### Install and load the packages:
# eRm:
citation("eRm")
## The original JSS article: Article about CML Estimation in eRm: Article
## about LLRAs in eRm: Book Chapter about LLRAs: Article about the
## performance of Quasi-Exact Tests in eRm: Article about the Performance
## of the nonparametric Q3 Tests in eRm:
##
## Mair P, Hatzinger R (2007). "Extended Rasch modeling: The eRm package
## for the application of IRT models in R." _Journal of Statistical
## Software_, *20*. doi:10.18637/jss.v020.i09
## <https://doi.org/10.18637/jss.v020.i09>.
##
## Mair P, Hatzinger R (2007). "CML based estimation of extended Rasch
## models with the eRm package in R." _Psychology Science_, *49*.
## doi:10.18637/jss.v020.i09 <https://doi.org/10.18637/jss.v020.i09>.
##
## Hatzinger R, Rusch T (2009). "IRT models with relaxed assumptions in
## eRm: A manual-like instruction." _Psychology Science Quarterly_,
## *51*.
##
## Rusch T, Maier M, Hatzinger R (2013). "Linear logistic models with
## relaxed assumptions in R." In Lausen B, van den Poel D, Ultsch A
## (eds.), _Algorithms from and for Nature and Life_, series Studies in
## Classification, Data Analysis, and Knowledge Organization.
## doi:10.1007/978-3-319-00035-0_34
## <https://doi.org/10.1007/978-3-319-00035-0_34>.
##
## Koller I, Maier M, Hatzinger R (2015). "An empirical power analysis
## of quasi-exact tests for the Rasch model: Measurement invariance in
## small samples." _Methodology_, *11*. doi:10.1027/1614-2241/a000090
## <https://doi.org/10.1027/1614-2241/a000090>.
##
## Debelak R, Koller I (2019). "Testing the local independence
## assumption of the Rasch model with Q3-based nonparametric model
## tests." _Applied Psychological Measurement_, *44*.
## doi:10.1177/0146621619835501
## <https://doi.org/10.1177/0146621619835501>.
##
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.
#install.packages("eRm")
library("eRm")
## Warning: package 'eRm' was built under R version 4.4.1
retail_5000_labels <- read.csv("retail_salespeople_statistic_64_labels.csv")
summary(retail_5000_labels)
## Position Age Gender Marital q01
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:2.000 1st Qu.:4.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.00
## Median :2.000 Median :5.000 Median :2.000 Median :2.000 Median :1.00
## Mean :2.466 Mean :4.673 Mean :1.902 Mean :1.589 Mean :1.35
## 3rd Qu.:3.000 3rd Qu.:6.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.00
## Max. :3.000 Max. :9.000 Max. :2.000 Max. :2.000 Max. :2.00
## q02 q03 q04 q05
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :1.000 Median :1.000 Median :1.000
## Mean :1.669 Mean :1.275 Mean :1.163 Mean :1.161
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q06 q07 q08 q09
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :2.000 Median :2.000 Median :1.000
## Mean :1.432 Mean :1.548 Mean :1.575 Mean :1.369
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q10 q11 q12 q13
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :2.000 Median :1.000 Median :2.000
## Mean :1.629 Mean :1.846 Mean :1.454 Mean :1.547
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q14 q15 q16 q17
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.401 Mean :1.198 Mean :1.425 Mean :1.842
## 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q18 q19 q20 q21
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
## Median :1.000 Median :1.000 Median :2.000 Median :2.000
## Mean :1.478 Mean :1.253 Mean :1.695 Mean :1.856
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q22 q23 q24 q25 q26
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.00
## Median :2.000 Median :1.000 Median :2.000 Median :2.000 Median :1.00
## Mean :1.525 Mean :1.333 Mean :1.523 Mean :1.863 Mean :1.48
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.00
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.00
## q27 q28 q29 q30
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.093 Mean :1.377 Mean :1.466 Mean :1.742
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q31 q32 q33 q34
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.055 Mean :1.153 Mean :1.126 Mean :1.666
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q35 q36 q37 q38
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
## Median :1.000 Median :2.000 Median :1.000 Median :2.000
## Mean :1.198 Mean :1.694 Mean :1.211 Mean :1.815
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q39 q40 q41 q42
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :1.000 Median :1.000 Median :1.000
## Mean :1.742 Mean :1.329 Mean :1.366 Mean :1.285
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q43 q44 q45 q46
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :2.000 Median :1.000 Median :1.000
## Mean :1.854 Mean :1.694 Mean :1.213 Mean :1.296
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q47 q48 q49 q50
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :2.000 Median :1.000
## Mean :1.489 Mean :1.313 Mean :1.623 Mean :1.237
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:1.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q51 q52 q53 q54 q55
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:1.000
