
Iteration: 2, Log-Lik: -534.246, Max-Change: 0.60847
Iteration: 3, Log-Lik: -531.882, Max-Change: 0.39205
Iteration: 4, Log-Lik: -530.852, Max-Change: 0.53347
Iteration: 5, Log-Lik: -530.646, Max-Change: 7.23756
Iteration: 6, Log-Lik: -530.492, Max-Change: 0.33958
Iteration: 7, Log-Lik: -530.490, Max-Change: 0.33891
Iteration: 8, Log-Lik: -530.436, Max-Change: 0.25473
Iteration: 9, Log-Lik: -530.394, Max-Change: 0.19928
Iteration: 10, Log-Lik: -530.390, Max-Change: 0.10935
Iteration: 11, Log-Lik: -530.292, Max-Change: 0.04600
Iteration: 12, Log-Lik: -530.284, Max-Change: 0.03750
Iteration: 13, Log-Lik: -530.273, Max-Change: 0.03269
Iteration: 14, Log-Lik: -530.272, Max-Change: 0.03639
Iteration: 15, Log-Lik: -530.271, Max-Change: 0.02347
Iteration: 16, Log-Lik: -530.270, Max-Change: 0.00915
Iteration: 17, Log-Lik: -530.270, Max-Change: 0.00189
Iteration: 18, Log-Lik: -530.270, Max-Change: 0.01593
Iteration: 19, Log-Lik: -530.270, Max-Change: 0.00024
Iteration: 20, Log-Lik: -530.270, Max-Change: 0.00092
Iteration: 21, Log-Lik: -530.270, Max-Change: 0.00017
Iteration: 22, Log-Lik: -530.270, Max-Change: 0.00074
Iteration: 23, Log-Lik: -530.270, Max-Change: 0.00042
Iteration: 24, Log-Lik: -530.270, Max-Change: 0.00078
Iteration: 25, Log-Lik: -530.270, Max-Change: 0.00045
Iteration: 26, Log-Lik: -530.270, Max-Change: 0.00076
Iteration: 27, Log-Lik: -530.270, Max-Change: 0.00030
Iteration: 28, Log-Lik: -530.270, Max-Change: 0.00024
Iteration: 29, Log-Lik: -530.270, Max-Change: 0.00078
Iteration: 30, Log-Lik: -530.270, Max-Change: 0.00016
Iteration: 31, Log-Lik: -530.270, Max-Change: 0.00076
Iteration: 32, Log-Lik: -530.270, Max-Change: 0.00035
Iteration: 33, Log-Lik: -530.270, Max-Change: 0.00077
Iteration: 34, Log-Lik: -530.270, Max-Change: 0.00038
Iteration: 35, Log-Lik: -530.270, Max-Change: 0.00076
Iteration: 36, Log-Lik: -530.270, Max-Change: 0.00027
Iteration: 37, Log-Lik: -530.270, Max-Change: 0.00021
Iteration: 38, Log-Lik: -530.270, Max-Change: 0.00075
Iteration: 39, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 40, Log-Lik: -530.270, Max-Change: 0.00075
Iteration: 41, Log-Lik: -530.270, Max-Change: 0.00031
Iteration: 42, Log-Lik: -530.270, Max-Change: 0.00075
Iteration: 43, Log-Lik: -530.270, Max-Change: 0.00034
Iteration: 44, Log-Lik: -530.270, Max-Change: 0.00075
Iteration: 45, Log-Lik: -530.270, Max-Change: 0.00024
Iteration: 46, Log-Lik: -530.270, Max-Change: 0.00019
Iteration: 47, Log-Lik: -530.270, Max-Change: 0.00073
Iteration: 48, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 49, Log-Lik: -530.270, Max-Change: 0.00074
Iteration: 50, Log-Lik: -530.270, Max-Change: 0.00028
Iteration: 51, Log-Lik: -530.270, Max-Change: 0.00072
Iteration: 52, Log-Lik: -530.270, Max-Change: 0.00031
Iteration: 53, Log-Lik: -530.270, Max-Change: 0.00075
Iteration: 54, Log-Lik: -530.270, Max-Change: 0.00022
Iteration: 55, Log-Lik: -530.270, Max-Change: 0.00018
Iteration: 56, Log-Lik: -530.270, Max-Change: 0.00071
Iteration: 57, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 58, Log-Lik: -530.270, Max-Change: 0.00074
Iteration: 59, Log-Lik: -530.270, Max-Change: 0.00026
Iteration: 60, Log-Lik: -530.270, Max-Change: 0.00069
Iteration: 61, Log-Lik: -530.270, Max-Change: 0.00030
Iteration: 62, Log-Lik: -530.270, Max-Change: 0.00074
