Prepare Data

Import surveys, combine into single data frame, delete identifying information, assign IDs, and separate out by scale for item examination.

# https://hansjoerg.me/2018/04/23/rasch-in-r-tutorial/

knitr::knit_hooks$set(
   error = function(x, options) {
     paste('\n\n<div class="alert alert-danger">',
           gsub('##', '\n', gsub('^##\ Error', '**Error**', x)),
           '</div>', sep = '\n')
   },
   warning = function(x, options) {
     paste('\n\n<div class="alert alert-warning">',
           gsub('##', '\n', gsub('^##\ Warning:', '**Warning**', x)),
           '</div>', sep = '\n')
   },
   message = function(x, options) {
     paste('\n\n<div class="alert alert-info">',
           gsub('##', '\n', x),
           '</div>', sep = '\n')
   }
)

# load libraries ----------------------------------------------------------
library(stringi)
library(psych)
library(DT)
library(naniar)
library(UpSetR)
library(nFactors)
library(lavaan)
library(corrplot)
library(tidyr)

library(ggplot2)
library(dplyr)
library("eRm")
library("ltm")
library("difR")
library("psych")

library(readr) # For import the data
library(TAM) # For running the Rating Scale Rasch Model
# library(plyr) # For plot the Item characteristic curves
library(WrightMap)# For plot the variable map
# library(eRm) # For another example

# load data ---------------------------------------------------------------
# alt <- read.csv(file="UBelong Post-Survey Pitt OChem Spring 2022 Alternative Scales_April 28, 2022_12.34.csv", header=T)
# alt <- alt[-c(1,2),]
# alt$scale <- "alt"
# 
# orig <- read.csv(file="UBelong Post-Survey Pitt OChem Spring 2022 Original Scales_April 28, 2022_12.35.csv", header=T)
# orig <- orig[-c(1,2),]
# orig$scale <- "orig"
# 
# df <- rbind.data.frame(alt, orig)
# df <- subset(df, select = -c(1:19))
# names(df)
# myFun <- function(n) {
#   a <- do.call(paste0, replicate(5, sample(LETTERS, n, TRUE), FALSE))
#   paste0(a, sprintf("%04d", sample(9999, n, TRUE)), sample(LETTERS, n, TRUE))
# }
# df$id <- myFun(nrow(df))
# write.csv(df, file="imported_anonymized.csv", row.names = F)

df <- read.csv(file="imported_anonymized.csv", header=T)

# extract items -----------------------------------------------------------
# new items
EEochem <- subset(df, select=c(scale,grep("EEochem", colnames(df)))) # entry expectations
CCdisc <- subset(df, select=grep("CCdisc", colnames(df))) # classroom climate
IDochem <- cbind.data.frame(subset(df, select=c(scale,grep("IDochem", colnames(df)))), subset(df, select=grep("FASochem", colnames(df)))) # identity
CSochem <- subset(df, select=grep("CSochem", colnames(df))) # career satisfaction

# established scales
MSchem <- subset(df, select=c(scale,grep("MSchem", colnames(df)))) # discipline growth mindset (chemistry)
IPchem <- subset(df, select=grep("IPchem", colnames(df))) # instructor growth mindset (chemistry)
SEchem <- subset(df, select=grep("SEchem", colnames(df))) # disciplinary self-efficacy (chemistry)
MSochem <- subset(df, select=c(scale, grep("MSochem", colnames(df)))) # disciplinary growth mindset (organic chemistry)
IPochem <- subset(df, select=grep("IPochem", colnames(df))) # instructor growth mindset (organic chemistry)
SEochem <- subset(df, select=grep("SEochem", colnames(df))) # disciplinary self-efficacy (organic chemistry)
CNEBochem_class <- cbind.data.frame(subset(subset(df, select=grep("CNEBochem", colnames(df))), select=c(1:3))) # entity norms and beliefs
CNEBochem_self <- cbind.data.frame(subset(subset(df, select=grep("CNEBochem", colnames(df))), select=c(4:6))) # entity norms and beliefs
CNHSochem_others <- cbind.data.frame(subset(subset(df, select=grep("CNHSochem", colnames(df))), select=c(1:3))) # help seeking
CNHSochem_self <- cbind.data.frame(subset(subset(df, select=grep("CNHSochem", colnames(df))), select=c(4:6))) # help seeking
CNSWochem <- subset(df, select=grep("CNSWochem", colnames(df))) # help seeking
FCochem <- subset(df, select=grep("FCochem", colnames(df))) # faculty caring