## Median :1.000 Median :1.00 Median :2.000 Median :1.00 Median :2.000
## Mean :1.207 Mean :1.27 Mean :1.516 Mean :1.29 Mean :1.728
## 3rd Qu.:1.000 3rd Qu.:2.00 3rd Qu.:2.000 3rd Qu.:2.00 3rd Qu.:2.000
## Max. :2.000 Max. :2.00 Max. :2.000 Max. :2.00 Max. :2.000
## q56 q57 q58 q59
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.246 Mean :1.402 Mean :1.347 Mean :1.603
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q60
## Min. :1.000
## 1st Qu.:1.000
## Median :1.000
## Mean :1.457
## 3rd Qu.:2.000
## Max. :2.000
# Remove the Person Variables:
retail_5000_60 <- subset(retail_5000_labels, select = -c(Position, Age, Gender, Marital))
# Check descriptive statistics:
summary(retail_5000_60)
## q01 q02 q03 q04 q05
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.00 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.00 Median :2.000 Median :1.000 Median :1.000 Median :1.000
## Mean :1.35 Mean :1.669 Mean :1.275 Mean :1.163 Mean :1.161
## 3rd Qu.:2.00 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :2.00 Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q06 q07 q08 q09
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :2.000 Median :2.000 Median :1.000
## Mean :1.432 Mean :1.548 Mean :1.575 Mean :1.369
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q10 q11 q12 q13
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :2.000 Median :1.000 Median :2.000
## Mean :1.629 Mean :1.846 Mean :1.454 Mean :1.547
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q14 q15 q16 q17
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.401 Mean :1.198 Mean :1.425 Mean :1.842
## 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q18 q19 q20 q21
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
## Median :1.000 Median :1.000 Median :2.000 Median :2.000
## Mean :1.478 Mean :1.253 Mean :1.695 Mean :1.856
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q22 q23 q24 q25 q26
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.00
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.00
## Median :2.000 Median :1.000 Median :2.000 Median :2.000 Median :1.00
## Mean :1.525 Mean :1.333 Mean :1.523 Mean :1.863 Mean :1.48
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.00
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.00
## q27 q28 q29 q30
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.093 Mean :1.377 Mean :1.466 Mean :1.742
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q31 q32 q33 q34
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.055 Mean :1.153 Mean :1.126 Mean :1.666
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q35 q36 q37 q38
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
## Median :1.000 Median :2.000 Median :1.000 Median :2.000
## Mean :1.198 Mean :1.694 Mean :1.211 Mean :1.815
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q39 q40 q41 q42
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :1.000 Median :1.000 Median :1.000
## Mean :1.742 Mean :1.329 Mean :1.366 Mean :1.285
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q43 q44 q45 q46
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :2.000 Median :1.000 Median :1.000
## Mean :1.854 Mean :1.694 Mean :1.213 Mean :1.296
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q47 q48 q49 q50
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :2.000 Median :1.000
## Mean :1.489 Mean :1.313 Mean :1.623 Mean :1.237
## 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:1.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q51 q52 q53 q54 q55
## Min. :1.000 Min. :1.00 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:1.000
## Median :1.000 Median :1.00 Median :2.000 Median :1.00 Median :2.000
## Mean :1.207 Mean :1.27 Mean :1.516 Mean :1.29 Mean :1.728
## 3rd Qu.:1.000 3rd Qu.:2.00 3rd Qu.:2.000 3rd Qu.:2.00 3rd Qu.:2.000
## Max. :2.000 Max. :2.00 Max. :2.000 Max. :2.00 Max. :2.000
## q56 q57 q58 q59
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :1.000 Median :1.000 Median :1.000 Median :2.000
## Mean :1.246 Mean :1.402 Mean :1.347 Mean :1.603
## 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :2.000 Max. :2.000 Max. :2.000 Max. :2.000
## q60
## Min. :1.000
## 1st Qu.:1.000
## Median :1.000
## Mean :1.457
## 3rd Qu.:2.000
## Max. :2.000
# Run the Dichotomous Rasch Model
dichot.retail_5000_60 <- RM(retail_5000_60)
## Warning:
## The following items have no 0-responses:
## q01 q02 q03 q04 q05 q06 q07 q08 q09 q10 q11 q12 q13 q14 q15 q16 q17 q18 q19 q20 q21 q22 q23 q24 q25 q26 q27 q28 q29 q30 q31 q32 q33 q34 q35 q36 q37 q38 q39 q40 q41 q42 q43 q44 q45 q46 q47 q48 q49 q50 q51 q52 q53 q54 q55 q56 q57 q58 q59 q60
## Responses are shifted such that lowest category is 0.
# Request a summary of the model results
summary(dichot.retail_5000_60)