Iteration: 63, Log-Lik: -530.270, Max-Change: 0.00022
Iteration: 64, Log-Lik: -530.270, Max-Change: 0.00017
Iteration: 65, Log-Lik: -530.270, Max-Change: 0.00068
Iteration: 66, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 67, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 68, Log-Lik: -530.270, Max-Change: 0.00072
Iteration: 69, Log-Lik: -530.270, Max-Change: 0.00067
Iteration: 70, Log-Lik: -530.270, Max-Change: 0.00019
Iteration: 71, Log-Lik: -530.270, Max-Change: 0.00072
Iteration: 72, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 73, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 74, Log-Lik: -530.270, Max-Change: 0.00067
Iteration: 75, Log-Lik: -530.270, Max-Change: 0.00072
Iteration: 76, Log-Lik: -530.270, Max-Change: 0.00018
Iteration: 77, Log-Lik: -530.270, Max-Change: 0.00065
Iteration: 78, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 79, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 80, Log-Lik: -530.270, Max-Change: 0.00070
Iteration: 81, Log-Lik: -530.270, Max-Change: 0.00064
Iteration: 82, Log-Lik: -530.270, Max-Change: 0.00018
Iteration: 83, Log-Lik: -530.270, Max-Change: 0.00070
Iteration: 84, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 85, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 86, Log-Lik: -530.270, Max-Change: 0.00065
Iteration: 87, Log-Lik: -530.270, Max-Change: 0.00070
Iteration: 88, Log-Lik: -530.270, Max-Change: 0.00017
Iteration: 89, Log-Lik: -530.270, Max-Change: 0.00063
Iteration: 90, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 91, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 92, Log-Lik: -530.270, Max-Change: 0.00068
Iteration: 93, Log-Lik: -530.270, Max-Change: 0.00062
Iteration: 94, Log-Lik: -530.270, Max-Change: 0.00017
Iteration: 95, Log-Lik: -530.270, Max-Change: 0.00068
Iteration: 96, Log-Lik: -530.270, Max-Change: 0.00012
Iteration: 97, Log-Lik: -530.270, Max-Change: 0.00012
Iteration: 98, Log-Lik: -530.270, Max-Change: 0.00062
Iteration: 99, Log-Lik: -530.270, Max-Change: 0.00068
Iteration: 100, Log-Lik: -530.270, Max-Change: 0.00016
Iteration: 101, Log-Lik: -530.270, Max-Change: 0.00061
Iteration: 102, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 103, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 104, Log-Lik: -530.270, Max-Change: 0.00066
Iteration: 105, Log-Lik: -530.270, Max-Change: 0.00059
Iteration: 106, Log-Lik: -530.270, Max-Change: 0.00016
Iteration: 107, Log-Lik: -530.270, Max-Change: 0.00066
Iteration: 108, Log-Lik: -530.270, Max-Change: 0.00012
Iteration: 109, Log-Lik: -530.270, Max-Change: 0.00012
Iteration: 110, Log-Lik: -530.270, Max-Change: 0.00060
Iteration: 111, Log-Lik: -530.270, Max-Change: 0.00066
Iteration: 112, Log-Lik: -530.270, Max-Change: 0.00016
Iteration: 113, Log-Lik: -530.270, Max-Change: 0.00059
Iteration: 114, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 115, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 116, Log-Lik: -530.270, Max-Change: 0.00064
Iteration: 117, Log-Lik: -530.270, Max-Change: 0.00057
Iteration: 118, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 119, Log-Lik: -530.270, Max-Change: 0.00064
Iteration: 120, Log-Lik: -530.270, Max-Change: 0.00011
Iteration: 121, Log-Lik: -530.270, Max-Change: 0.00011