IDochem$FASochem03_rc[IDochem$FASochem03 == 1] <- 4
IDochem$FASochem03_rc[IDochem$FASochem03 == 2] <- 3
IDochem$FASochem03_rc[IDochem$FASochem03 == 3] <- 2
IDochem$FASochem03_rc[IDochem$FASochem03 == 4] <- 1
IDochem$FASochem03 <- IDochem$FASochem03_rc
IDochem <- subset(IDochem, select=-c(FASochem03_rc))

Identity

Items

I see myself as a [chemistry kind of person]
My parents see me as a [chemistry kind of person]
My instructors see me as a [chemistry kind of person]
My friends see me as a [chemistry kind of person]
My peers see me as a [chemistry kind of person]
I have had experiences in which I was recognized as a [chemistry kind of person]
Knowing chemistry is important for (1=no jobs; 2=a few jobs; 3=most jobs; 4=all jobs)
Knowing chemistry helps me understand how the world works. (1=never; 2=sometimes; 3=most of the time; 4=all of the time)
Thinking like a chemist will help me do well in (1=none of my classes; 2=a few of my classes; 3=most of my classes; 4=all of my classes)
Chemistry makes the world a better place to live
I look forward to my [chemistry] classes.
I don’t care about learning chemistry.
In general, I find [chemistry] (1=very boring; 2=boring; 3=interesting; 4=very interesting)

EFA & 1PL

Original document.

Rasch Rating Scale Models

Orig (All)

Summary

summary(rs_model)

## ------------------------------------------------------------
## TAM 4.0-16 (2022-05-13 13:23:23) 
## R version 4.1.2 (2021-11-01) x86_64, mingw32 | nodename=DESKTOP-UE2VMI8 | login=hthrp 
## 
## Date of Analysis: 2022-08-15 19:23:22 
## Time difference of 0.8761971 secs
## Computation time: 0.8761971 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: RSM
## Call:
## TAM::tam.mml(resp = d, irtmodel = "RSM")
## 
## ------------------------------------------------------------
## Number of iterations = 1000 
## Numeric integration with 21 integration points
## 
## Deviance = 1960.34 
## Log likelihood = -980.17 
## Number of persons = 81 
## Number of persons used = 80 
## Number of items = 12 
## Number of estimated parameters = 16 
##     Item threshold parameters = 15 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 1 
## 
## AIC = 1992  | penalty=32    | AIC=-2*LL + 2*p 
## AIC3 = 2008  | penalty=48    | AIC3=-2*LL + 3*p 
## BIC = 2030  | penalty=70.11    | BIC=-2*LL + log(n)*p 
## aBIC = 1979  | penalty=18.86    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 2046  | penalty=86.11    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 2001  | penalty=40.63    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## GHP = 1.03876     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 
## 
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.852
## ------------------------------------------------------------
## Covariances and Variances
##      [,1]
## [1,] 1.34
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##       [,1]
## [1,] 1.158
## ------------------------------------------------------------
## Regression Coefficients
##      [,1]
## [1,]    0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##          item  N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1   IDochem02 80 2.525   -2.392     -9.194    -11.820    -11.760     -9.569
## 2   IDochem03 80 2.312   -1.849     -8.651    -10.734    -10.131     -7.396
## 3   IDochem04 80 2.587   -2.549     -9.351    -12.134    -12.231    -10.197
## 4   IDochem05 79 2.519   -2.364     -9.165    -11.763    -11.674     -9.454
## 5   IDochem06 80 2.612   -2.612     -9.414    -12.260    -12.419    -10.448
## 6   IDochem10 80 3.025   -3.657    -10.459    -14.350    -15.555    -14.629
## 7   IDochem07 80 2.275   -1.751     -8.553    -10.538     -9.837     -7.005
## 8   IDochem08 80 2.550   -2.455     -9.257    -11.946    -11.948     -9.820
## 9   IDochem09 80 2.487   -2.297     -9.099    -11.631    -11.476     -9.190
## 10 FASochem02 80 2.362   -1.978     -8.780    -10.992    -10.519     -7.913
## 11 FASochem03 80 2.900   -3.335    -10.137    -13.706    -14.589    -13.340
## 12 FASochem05 80 2.775   -3.019     -9.821    -13.074    -13.641    -12.077
##    B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
## 1            1           2           3           4
## 2            1           2           3           4
## 3            1           2           3           4
## 4            1           2           3           4
## 5            1           2           3           4
## 6            1           2           3           4
## 7            1           2           3           4
## 8            1           2           3           4
## 9            1           2           3           4
## 10           1           2           3           4
## 11           1           2           3           4
## 12           1           2           3           4
## 
## Item Parameters Xsi
##               xsi se.xsi
## IDochem02  -2.392  0.178
## IDochem03  -1.849  0.180
## IDochem04  -2.549  0.177
## IDochem05  -2.364  0.179
## IDochem06  -2.612  0.177
## IDochem10  -3.657  0.181
## IDochem07  -1.751  0.181
## IDochem08  -2.455  0.177
## IDochem09  -2.297  0.178
## FASochem02 -1.978  0.179
## FASochem03 -3.335  0.178
## FASochem05 -3.019  0.177
## Cat1       -6.802  0.111
## Cat2       -0.234  0.087
## Cat3        2.452  0.070
## 
## Item Parameters in IRT parameterization
##          item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1   IDochem02     1 -2.392   -6.802   -0.234    2.452    4.584
## 2   IDochem03     1 -1.849   -6.802   -0.234    2.452    4.584
## 3   IDochem04     1 -2.549   -6.802   -0.234    2.452    4.584
## 4   IDochem05     1 -2.364   -6.802   -0.234    2.452    4.584
## 5   IDochem06     1 -2.612   -6.802   -0.234    2.452    4.584
## 6   IDochem10     1 -3.657   -6.802   -0.234    2.452    4.584
## 7   IDochem07     1 -1.751   -6.802   -0.234    2.452    4.584
## 8   IDochem08     1 -2.455   -6.802   -0.234    2.452    4.584
## 9   IDochem09     1 -2.297   -6.802   -0.234    2.452    4.584
## 10 FASochem02     1 -1.978   -6.802   -0.234    2.452    4.584
## 11 FASochem03     1 -3.335   -6.802   -0.234    2.452    4.584
## 12 FASochem05     1 -3.019   -6.802   -0.234    2.452    4.584