##
## Results of RM estimation:
##
## Call: RM(X = retail_5000_60)
##
## Conditional log-likelihood: -159238.8
## Number of iterations: 21
## Number of parameters: 59
##
## Item (Category) Difficulty Parameters (eta): with 0.95 CI:
## Estimate Std. Error lower CI upper CI
## q02 -0.959 0.030 -1.018 -0.899
## q03 0.746 0.032 0.684 0.808
## q04 1.421 0.038 1.346 1.496
## q05 1.436 0.038 1.361 1.511
## q06 0.038 0.029 -0.019 0.094
## q07 -0.440 0.029 -0.496 -0.384
## q08 -0.552 0.029 -0.608 -0.495
## q09 0.306 0.029 0.248 0.363
## q10 -0.779 0.029 -0.836 -0.721
## q11 -1.977 0.039 -2.054 -1.900
## q12 -0.052 0.029 -0.108 0.004
## q13 -0.433 0.029 -0.489 -0.377
## q14 0.168 0.029 0.112 0.225
## q15 1.178 0.035 1.109 1.248
## q16 0.064 0.029 0.008 0.120
## q17 -1.945 0.039 -2.020 -1.869
## q18 -0.151 0.028 -0.206 -0.095
## q19 0.856 0.032 0.793 0.920
## q20 -1.082 0.031 -1.142 -1.021
## q21 -2.057 0.040 -2.136 -1.978
## q22 -0.343 0.028 -0.399 -0.287
## q23 0.464 0.030 0.405 0.523
## q24 -0.335 0.028 -0.391 -0.279
## q25 -2.116 0.041 -2.196 -2.036
## q26 -0.160 0.028 -0.215 -0.104
## q27 2.063 0.048 1.968 2.157
## q28 0.269 0.029 0.212 0.327
## q29 -0.103 0.028 -0.159 -0.047
## q30 -1.321 0.032 -1.385 -1.258
## q31 2.631 0.061 2.511 2.751
## q32 1.496 0.039 1.419 1.572
## q33 1.718 0.042 1.635 1.801
## q34 -0.946 0.030 -1.005 -0.887
## q35 1.176 0.035 1.107 1.245
## q36 -1.075 0.031 -1.135 -1.015
## q37 1.096 0.035 1.029 1.164
## q38 -1.752 0.036 -1.824 -1.681
## q39 -1.321 0.032 -1.385 -1.258
## q40 0.483 0.030 0.424 0.542
## q41 0.318 0.029 0.260 0.376
## q42 0.691 0.031 0.630 0.753
## q43 -2.044 0.040 -2.122 -1.966
## q44 -1.078 0.031 -1.138 -1.018
## q45 1.088 0.034 1.020 1.155
## q46 0.638 0.031 0.577 0.699
## q47 -0.196 0.028 -0.252 -0.141
## q48 0.559 0.031 0.499 0.618
## q49 -0.756 0.029 -0.813 -0.698
## q50 0.948 0.033 0.883 1.013
## q51 1.122 0.035 1.054 1.190
## q52 0.770 0.032 0.708 0.833
## q53 -0.308 0.028 -0.364 -0.252
## q54 0.671 0.031 0.609 0.732
## q55 -1.246 0.032 -1.308 -1.183
## q56 0.894 0.033 0.830 0.958
## q57 0.163 0.029 0.107 0.220
## q58 0.403 0.030 0.345 0.462
## q59 -0.669 0.029 -0.726 -0.612
## q60 -0.068 0.028 -0.124 -0.012
##
## Item Easiness Parameters (beta) with 0.95 CI:
## Estimate Std. Error lower CI upper CI
## beta q01 -0.388 0.030 -0.446 -0.330
## beta q02 0.959 0.030 0.899 1.018
## beta q03 -0.746 0.032 -0.808 -0.684
## beta q04 -1.421 0.038 -1.496 -1.346
## beta q05 -1.436 0.038 -1.511 -1.361
## beta q06 -0.038 0.029 -0.094 0.019
## beta q07 0.440 0.029 0.384 0.496
## beta q08 0.552 0.029 0.495 0.608
## beta q09 -0.306 0.029 -0.363 -0.248
## beta q10 0.779 0.029 0.721 0.836
## beta q11 1.977 0.039 1.900 2.054
## beta q12 0.052 0.029 -0.004 0.108
## beta q13 0.433 0.029 0.377 0.489
## beta q14 -0.168 0.029 -0.225 -0.112
## beta q15 -1.178 0.035 -1.248 -1.109
## beta q16 -0.064 0.029 -0.120 -0.008
## beta q17 1.945 0.039 1.869 2.020
## beta q18 0.151 0.028 0.095 0.206
## beta q19 -0.856 0.032 -0.920 -0.793
## beta q20 1.082 0.031 1.021 1.142
## beta q21 2.057 0.040 1.978 2.136
## beta q22 0.343 0.028 0.287 0.399
## beta q23 -0.464 0.030 -0.523 -0.405
## beta q24 0.335 0.028 0.279 0.391
## beta q25 2.116 0.041 2.036 2.196
## beta q26 0.160 0.028 0.104 0.215
## beta q27 -2.063 0.048 -2.157 -1.968
## beta q28 -0.269 0.029 -0.327 -0.212
## beta q29 0.103 0.028 0.047 0.159
## beta q30 1.321 0.032 1.258 1.385
## beta q31 -2.631 0.061 -2.751 -2.511
## beta q32 -1.496 0.039 -1.572 -1.419
## beta q33 -1.718 0.042 -1.801 -1.635
## beta q34 0.946 0.030 0.887 1.005
## beta q35 -1.176 0.035 -1.245 -1.107
## beta q36 1.075 0.031 1.015 1.135
## beta q37 -1.096 0.035 -1.164 -1.029
## beta q38 1.752 0.036 1.681 1.824
## beta q39 1.321 0.032 1.258 1.385
## beta q40 -0.483 0.030 -0.542 -0.424
## beta q41 -0.318 0.029 -0.376 -0.260
## beta q42 -0.691 0.031 -0.753 -0.630
## beta q43 2.044 0.040 1.966 2.122
## beta q44 1.078 0.031 1.018 1.138
## beta q45 -1.088 0.034 -1.155 -1.020
## beta q46 -0.638 0.031 -0.699 -0.577
## beta q47 0.196 0.028 0.141 0.252
## beta q48 -0.559 0.031 -0.618 -0.499
## beta q49 0.756 0.029 0.698 0.813
## beta q50 -0.948 0.033 -1.013 -0.883
## beta q51 -1.122 0.035 -1.190 -1.054
## beta q52 -0.770 0.032 -0.833 -0.708
## beta q53 0.308 0.028 0.252 0.364
## beta q54 -0.671 0.031 -0.732 -0.609
## beta q55 1.246 0.032 1.183 1.308
## beta q56 -0.894 0.033 -0.958 -0.830
## beta q57 -0.163 0.029 -0.220 -0.107
## beta q58 -0.403 0.030 -0.462 -0.345
## beta q59 0.669 0.029 0.612 0.726
## beta q60 0.068 0.028 0.012 0.124
# Plot the Wright Map
plotPImap(dichot.retail_5000_60, main = "Retail Salespeople Wright Map", irug = FALSE)
### Examine Item Parameters:
# View individual item parameters:
difficulty <- dichot.retail_5000_60$etapar
difficulty
## q02 q03 q04 q05 q06 q07
## -0.95859562 0.74562586 1.42121919 1.43612710 0.03760367 -0.43990586
## q08 q09 q10 q11 q12 q13
## -0.55177162 0.30585511 -0.77850285 -1.97692039 -0.05236516 -0.43332127
## q14 q15 q16 q17 q18 q19
## 0.16831095 1.17846060 0.06420157 -1.94451902 -0.15061755 0.85625377
## q20 q21 q22 q23 q24 q25
## -1.08185027 -2.05705140 -0.34313841 0.46387370 -0.33496595 -2.11590459
## q26 q27 q28 q29 q30 q31
## -0.15959773 2.06277327 0.26933208 -0.10320536 -1.32136361 2.63089029
## q32 q33 q34 q35 q36 q37
## 1.49572963 1.71796448 -0.94572855 1.17591458 -1.07512271 1.09637490
## q38 q39 q40 q41 q42 q43
## -1.75244994 -1.32136362 0.48313280 0.31810373 0.69129810 -2.04393128
## q44 q45 q46 q47 q48 q49
## -1.07800382 1.08789141 0.63817411 -0.19630850 0.55861749 -0.75584661
## q50 q51 q52 q53 q54 q55
## 0.94827938 1.12207348 0.77018940 -0.30801797 0.67050207 -1.24593438
## q56 q57 q58 q59 q60
## 0.89408746 0.16322975 0.40320156 -0.66895362 -0.06796626
# Calculate the location for item 1:
n.items <- ncol(retail_5000_60)