Iteration: 122, Log-Lik: -530.270, Max-Change: 0.00058
Iteration: 123, Log-Lik: -530.270, Max-Change: 0.00064
Iteration: 124, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 125, Log-Lik: -530.270, Max-Change: 0.00057
Iteration: 126, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 127, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 128, Log-Lik: -530.270, Max-Change: 0.00062
Iteration: 129, Log-Lik: -530.270, Max-Change: 0.00055
Iteration: 130, Log-Lik: -530.270, Max-Change: 0.00015
Iteration: 131, Log-Lik: -530.270, Max-Change: 0.00062
Iteration: 132, Log-Lik: -530.270, Max-Change: 0.00011
Iteration: 133, Log-Lik: -530.270, Max-Change: 0.00011
Iteration: 134, Log-Lik: -530.270, Max-Change: 0.00056
Iteration: 135, Log-Lik: -530.270, Max-Change: 0.00062
Iteration: 136, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 137, Log-Lik: -530.270, Max-Change: 0.00055
Iteration: 138, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 139, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 140, Log-Lik: -530.270, Max-Change: 0.00060
Iteration: 141, Log-Lik: -530.270, Max-Change: 0.00053
Iteration: 142, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 143, Log-Lik: -530.270, Max-Change: 0.00060
Iteration: 144, Log-Lik: -530.270, Max-Change: 0.00010
Iteration: 145, Log-Lik: -530.270, Max-Change: 0.00010
Iteration: 146, Log-Lik: -530.270, Max-Change: 0.00054
Iteration: 147, Log-Lik: -530.270, Max-Change: 0.00061
Iteration: 148, Log-Lik: -530.270, Max-Change: 0.00014
Iteration: 149, Log-Lik: -530.270, Max-Change: 0.00053
Iteration: 150, Log-Lik: -530.270, Max-Change: 0.00012
Iteration: 151, Log-Lik: -530.270, Max-Change: 0.00012
Iteration: 152, Log-Lik: -530.270, Max-Change: 0.00058
Iteration: 153, Log-Lik: -530.270, Max-Change: 0.00051
Iteration: 154, Log-Lik: -530.270, Max-Change: 0.00013
Iteration: 155, Log-Lik: -530.270, Max-Change: 0.00058
Iteration: 156, Log-Lik: -530.270, Max-Change: 0.00010
Iteration: 157, Log-Lik: -530.270, Max-Change: 0.00010
summary(mirtmodel3PL)
## F1 h2
## X3 0.827 0.684
## X4 0.772 0.596
## X8 0.513 0.263
## X11 0.510 0.261
## X13 0.778 0.605
## X15 0.610 0.372
## X17 0.633 0.401
## X18 0.557 0.310
## X25 0.577 0.333
##
## SS loadings: 3.825
## Proportion Var: 0.425
##
## Factor correlations:
##
## F1
## F1 1
coef(mirtmodel3PL, IRTpars = T) #coefficiants
## $X3
## a b g u
## par 2.504 -0.414 0.576 1
##
## $X4
## a b g u
## par 2.069 0.086 0.23 1
##
## $X8
## a b g u
## par 1.017 -0.196 0 1
##
## $X11
## a b g u
## par 1.01 -0.151 0 1
##
## $X13
## a b g u
## par 2.105 -1.136 0 1
##
## $X15
## a b g u
## par 1.311 1.022 0 1
##
## $X17
## a b g u
## par 1.392 0.23 0.056 1
##
## $X18
## a b g u
## par 1.142 -1.102 0 1
##
## $X25
## a b g u
## par 1.201 -0.316 0.191 1
##
## $GroupPars
## MEAN_1 COV_11
## par 0 1
plot(mirtmodel3PL, type = "trace") #curves for all items
plot(mirtmodel3PL, type = "info") # test information curve
plot(mirtmodel3PL) #expected total score
itemfit(mirtmodel3PL) #item fit statistics
## item S_X2 df.S_X2 p.S_X2
## 1 X3 1.928 3 0.587
## 2 X4 4.622 3 0.202
## 3 X8 9.609 4 0.048
## 4 X11 5.624 4 0.229
## 5 X13 4.319 2 0.115
## 6 X15 2.602 2 0.272
## 7 X17 5.128 3 0.163
## 8 X18 6.625 3 0.085
## 9 X25 2.732 4 0.604
#compare models
anova(mirtmodel2PL, mirtmodel3PL)