Wright Map or Variable Map

IRT.WrightMap(rs_model,show.thr.lab=TRUE)

Item Estimates & Fit Statistics

rs_model$xsi # The first column is the item difficulty. In this case, is the rater's rating severity.

##                   xsi     se.xsi
## IDochem02  -2.3922410 0.17759344
## IDochem03  -1.8489879 0.18023736
## IDochem04  -2.5492505 0.17719011
## IDochem05  -2.3635504 0.17873910
## IDochem06  -2.6119877 0.17708155
## IDochem10  -3.6571868 0.18078944
## IDochem07  -1.7511839 0.18088841
## IDochem08  -2.4549610 0.17741037
## IDochem09  -2.2974531 0.17792244
## FASochem02 -1.9783526 0.17945170
## FASochem03 -3.3350727 0.17839522
## FASochem05 -3.0193095 0.17719537
## Cat1       -6.8017286 0.11141753
## Cat2       -0.2340606 0.08736358
## Cat3        2.4522527 0.07005979

tam.fit(rs_model)

## Item fit calculation based on 100 simulations
## |**********|
## |----------|

## $itemfit
##     parameter    Outfit   Outfit_t      Outfit_p  Outfit_pholm     Infit
## 1   IDochem02 1.0580198  0.4183889  6.756628e-01  1.000000e+00 1.0732614
## 2   IDochem03 0.8715770 -0.8290407  4.070814e-01  1.000000e+00 0.8838798
## 3   IDochem04 0.7981729 -1.4079651  1.591414e-01  1.000000e+00 0.7964991
## 4   IDochem05 0.7644241 -1.6535519  9.821859e-02  1.000000e+00 0.7641900
## 5   IDochem06 1.1602233  1.0626448  2.879430e-01  1.000000e+00 1.1570150
## 6   IDochem10 1.0467058  0.3539523  7.233747e-01  1.000000e+00 1.0661925
## 7   IDochem07 1.1176168  0.7718125  4.402255e-01  1.000000e+00 1.1073863
## 8   IDochem08 1.3090739  1.9104215  5.607897e-02  6.729476e-01 1.2669818
## 9   IDochem09 0.8534778 -0.9786046  3.277754e-01  1.000000e+00 0.8461434
## 10 FASochem02 1.1142439  0.7628075  4.455782e-01  1.000000e+00 1.1043892
## 11 FASochem03 1.1514330  1.0217230  3.069120e-01  1.000000e+00 1.1773050
## 12 FASochem05 0.7653562 -1.6900651  9.101550e-02  1.000000e+00 0.7614478
## 13       Cat1 2.0882943 12.0766598  1.403043e-33  1.823956e-32 1.6809389
## 14       Cat2 2.3261933 18.6176985  2.309276e-77  3.232987e-76 2.2625000
## 15       Cat3 1.6763346 27.0117501 1.075583e-160 1.613375e-159 1.7262046
##       Infit_t       Infit_p   Infit_pholm
## 1   0.5161962  6.057174e-01  1.000000e+00
## 2  -0.7418750  4.581631e-01  1.000000e+00
## 3  -1.4206938  1.554058e-01  1.000000e+00
## 4  -1.6550332  9.791777e-02  1.000000e+00
## 5   1.0434298  2.967493e-01  1.000000e+00
## 6   0.4822991  6.295935e-01  1.000000e+00
## 7   0.7151123  4.745396e-01  1.000000e+00
## 8   1.6784753  9.325435e-02  1.000000e+00
## 9  -1.0311953  3.024492e-01  1.000000e+00
## 10  0.7026252  4.822893e-01  1.000000e+00
## 11  1.1803916  2.378445e-01  1.000000e+00
## 12 -1.7228018  8.492437e-02  1.000000e+00
## 13  8.2918364  1.115133e-16  1.449673e-15
## 14 17.9093779  9.964303e-72  1.395002e-70
## 15 28.7088928 2.954800e-181 4.432200e-180
## 
## $time
## [1] "2022-08-15 19:23:22 EDT" "2022-08-15 19:23:22 EDT"
## 
## $CALL
## tam.fit(tamobj = rs_model)
## 
## attr(,"class")
## [1] "tam.fit"

Test Information Function

imod1 <- TAM::IRT.informationCurves( rs_model, theta=seq(-5,5,len=100) )