i1 <- 0 - sum(difficulty[1:(n.items - 1)])
difficulty.all <- c(i1, difficulty[c(1:(n.items - 1))])
difficulty.all
## q02 q03 q04 q05 q06
## 0.38793241 -0.95859562 0.74562586 1.42121919 1.43612710 0.03760367
## q07 q08 q09 q10 q11 q12
## -0.43990586 -0.55177162 0.30585511 -0.77850285 -1.97692039 -0.05236516
## q13 q14 q15 q16 q17 q18
## -0.43332127 0.16831095 1.17846060 0.06420157 -1.94451902 -0.15061755
## q19 q20 q21 q22 q23 q24
## 0.85625377 -1.08185027 -2.05705140 -0.34313841 0.46387370 -0.33496595
## q25 q26 q27 q28 q29 q30
## -2.11590459 -0.15959773 2.06277327 0.26933208 -0.10320536 -1.32136361
## q31 q32 q33 q34 q35 q36
## 2.63089029 1.49572963 1.71796448 -0.94572855 1.17591458 -1.07512271
## q37 q38 q39 q40 q41 q42
## 1.09637490 -1.75244994 -1.32136362 0.48313280 0.31810373 0.69129810
## q43 q44 q45 q46 q47 q48
## -2.04393128 -1.07800382 1.08789141 0.63817411 -0.19630850 0.55861749
## q49 q50 q51 q52 q53 q54
## -0.75584661 0.94827938 1.12207348 0.77018940 -0.30801797 0.67050207
## q55 q56 q57 q58 q59 q60
## -1.24593438 0.89408746 0.16322975 0.40320156 -0.66895362 -0.06796626
# Alternative method to calculate item difficulty (easiness * -1):
difficulty2 <- dichot.retail_5000_60$betapar * -1
difficulty2
## beta q01 beta q02 beta q03 beta q04 beta q05 beta q06
## 0.38793241 -0.95859562 0.74562586 1.42121919 1.43612710 0.03760367
## beta q07 beta q08 beta q09 beta q10 beta q11 beta q12
## -0.43990586 -0.55177162 0.30585511 -0.77850285 -1.97692039 -0.05236516
## beta q13 beta q14 beta q15 beta q16 beta q17 beta q18
## -0.43332127 0.16831095 1.17846060 0.06420157 -1.94451902 -0.15061755
## beta q19 beta q20 beta q21 beta q22 beta q23 beta q24
## 0.85625377 -1.08185027 -2.05705140 -0.34313841 0.46387370 -0.33496595
## beta q25 beta q26 beta q27 beta q28 beta q29 beta q30
## -2.11590459 -0.15959773 2.06277327 0.26933208 -0.10320536 -1.32136361
## beta q31 beta q32 beta q33 beta q34 beta q35 beta q36
## 2.63089029 1.49572963 1.71796448 -0.94572855 1.17591458 -1.07512271
## beta q37 beta q38 beta q39 beta q40 beta q41 beta q42
## 1.09637490 -1.75244994 -1.32136362 0.48313280 0.31810373 0.69129810
## beta q43 beta q44 beta q45 beta q46 beta q47 beta q48
## -2.04393128 -1.07800382 1.08789141 0.63817411 -0.19630850 0.55861749
## beta q49 beta q50 beta q51 beta q52 beta q53 beta q54
## -0.75584661 0.94827938 1.12207348 0.77018940 -0.30801797 0.67050207
## beta q55 beta q56 beta q57 beta q58 beta q59 beta q60
## -1.24593438 0.89408746 0.16322975 0.40320156 -0.66895362 -0.06796626
# View standard errors for item parameters:
dichot.retail_5000_60$se.beta
## [1] 0.02970309 0.03015636 0.03167038 0.03812364 0.03831056 0.02864922
## [7] 0.02854284 0.02873696 0.02937977 0.02938829 0.03909749 0.02851330
## [13] 0.02853399 0.02894393 0.03536187 0.02869992 0.03867949 0.02842647
## [19] 0.03247198 0.03081340 0.04017345 0.02844210 0.03004270 0.02843642
## [25] 0.04100300 0.02842172 0.04820033 0.02925135 0.02846025 0.03240657
## [31] 0.06119803 0.03907918 0.04224970 0.03009399 0.03533562 0.03077474
## [37] 0.03454467 0.03639665 0.03240665 0.03013553 0.02942489 0.03131089
## [43] 0.03999314 0.03079134 0.03446327 0.03098067 0.02840788 0.03052526
## [49] 0.02930754 0.03321149 0.03479432 0.03184029 0.02842092 0.03117918
## [55] 0.03185880 0.03276790 0.02893028 0.02976737 0.02903009 0.02849516
# Examine descriptive statistics for item parameters:
summary(difficulty.all)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.1159 -0.7615 0.0509 0.0000 0.7518 2.6309
sd(difficulty.all)
## [1] 1.088567
summary(dichot.retail_5000_60$se.beta)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.02841 0.02894 0.03078 0.03275 0.03461 0.06120
sd(dichot.retail_5000_60$se.beta)
## [1] 0.005752056
hist(difficulty.all, main = "Histogram of Item Difficulty Estimates for the Retail Salespeople Data",
xlab = "Item Difficulty Estimates in Logits")
### Inserted this from the book page 17
###items.to.plot <- c(1:3)
plotICC(dichot.retail_5000_60, ask = FALSE)
personnel.locations <- person.parameter(dichot.retail_5000_60)
achievement <- personnel.locations$theta.table
achievement$id <-rownames(achievement)
# Add standard errors to person achievement object:
se <- as.data.frame(personnel.locations$se.theta$NAgroup1)
se$id <- rownames(se)
names(se) <- c("person_se", "id")
achievement.with.se <- merge(achievement, se, by = "id" )
# Examine descriptive statistics for person parameters:
summary(achievement)
## Person Parameter NAgroup Interpolated id
## Min. :-3.44748 Min. :1 Mode :logical Length:5000
## 1st Qu.:-0.49516 1st Qu.:1 FALSE:5000 Class :character
## Median :-0.23915 Median :1 Mode :character
## Mean :-0.24889 Mean :1
## 3rd Qu.: 0.01157 3rd Qu.:1
## Max. : 2.83268 Max. :1
hist(achievement$`Person Parameter`, main = "Histogram of Person Achievement Estimates for the Retail Salespersons Data",
xlab = "Person Achievement Estimates in Logits")