##
## Model 1: mirt(data = ctt.data[, c(-1, -2, -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, -5, -6, -7, -9, -10, -12, -14,
## -16, -19, -20, -21, -22, -23, -24)], model = 1, itemtype = "3PL")
## AIC AICc SABIC BIC logLik X2 df p
## 1 1097.401 1105.354 1088.307 1145.172 -530.70 NaN NaN NaN
## 2 1114.539 1134.176 1100.898 1186.196 -530.27 0.861 9 1
#Matrix 2 [,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -18, -19, -20, -21, -23, -24)]
responses <- as.matrix(ctt.data[,c( -1, -2, -5, -6, -7, -9, -10, -12, -14, -16, -19, -20, -21, -22, -23, -24)])
dimnames(responses) <- NULL
(N <- dim(responses) [2])
## [1] 9
(K <- dim(responses) [1])
## [1] 105
#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] 0.6882234
##
## $`Number of items`
## [1] 9
##
## $`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] 0.6923832
# 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] 0.6327714
#Covariances
covar = cov(responses, method = "pearson")
covar
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.13040293 0.05384615 0.02582418 0.02435897 0.04761905 0.02179487
## [2,] 0.05384615 0.24230769 0.06538462 0.05192308 0.03846154 0.05961538
## [3,] 0.02582418 0.06538462 0.25054945 0.07307692 0.03708791 0.02692308
## [4,] 0.02435897 0.05192308 0.07307692 0.25128205 0.04487179 0.02948718
## [5,] 0.04761905 0.03846154 0.03708791 0.04487179 0.15567766 0.03205128
## [6,] 0.02179487 0.05961538 0.02692308 0.02948718 0.03205128 0.19743590
## [7,] 0.01556777 0.04807692 0.03708791 0.07051282 0.05311355 0.05448718
## [8,] 0.01666667 0.03653846 0.06923077 0.02820513 0.05448718 0.02371795
## [9,] 0.02417582 0.04423077 0.03406593 0.03076923 0.04945055 0.04423077
## [,7] [,8] [,9]
## [1,] 0.01556777 0.01666667 0.02417582
## [2,] 0.04807692 0.03653846 0.04423077
## [3,] 0.03708791 0.06923077 0.03406593
## [4,] 0.07051282 0.02820513 0.03076923
## [5,] 0.05311355 0.05448718 0.04945055
## [6,] 0.05448718 0.02371795 0.04423077
## [7,] 0.25183150 0.05128205 0.04945055
## [8,] 0.05128205 0.19743590 0.03269231
## [9,] 0.04945055 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]
## [1,] 1.00000000 0.3029196 0.1428684 0.1345658 0.3342134 0.1358306
## [2,] 0.30291963 1.0000000 0.2653660 0.2104244 0.1980295 0.2725597
## [3,] 0.14286836 0.2653660 1.0000000 0.2912412 0.1877900 0.1210500
## [4,] 0.13456577 0.2104244 0.2912412 1.0000000 0.2268713 0.1323852
## [5,] 0.33421342 0.1980295 0.1877900 0.2268713 1.0000000 0.1828181
## [6,] 0.13583059 0.2725597 0.1210500 0.1323852 0.1828181 1.0000000
## [7,] 0.08590681 0.1946247 0.1476490 0.2803060 0.2682484 0.2443578
## [8,] 0.10387045 0.1670527 0.3112715 0.1266293 0.3107908 0.1201299
## [9,] 0.14036962 0.1883981 0.1426951 0.1286979 0.2627807 0.2087118
## [,7] [,8] [,9]
## [1,] 0.08590681 0.1038705 0.1403696
## [2,] 0.19462474 0.1670527 0.1883981
## [3,] 0.14764904 0.3112715 0.1426951
## [4,] 0.28030596 0.1266293 0.1286979
## [5,] 0.26824843 0.3107908 0.2627807
## [6,] 0.24435782 0.1201299 0.2087118
## [7,] 1.00000000 0.2299838 0.2066101
## [8,] 0.22998383 1.0000000 0.1542652
## [9,] 0.20661013 0.1542652 1.0000000
#CTT
#Reliability
str(reliability(responses, itemal=TRUE), vec.len = 15) #vec.len numeric (>= 0) indicating how many 'first few' elements are displayed of each vector.