plot(imod1)

Orig (1F)

Summary

summary(rs_model)

## ------------------------------------------------------------
## TAM 4.0-16 (2022-05-13 13:23:23) 
## R version 4.1.2 (2021-11-01) x86_64, mingw32 | nodename=DESKTOP-UE2VMI8 | login=hthrp 
## 
## Date of Analysis: 2022-08-15 19:23:23 
## Time difference of 0.8801961 secs
## Computation time: 0.8801961 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: RSM
## Call:
## TAM::tam.mml(resp = d1, irtmodel = "RSM")
## 
## ------------------------------------------------------------
## Number of iterations = 1000 
## Numeric integration with 21 integration points
## 
## Deviance = 607.23 
## Log likelihood = -303.62 
## Number of persons = 81 
## Number of persons used = 80 
## Number of items = 4 
## Number of estimated parameters = 8 
##     Item threshold parameters = 7 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 1 
## 
## AIC = 623  | penalty=16    | AIC=-2*LL + 2*p 
## AIC3 = 631  | penalty=24    | AIC3=-2*LL + 3*p 
## BIC = 642  | penalty=35.06    | BIC=-2*LL + log(n)*p 
## aBIC = 617  | penalty=9.43    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 650  | penalty=43.06    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 625  | penalty=18.03    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## GHP = 0.97686     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 
## 
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.845
## ------------------------------------------------------------
## Covariances and Variances
##       [,1]
## [1,] 5.409
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##       [,1]
## [1,] 2.326
## ------------------------------------------------------------
## Regression Coefficients
##      [,1]
## [1,]    0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##        item  N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1 IDochem02 80 2.525   -3.096    -12.105    -15.819    -15.865    -12.384
## 2 IDochem04 80 2.587   -3.334    -12.343    -16.294    -16.578    -13.336
## 3 IDochem05 79 2.519   -3.063    -12.072    -15.753    -15.767    -12.254
## 4 IDochem06 80 2.612   -3.429    -12.438    -16.485    -16.864    -13.717
##   B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
## 1           1           2           3           4
## 2           1           2           3           4
## 3           1           2           3           4
## 4           1           2           3           4
## 
## Item Parameters Xsi
##              xsi se.xsi
## IDochem02 -3.096  0.218
## IDochem04 -3.334  0.218
## IDochem05 -3.063  0.220
## IDochem06 -3.429  0.218
## Cat1      -9.009  0.232
## Cat2      -0.618  0.175
## Cat3       3.050  0.132
## 
## Item Parameters in IRT parameterization
##        item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1 IDochem02     1 -3.096   -9.009   -0.618     3.05    6.576
## 2 IDochem04     1 -3.334   -9.009   -0.618     3.05    6.576
## 3 IDochem05     1 -3.063   -9.009   -0.618     3.05    6.576
## 4 IDochem06     1 -3.429   -9.009   -0.618     3.05    6.576