# Examine item fit statistics:
### Why the switch to person locations?
person.locations <- person.parameter(dichot.retail_5000_60)
item.fit <- itemfit(personnel.locations)
item.fit
##
## Itemfit Statistics:
## Chisq df p-value Outfit MSQ Infit MSQ Outfit t Infit t Discrim
## q01 4741.977 4999 0.995 0.948 0.947 -4.476 -5.526 0.316
## q02 5089.216 4999 0.183 1.018 1.009 1.435 0.844 0.081
## q03 5089.245 4999 0.183 1.018 0.995 1.058 -0.336 0.111
## q04 4923.009 4999 0.776 0.985 0.971 -0.529 -1.153 0.146
## q05 4973.003 4999 0.600 0.995 0.982 -0.176 -0.712 0.119
## q06 5014.955 4999 0.434 1.003 1.002 0.385 0.248 0.140
## q07 5141.282 4999 0.078 1.028 1.024 4.018 4.094 0.069
## q08 4987.242 4999 0.544 0.997 0.994 -0.326 -0.831 0.146
## q09 4735.826 4999 0.996 0.947 0.951 -5.034 -5.698 0.316
## q10 5279.618 4999 0.003 1.056 1.043 5.437 4.781 -0.027
## q11 4471.482 4999 1.000 0.894 0.940 -3.711 -2.331 0.265
## q12 5068.031 4999 0.244 1.014 1.010 1.899 1.758 0.104
## q13 5094.452 4999 0.170 1.019 1.019 2.709 3.181 0.069
## q14 5159.002 4999 0.056 1.032 1.022 3.466 3.006 0.063
## q15 4904.417 4999 0.828 0.981 0.978 -0.789 -1.041 0.154
## q16 5009.707 4999 0.455 1.002 1.001 0.244 0.125 0.142
## q17 4925.513 4999 0.768 0.985 0.968 -0.510 -1.264 0.124
## q18 5288.021 4999 0.002 1.058 1.052 8.516 9.547 -0.026
## q19 4605.146 4999 1.000 0.921 0.947 -4.355 -3.417 0.285
## q20 5267.538 4999 0.004 1.054 1.031 3.731 2.474 0.009
## q21 5295.039 4999 0.002 1.059 0.995 1.871 -0.158 0.015
## q22 5064.900 4999 0.254 1.013 1.011 1.974 1.943 0.114
## q23 5060.920 4999 0.267 1.012 1.007 0.957 0.625 0.117
## q24 4895.754 4999 0.849 0.979 0.982 -3.211 -3.330 0.197
## q25 5295.367 4999 0.002 1.059 0.996 1.802 -0.126 0.001
## q26 4855.501 4999 0.925 0.971 0.973 -4.414 -5.004 0.238
## q27 4695.935 4999 0.999 0.939 0.963 -1.420 -0.977 0.148
## q28 4750.570 4999 0.994 0.950 0.963 -4.954 -4.470 0.253
## q29 5163.025 4999 0.052 1.033 1.031 4.713 5.581 0.045
## q30 4697.624 4999 0.999 0.940 0.954 -3.476 -2.981 0.261
## q31 4938.815 4999 0.725 0.988 0.963 -0.185 -0.688 0.085
## q32 4815.864 4999 0.968 0.963 0.972 -1.222 -1.054 0.140
## q33 4648.772 4999 1.000 0.930 0.961 -2.043 -1.284 0.176
## q34 5195.323 4999 0.026 1.039 1.024 3.160 2.161 0.023
## q35 4981.598 4999 0.567 0.996 0.979 -0.145 -0.998 0.127
## q36 4688.654 4999 0.999 0.938 0.952 -4.534 -3.915 0.279
## q37 4937.148 4999 0.731 0.987 0.989 -0.549 -0.571 0.105
## q38 4953.218 4999 0.675 0.991 0.978 -0.365 -0.992 0.121
## q39 4704.759 4999 0.999 0.941 0.962 -3.392 -2.409 0.246
## q40 5262.402 4999 0.005 1.052 1.035 3.972 3.213 -0.007
## q41 4753.368 4999 0.994 0.951 0.959 -4.628 -4.703 0.289
## q42 4597.421 4999 1.000 0.919 0.942 -5.161 -4.399 0.333
## q43 4733.648 4999 0.996 0.947 0.947 -1.749 -1.952 0.189
## q44 4871.450 4999 0.900 0.974 0.974 -1.840 -2.079 0.187
## q45 4717.307 4999 0.998 0.943 0.963 -2.552 -1.912 0.227
## q46 5026.462 4999 0.389 1.005 0.992 0.352 -0.593 0.139
## q47 5183.962 4999 0.033 1.037 1.035 5.588 6.503 0.027
## q48 4865.622 4999 0.910 0.973 0.982 -1.924 -1.506 0.168
## q49 4978.804 4999 0.578 0.996 0.996 -0.428 -0.499 0.140
## q50 4736.384 4999 0.996 0.947 0.963 -2.661 -2.194 0.217
## q51 4795.565 4999 0.980 0.959 0.974 -1.785 -1.309 0.162
## q52 5230.739 4999 0.011 1.046 1.025 2.643 1.698 0.003
## q53 4983.180 4999 0.560 0.997 1.000 -0.518 -0.087 0.144
## q54 5234.667 4999 0.010 1.047 1.023 2.947 1.691 0.019
## q55 5050.161 4999 0.303 1.010 1.003 0.610 0.202 0.082
## q56 5225.706 4999 0.013 1.045 1.004 2.320 0.236 0.057
## q57 4940.192 4999 0.720 0.988 0.995 -1.327 -0.708 0.136
## q58 5144.680 4999 0.074 1.029 1.024 2.408 2.371 0.027
## q59 4894.813 4999 0.851 0.979 0.982 -2.383 -2.353 0.208
## q60 5360.578 4999 0.000 1.072 1.059 10.004 10.172 -0.064
## Calculate reliability of item separation:
# Get Item scores
ItemScores <- colSums(retail_5000_labels)