## List of 9
## $ nItem : int 9
## $ nPerson : int 105
## $ alpha : num 0.688
## $ scaleMean : num 5.47
## $ scaleSD : num 2.21
## $ alphaIfDeleted: num [1:9(1d)] 0.673 0.652 0.66 0.664 0.648 0.67 0.658 0.665 0.671
## $ pBis : num [1:9(1d)] 0.306 0.411 0.372 0.355 0.451 0.324 0.383 0.348 0.322
## $ bis : num [1:9(1d)] 0.427 0.496 0.446 0.434 0.579 0.481 0.477 0.426 0.394
## $ itemMean : num [1:9] 0.848 0.6 0.543 0.533 0.81 0.267 0.476 0.733 0.657
## - attr(*, "class")= chr "reliability"
#Alpha and Omega
ci.reliability(data = responses, type = "1", interval.type = "bca", B = 1000)
## $est
## [1] 0.6882234
##
## $se
## [1] 0.04625676
##
## $ci.lower
## [1] 0.586372
##
## $ci.upper
## [1] 0.7647472
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "alpha"
##
## $interval.type
## [1] "bca bootstrap"
ci.reliability(data = responses, type = "3", interval.type = "bca", B = 1000) #Omega
## $est
## [1] 0.6898112
##
## $se
## [1] 0.04675821
##
## $ci.lower
## [1] 0.5889042
##
## $ci.upper
## [1] 0.7626437
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "omega"
##
## $interval.type
## [1] "bca bootstrap"
ci.reliability(data = responses, type = "5", interval.type = "bca", B = 1000) #Categorical omega!
## $est
## [1] 0.7106732
##
## $se
## [1] 0.04599442
##
## $ci.lower
## [1] 0.5372324
##
## $ci.upper
## [1] 0.7711012
##
## $conf.level
## [1] 0.95
##
## $type
## [1] "categorical omega"
##
## $interval.type
## [1] "bca bootstrap"
#Item analysis
knitr::kable(item.exam(responses, y = NULL, discrim = TRUE),
align = "c",
caption = "Item Analysis")
Item Analysis
| 0.3611135 |
0.4504461 |
0.3064193 |
0.8476190 |
0.3714286 |
NA |
0.1618857 |
0.1101240 |
NA |
| 0.4922476 |
0.5873975 |
0.4112586 |
0.6000000 |
0.6857143 |
NA |
0.2877648 |
0.2014748 |
NA |
| 0.5005491 |
0.5585739 |
0.3721480 |
0.5428571 |
0.6285714 |
NA |
0.2782591 |
0.1853892 |
NA |
| 0.5012804 |
0.5444791 |
0.3546408 |
0.5333333 |
0.6000000 |
NA |
0.2716339 |
0.1769259 |
NA |
| 0.3945601 |
0.5868499 |
0.4506073 |
0.8095238 |
0.4571429 |
NA |
0.2304423 |
0.1769430 |
NA |
| 0.4443376 |
0.4976575 |
0.3239787 |
0.2666667 |
0.5142857 |
NA |
0.2200724 |
0.1432688 |
NA |
| 0.5018282 |
0.5681087 |
0.3833020 |
0.4761905 |
0.6285714 |
NA |
0.2837321 |
0.1914336 |
NA |
| 0.4443376 |
0.5185018 |
0.3484520 |
0.7333333 |
0.4571429 |
NA |
0.2292901 |
0.1540913 |
NA |
| 0.4769408 |
0.5079386 |
0.3216245 |
0.6571429 |
0.5428571 |
NA |
0.2411003 |
0.1526636 |
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: 9
## Sample units: 105
## alpha: 0.691
H <- cronbach.alpha(responses, standardized = TRUE)
spearman.brown(H$alpha, input = 0.95, n.or.r = "r")
## $n.new
## [1] 8.500031
rel95 <- spearman.brown(H$alpha, input = 0.95, n.or.r = "r") #returns number of items neede to attain 0.95 reliability
rel.Factor <- rel95$n.new*11 #11=number of items in the model
round(rel.Factor)
## [1] 94
#Splithalf coeff.