ItemScores
## Position Age Gender Marital q01 q02 q03 q04
## 12329 23363 9510 7944 6750 8344 6373 5813
## q05 q06 q07 q08 q09 q10 q11 q12
## 5803 7159 7742 7877 6843 8143 9229 7268
## q13 q14 q15 q16 q17 q18 q19 q20
## 7734 7003 5990 7127 9208 7388 6267 8475
## q21 q22 q23 q24 q25 q26 q27 q28
## 9279 7624 6666 7614 9314 7399 5466 6885
## q29 q30 q31 q32 q33 q34 q35 q36
## 7330 8712 5276 5764 5632 8330 5992 8468
## q37 q38 q39 q40 q41 q42 q43 q44
## 6056 9074 8712 6645 6829 6427 9271 8471
## q45 q46 q47 q48 q49 q50 q51 q52
## 6063 6481 7444 6564 8117 6183 6035 6349
## q53 q54 q55 q56 q57 q58 q59 q60
## 7581 6448 8640 6232 7009 6733 8016 7287
# Get Item SD
ItemSD <- apply(retail_5000_labels,2,sd)
ItemSD
## Position Age Gender Marital q01 q02 q03 q04
## 0.5470742 1.6532259 0.2973444 0.4921006 0.4770173 0.4706919 0.4463571 0.3690372
## q05 q06 q07 q08 q09 q10 q11 q12
## 0.3671983 0.4953765 0.4977017 0.4943316 0.4824734 0.4832274 0.3611765 0.4978922
## q13 q14 q15 q16 q17 q18 q19 q20
## 0.4978547 0.4900690 0.3985320 0.4944530 0.3651522 0.4995479 0.4350015 0.4604535
## q21 q22 q23 q24 q25 q26 q27 q28
## 0.3513275 0.4994345 0.4714045 0.4995298 0.3440928 0.4996418 0.2907416 0.4846834
## q29 q30 q31 q32 q33 q34 q35 q36
## 0.4988926 0.4373563 0.2283931 0.3598306 0.3323329 0.4716869 0.3988349 0.4610440
## q37 q38 q39 q40 q41 q42 q43 q44
## 0.4082008 0.3884986 0.4373563 0.4698970 0.4817019 0.4516499 0.3529409 0.4607915
## q45 q46 q47 q48 q49 q50 q51 q52
## 0.4091879 0.4566260 0.4999245 0.4636800 0.4845817 0.4250371 0.4051960 0.4439002
## q53 q54 q55 q56 q57 q58 q59 q60
## 0.4997875 0.4536221 0.4450344 0.4309573 0.4903110 0.4759346 0.4892828 0.4982318
# Calculate the se of the Item
ItemSE <- ItemSD/sqrt(length(ItemSD))
ItemSE
## Position Age Gender Marital q01 q02 q03
## 0.06838428 0.20665324 0.03716805 0.06151257 0.05962716 0.05883649 0.05579464
## q04 q05 q06 q07 q08 q09 q10
## 0.04612965 0.04589979 0.06192206 0.06221271 0.06179145 0.06030918 0.06040343
## q11 q12 q13 q14 q15 q16 q17
## 0.04514706 0.06223652 0.06223184 0.06125863 0.04981650 0.06180662 0.04564402
## q18 q19 q20 q21 q22 q23 q24
## 0.06244349 0.05437518 0.05755668 0.04391594 0.06242932 0.05892556 0.06244123
## q25 q26 q27 q28 q29 q30 q31
## 0.04301160 0.06245522 0.03634270 0.06058542 0.06236157 0.05466953 0.02854913
## q32 q33 q34 q35 q36 q37 q38
## 0.04497882 0.04154161 0.05896086 0.04985436 0.05763050 0.05102510 0.04856232
## q39 q40 q41 q42 q43 q44 q45
## 0.05466953 0.05873712 0.06021274 0.05645624 0.04411761 0.05759894 0.05114849
## q46 q47 q48 q49 q50 q51 q52
## 0.05707824 0.06249057 0.05796000 0.06057271 0.05312964 0.05064951 0.05548752
## q53 q54 q55 q56 q57 q58 q59
## 0.06247343 0.05670276 0.05562930 0.05386966 0.06128887 0.05949182 0.06116035
## q60
## 0.06227897
# compute the Observed Variance (also known as Total Person Variability or Squared Standard Deviation)
SSD.ItemScores <- var(ItemScores)
SSD.ItemScores
## [1] 5626823
# compute the Mean Square Measurement error (also known as Model Error variance)
Item.MSE <- sum((ItemSE)^2) / length(ItemSE)
Item.MSE
## [1] 0.003738394
# compute the Item Separation Reliability
item.separation.reliability <- (SSD.ItemScores-Item.MSE) / SSD.ItemScores
item.separation.reliability
## [1] 1
###Item Separability matches the book.