splitHalf(responses, raw = FALSE, brute = FALSE, n.sample = 1000, covar = FALSE, check.keys = FALSE, key = NULL, use = "complete") # at use = complete/pairwise
## Split half reliabilities
## Call: splitHalf(r = responses, raw = FALSE, brute = FALSE, n.sample = 1000,
## covar = FALSE, check.keys = FALSE, key = NULL, use = "complete")
##
## Maximum split half reliability (lambda 4) = 0.77
## Guttman lambda 6 = 0.68
## Average split half reliability = 0.67
## Guttman lambda 3 (alpha) = 0.69
## Minimum split half reliability (beta) = 0.61
#Striatums H-index
H #standardised alpha
##
## Standardized Cronbach's alpha for the 'responses' data-set
##
## Items: 9
## Sample units: 105
## alpha: 0.691
G <- sqrt(H$alpha/(1-H$alpha))
G
## [1] 1.495087
Striatums = (4*G+1)/3
Striatums
## [1] 2.326783
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] 0.4850923
# 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,] 0.4850923
#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] 1.23665
# 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
| -1.03 |
1 |
3.03 |
| 6.97 |
9 |
11.03 |
| 4.97 |
7 |
9.03 |
| 5.97 |
8 |
10.03 |
| 1.97 |
4 |
6.03 |
| 5.97 |
8 |
10.03 |
| 3.97 |
6 |
8.03 |
| 3.97 |
6 |
8.03 |
| 0.97 |
3 |
5.03 |
| 1.97 |
4 |
6.03 |
| 4.97 |
7 |
9.03 |
| 0.97 |
3 |
5.03 |
| 3.97 |
6 |
8.03 |
| 3.97 |
6 |
8.03 |
| 3.97 |
6 |
8.03 |
| 1.97 |
4 |
6.03 |
| 3.97 |
6 |
8.03 |
| 0.97 |
3 |
5.03 |
| 3.97 |
6 |
8.03 |
| 2.97 |
5 |
7.03 |
| 5.97 |
8 |
10.03 |
| 3.97 |
6 |
8.03 |
| 5.97 |
8 |
10.03 |
| 5.97 |
8 |
10.03 |
| 3.97 |
6 |
8.03 |
| 4.97 |
7 |
9.03 |
| 4.97 |
7 |
9.03 |
| 2.97 |
5 |
7.03 |
| -0.03 |
2 |
4.03 |
| 6.97 |
9 |
11.03 |
| 3.97 |
6 |
8.03 |
| -0.03 |
2 |
4.03 |
| 5.97 |
8 |
10.03 |
| 2.97 |
5 |
7.03 |
| -0.03 |
2 |
4.03 |
| 4.97 |
7 |
9.03 |
| 3.97 |
6 |
8.03 |
| 6.97 |
9 |
11.03 |
| 2.97 |
5 |
7.03 |
| 2.97 |
5 |
7.03 |
| 3.97 |
6 |
8.03 |
| -0.03 |
2 |
4.03 |
| 2.97 |
5 |
7.03 |
| 2.97 |
5 |
7.03 |
| 0.97 |
3 |
5.03 |
| -0.03 |
2 |
4.03 |
| 5.97 |
8 |
10.03 |
| 5.97 |
8 |
10.03 |
| -1.03 |
1 |
3.03 |
| 2.97 |
5 |
7.03 |
| 5.97 |
8 |
10.03 |
| 3.97 |
6 |
8.03 |
| 4.97 |
7 |
9.03 |
| -0.03 |
2 |
4.03 |
| -1.03 |
1 |
3.03 |
| 0.97 |
3 |
5.03 |
| 3.97 |
6 |
8.03 |
| 3.97 |
6 |
8.03 |
| 3.97 |
6 |
8.03 |
| -2.03 |
0 |
2.03 |
| 2.97 |
5 |
7.03 |
| 1.97 |
4 |
6.03 |
| 4.97 |
7 |
9.03 |
| -0.03 |
2 |
4.03 |
| 5.97 |
8 |
10.03 |
| 4.97 |
7 |
9.03 |
| 1.97 |
4 |
6.03 |
| 4.97 |
7 |
9.03 |
| 1.97 |
4 |
6.03 |
| 4.97 |
7 |
9.03 |
| 4.97 |
7 |
9.03 |
| 4.97 |
7 |
9.03 |
| 4.97 |
7 |
9.03 |
| 5.97 |
8 |
10.03 |
| 5.97 |
8 |
10.03 |
| 3.97 |
6 |
8.03 |
| 4.97 |