## Examine person fit statistics:
person.fit <- personfit(personnel.locations)
summary(person.fit$p.infitMSQ)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.6059 0.8768 0.9718 0.9944 1.0895 1.8874
summary(person.fit$p.outfitMSQ)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.5377 0.8225 0.9377 0.9933 1.1118 2.9633
# Examine person reliability:
person_rel <- SepRel(personnel.locations)
person_rel$sep.rel
## [1] 0.5219916
### Summarize the results in tables
summary.table.statistics <- c("Logit Scale Location Mean",
"Logit Scale Location SD",
"Standard Error Mean",
"Standard Error SD",
"Outfit MSE Mean",
"Outfit MSE SD",
"Infit MSE Mean",
"Infit MSE SD",
"Std. Outfit Mean",
"Std. Outfit SD",
"Std. Infit Mean",
"Std. Infit SD",
"Reliability of Separation")
item.summary.results <- rbind(mean(difficulty.all),
sd(difficulty.all),
mean(dichot.retail_5000_60$se.beta),
sd(dichot.retail_5000_60$se.beta),
mean(item.fit$i.outfitMSQ),
sd(item.fit$i.outfitMSQ),
mean(item.fit$i.infitMSQ),
sd(item.fit$i.infitMSQ),
mean(item.fit$i.outfitZ),
sd(item.fit$i.outfitZ),
mean(item.fit$i.infitMSQ),
sd(item.fit$i.infitZ),
item.separation.reliability)
person.summary.results <- rbind(mean(achievement.with.se$`Person Parameter`),
sd(achievement.with.se$`Person Parameter`),
mean(achievement.with.se$person_se, na.rm = TRUE),
sd(achievement.with.se$person_se, na.rm = TRUE),
mean(person.fit$p.outfitMSQ),
sd(person.fit$p.outfitMSQ),
mean(person.fit$p.infitMSQ),
sd(person.fit$p.infitMSQ),
mean(person.fit$p.outfitZ),
sd(person.fit$p.outfitZ),
mean(person.fit$p.infitZ),
sd(person.fit$p.infitZ),
person_rel$sep.rel)
# Round the values for presentation in a table:
item.summary.results_rounded <- round(item.summary.results, digits = 2)
person.summary.results_rounded <- round(person.summary.results, digits = 2)
Table1 <- cbind.data.frame(summary.table.statistics,
item.summary.results_rounded,
person.summary.results_rounded)
### Tables 1 & 2
# add descriptive column labels:
names(Table1) <- c("Statistic", "Items", "Persons")
print.data.frame(Table1, row.names = FALSE)
## Statistic Items Persons
## Logit Scale Location Mean 0.00 -0.25
## Logit Scale Location SD 1.09 0.43
## Standard Error Mean 0.03 0.29
## Standard Error SD 0.01 0.01
## Outfit MSE Mean 0.99 0.99
## Outfit MSE SD 0.04 0.25
## Infit MSE Mean 0.99 0.99
## Infit MSE SD 0.03 0.16
## Std. Outfit Mean 0.02 -0.10
## Std. Outfit SD 3.31 1.32
## Std. Infit Mean 0.99 -0.08
## Std. Infit SD 3.22 1.35
## Reliability of Separation 1.00 0.52
## Item calibration table:
# Calculate the proportion correct for each task:
PropCorrect <- apply(retail_5000_60, 2, mean)
# Calculate the proportion correct for each task:
PropCorrect <- apply(retail_5000_60, 2, mean)
# Combine item calibration results in a table:
Table2 <- cbind.data.frame(colnames(retail_5000_60),
PropCorrect,
difficulty.all,
dichot.retail_5000_60$se.beta,
item.fit$i.outfitMSQ,
item.fit$i.outfitZ,
item.fit$i.infitMSQ,
item.fit$i.infitZ)
names(Table2) <- c("Task ID", "Proportion Correct", "Item Location","Item SE","Outfit MSE","Std. Outfit", "Infit MSE","Std. Infit")
# Sort Table 2 by Item difficulty:
Table2 <- Table2[order(-Table2$`Item Location`),]
# Round the numeric values (all columns except the first one) to 2 digits:
Table2[, -1] <- round(Table2[,-1], digits = 2)
print.data.frame(Table2, row.names = FALSE)
## Task ID Proportion Correct Item Location Item SE Outfit MSE Std. Outfit
## q31 1.06 2.63 0.06 0.99 -0.19
## q27 1.09 2.06 0.05 0.94 -1.42
## q33 1.13 1.72 0.04 0.93 -2.04
## q32 1.15 1.50 0.04 0.96 -1.22
## q05 1.16 1.44 0.04 0.99 -0.18
## q04 1.16 1.42 0.04 0.98 -0.53
## q15 1.20 1.18 0.04 0.98 -0.79
## q35 1.20 1.18 0.04 1.00 -0.14
## q51 1.21 1.12 0.03 0.96 -1.79
## q37 1.21 1.10 0.03 0.99 -0.55
## q45 1.21 1.09 0.03 0.94 -2.55
## q50 1.24 0.95 0.03 0.95 -2.66
## q56 1.25 0.89 0.03 1.05 2.32
## q19 1.25 0.86 0.03 0.92 -4.35
## q52 1.27 0.77 0.03 1.05 2.64
## q03 1.27 0.75 0.03 1.02 1.06
## q42 1.29 0.69 0.03 0.92 -5.16
## q54 1.29 0.67 0.03 1.05 2.95
## q46 1.30 0.64 0.03 1.01 0.35
## q48 1.31 0.56 0.03 0.97 -1.92
## q40 1.33 0.48 0.03 1.05 3.97
## q23 1.33 0.46 0.03 1.01 0.96
## q58 1.35 0.40 0.03 1.03 2.41
## q01 1.35 0.39 0.03 0.95 -4.48
## q41 1.37 0.32 0.03 0.95 -4.63
## q09 1.37 0.31 0.03 0.95 -5.03
## q28 1.38 0.27 0.03 0.95 -4.95
## q14 1.40 0.17 0.03 1.03 3.47
## q57 1.40 0.16 0.03 0.99 -1.33
## q16 1.43 0.06 0.03 1.00 0.24
## q06 1.43 0.04 0.03 1.00 0.38
## q12 1.45 -0.05 0.03 1.01 1.90
## q60 1.46 -0.07 0.03 1.07 10.00
## q29 1.47 -0.10 0.03 1.03 4.71
## q18 1.48 -0.15 0.03 1.06 8.52
## q26 1.48 -0.16 0.03 0.97 -4.41
## q47 1.49 -0.20 0.03 1.04 5.59
## q53 1.52 -0.31 0.03 1.00 -0.52
## q24 1.52 -0.33 0.03 0.98 -3.21
## q22 1.52 -0.34 0.03 1.01 1.97
## q13 1.55 -0.43 0.03 1.02 2.71
## q07 1.55 -0.44 0.03 1.03 4.02
## q08 1.58 -0.55 0.03 1.00 -0.33
## q59 1.60 -0.67 0.03 0.98 -2.38
## q49 1.62 -0.76 0.03 1.00 -0.43
## q10 1.63 -0.78 0.03 1.06 5.44
## q34 1.67 -0.95 0.03 1.04 3.16
## q02 1.67 -0.96 0.03 1.02 1.44
## q36 1.69 -1.08 0.03 0.94 -4.53
## q44 1.69 -1.08 0.03 0.97 -1.84
## q20 1.70 -1.08 0.03 1.05 3.73
## q55 1.73 -1.25 0.03 1.01 0.61
## q30 1.74 -1.32 0.03 0.94 -3.48
## q39 1.74 -1.32 0.03 0.94 -3.39
## q38 1.81 -1.75 0.04 0.99 -0.37
## q17 1.84 -1.94 0.04 0.99 -0.51
## q11 1.85 -1.98 0.04 0.89 -3.71
## q43 1.85 -2.04 0.04 0.95 -1.75
## q21 1.86 -2.06 0.04 1.06 1.87
## q25 1.86 -2.12 0.04 1.06 1.80
## Infit MSE Std. Infit
## 0.96 -0.69
## 0.96 -0.98
## 0.96 -1.28
## 0.97 -1.05
## 0.98 -0.71
## 0.97 -1.15
## 0.98 -1.04
## 0.98 -1.00
## 0.97 -1.31
## 0.99 -0.57
## 0.96 -1.91
## 0.96 -2.19
## 1.00 0.24
## 0.95 -3.42
## 1.02 1.70
## 1.00 -0.34
## 0.94 -4.40
## 1.02 1.69
## 0.99 -0.59
## 0.98 -1.51
## 1.04 3.21
## 1.01 0.63
## 1.02 2.37
## 0.95 -5.53
## 0.96 -4.70
## 0.95 -5.70
## 0.96 -4.47
## 1.02 3.01
## 0.99 -0.71
## 1.00 0.13
## 1.00 0.25
## 1.01 1.76
## 1.06 10.17
## 1.03 5.58
## 1.05 9.55
## 0.97 -5.00
## 1.03 6.50
## 1.00 -0.09
## 0.98 -3.33
## 1.01 1.94
## 1.02 3.18
## 1.02 4.09
## 0.99 -0.83
## 0.98 -2.35
## 1.00 -0.50
## 1.04 4.78
## 1.02 2.16
## 1.01 0.84
## 0.95 -3.91
## 0.97 -2.08
## 1.03 2.47
## 1.00 0.20
## 0.95 -2.98
## 0.96 -2.41
## 0.98 -0.99
## 0.97 -1.26
## 0.94 -2.33
## 0.95 -1.95
## 1.00 -0.16
## 1.00 -0.13
## Person calibration table:
# Calculate proportion correct for persons:
PersonPropCorrect <- apply(personnel.locations$X.ex, 1, mean)
# Combine person calibration results in a table:
PersonPropCorrect <- apply(personnel.locations$X.ex, 1, mean)
# Combine person calibration results in a table:
Table3 <- cbind.data.frame(achievement.with.se$id,
PersonPropCorrect,
achievement.with.se$`Person Parameter`,
achievement.with.se$person_se,
person.fit$p.outfitMSQ,
person.fit$p.outfitZ,
person.fit$p.infitMSQ,
person.fit$p.infitZ)
names(Table3) <- c("Person ID", "Proportion Correct", "Person Location","Person SE","Outfit MSE","Std. Outfit", "Infit MSE","Std. Infit")
# Round the numeric values (all columns except the first one) to 2 digits:
Table3[, -1] <- round(Table3[,-1], digits = 2)
print.data.frame(Table3 [1:6, ], row.names = FALSE)
## Person ID Proportion Correct Person Location Person SE Outfit MSE Std. Outfit
## 1 0.55 0.26 0.29 1.62 3.21
## 10 0.40 -0.41 0.29 0.85 -0.85
## 100 0.40 -0.76 0.30 1.46 2.31
## 1000 0.42 0.09 0.29 0.68 -2.02
## 1001 0.25 -0.32 0.29 0.88 -0.32
## 1002 0.42 -0.16 0.29 0.96 -0.17
## Infit MSE Std. Infit
## 1.41 3.34
## 0.90 -0.81
## 1.10 0.85
## 0.75 -2.24
## 1.01 0.11
## 1.00 0.04
write.csv(Table3, file = "Table3.CSV", row.names = FALSE)
write.csv(Table2, file = "Table2.CSV", row.names = FALSE)
write.csv(Table1, file = "Table1.CSV", row.names = FALSE)