7 |
9.03 |
| 4.97 |
7 |
9.03 |
| 5.97 |
8 |
10.03 |
| -1.03 |
1 |
3.03 |
| 5.97 |
8 |
10.03 |
| 5.97 |
8 |
10.03 |
| 1.97 |
4 |
6.03 |
| 6.97 |
9 |
11.03 |
| 1.97 |
4 |
6.03 |
| 4.97 |
7 |
9.03 |
| 1.97 |
4 |
6.03 |
| 3.97 |
6 |
8.03 |
| 0.97 |
3 |
5.03 |
| 5.97 |
8 |
10.03 |
| 4.97 |
7 |
9.03 |
| -1.03 |
1 |
3.03 |
| 1.97 |
4 |
6.03 |
| 4.97 |
7 |
9.03 |
| 4.97 |
7 |
9.03 |
| 2.97 |
5 |
7.03 |
| 2.97 |
5 |
7.03 |
| 1.97 |
4 |
6.03 |
| 0.97 |
3 |
5.03 |
| -0.03 |
2 |
4.03 |
| 5.97 |
8 |
10.03 |
| 0.97 |
3 |
5.03 |
| 2.97 |
5 |
7.03 |
| 3.97 |
6 |
8.03 |
| 3.97 |
6 |
8.03 |
#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 |
0.3064193 |
0.4269808 |
0.8476190 |
0.6730051 |
|
| 2 |
0.4112586 |
0.4956531 |
0.6000000 |
0.6515996 |
|
| 3 |
0.3721480 |
0.4464529 |
0.5428571 |
0.6603436 |
|
| 4 |
0.3546408 |
0.4339390 |
0.5333333 |
0.6642496 |
|
| 5 |
0.4506073 |
0.5786764 |
0.8095238 |
0.6475775 |
|
| 6 |
0.3239787 |
0.4809361 |
0.2666667 |
0.6697127 |
|
| 7 |
0.3833020 |
0.4768857 |
0.4761905 |
0.6578604 |
|
| 8 |
0.3484520 |
0.4257797 |
0.7333333 |
0.6649574 |
|
| 9 |
0.3216245 |
0.3942851 |
0.6571429 |
0.6707615 |
|
#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
| 6 |
6 |
0.2666667 |
| 7 |
7 |
0.4761905 |
| 4 |
4 |
0.5333333 |
| 3 |
3 |
0.5428571 |
| 2 |
2 |
0.6000000 |
| 9 |
9 |
0.6571429 |
| 8 |
8 |
0.7333333 |
| 5 |
5 |
0.8095238 |
| 1 |
1 |
0.8476190 |
#Item discrimination
item.discrimination <-
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)
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 = "red")
return(item.discrimination[order(item.discrimination$discrimination),])
}
dump("item.discrimination", file = "item.discrimination.R")
knitr::kable(item.discrimination(responses),
align = "c",
caption = "Item Discrimination")
Item Discrimination
| 1 |
1 |
0.3064193 |
| 9 |
9 |
0.3216245 |
| 6 |
6 |
0.3239787 |
| 8 |
8 |
0.3484520 |
| 4 |
4 |
0.3546408 |
| 3 |
3 |
0.3721480 |
| 7 |
7 |
0.3833020 |
| 2 |
2 |
0.4112586 |
| 5 |
5 |
0.4506073 |
#Item total correlation
test_item.total <-
function(responses){
# CRITICAL VALUES
cvpb = 0.20
cvdl = 0.15
cvdu = 0.85
require(CTT, warn.conflicts = FALSE, quietly = TRUE)
ctt.analysis <- CTT::reliability(responses, itemal = TRUE, NA.Delete = TRUE)
test_item.total <- data.frame(item = 1:ctt.analysis$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")
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
| 9 |
9 |
0.3942851 |
| 8 |
8 |
0.4257797 |
| 1 |
1 |
0.4269808 |
| 4 |
4 |
0.4339390 |
| 3 |
3 |
0.4464529 |
| 7 |
7 |
0.4768857 |
| 6 |
6 |
0.4809361 |
| 2 |
2 |
0.4956531 |
| 5 |
5 |
0.5786764 |