Wright Map or Variable Map

IRT.WrightMap(rs_model,show.thr.lab=TRUE)

Item Estimates & Fit Statistics

rs_model$xsi # The first column is the item difficulty. In this case, is the rater's rating severity.

##                  xsi    se.xsi
## IDochem02 -3.0960995 0.2182412
## IDochem04 -3.3339357 0.2182367
## IDochem05 -3.0634176 0.2197044
## IDochem06 -3.4291983 0.2182685
## Cat1      -9.0087024 0.2316786
## Cat2      -0.6178376 0.1745352
## Cat3       3.0500609 0.1324678

tam.fit(rs_model)

## Item fit calculation based on 100 simulations
## |**********|
## |-------|

## $itemfit
##   parameter    Outfit   Outfit_t     Outfit_p Outfit_pholm     Infit    Infit_t
## 1 IDochem02 1.0700466  0.4628230 6.434912e-01 1.000000e+00 1.0905347  0.5904719
## 2 IDochem04 0.7107482 -2.0209778 4.328207e-02 1.731283e-01 0.7328194 -1.8438213
## 3 IDochem05 0.6436219 -2.5579822 1.052815e-02 6.316889e-02 0.6576947 -2.4347384
## 4 IDochem06 1.2411574  1.4382363 1.503670e-01 4.511011e-01 1.2474512  1.4841420
## 5      Cat1 1.2417760  0.0705901 9.437240e-01 1.000000e+00 1.4001622  2.4816115
## 6      Cat2 1.2929866  2.2195772 2.644748e-02 1.322374e-01 1.5143741  4.0282545
## 7      Cat3 1.4268956  6.5839947 4.579733e-11 3.205813e-10 1.3953639  6.4289642
##        Infit_p  Infit_pholm
## 1 5.548744e-01 5.548744e-01
## 2 6.520919e-02 1.956276e-01
## 3 1.490256e-02 6.539489e-02
## 4 1.377713e-01 2.755425e-01
## 5 1.307898e-02 6.539489e-02
## 6 5.619249e-05 3.371549e-04
## 7 1.284764e-10 8.993345e-10
## 
## $time
## [1] "2022-08-15 19:23:24 EDT" "2022-08-15 19:23:24 EDT"
## 
## $CALL
## tam.fit(tamobj = rs_model)
## 
## attr(,"class")
## [1] "tam.fit"

Test Information Function

imod1 <- TAM::IRT.informationCurves( rs_model, theta=seq(-5,5,len=100) )
plot(imod1)

Orig (2F)

Summary

summary(rs_model)

## ------------------------------------------------------------
## TAM 4.0-16 (2022-05-13 13:23:23) 
## R version 4.1.2 (2021-11-01) x86_64, mingw32 | nodename=DESKTOP-UE2VMI8 | login=hthrp 
## 
## Date of Analysis: 2022-08-15 19:23:25 
## Time difference of 0.8661969 secs
## Computation time: 0.8661969 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: RSM
## Call:
## TAM::tam.mml(resp = d2, irtmodel = "RSM")
## 
## ------------------------------------------------------------
## Number of iterations = 1000 
## Numeric integration with 21 integration points
## 
## Deviance = 843.69 
## Log likelihood = -421.84 
## Number of persons = 81 
## Number of persons used = 80 
## Number of items = 5 
## Number of estimated parameters = 9 
##     Item threshold parameters = 8 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 1 
## 
## AIC = 862  | penalty=18    | AIC=-2*LL + 2*p 
## AIC3 = 871  | penalty=27    | AIC3=-2*LL + 3*p 
## BIC = 883  | penalty=39.44    | BIC=-2*LL + log(n)*p 
## aBIC = 854  | penalty=10.61    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 892  | penalty=48.44    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 864  | penalty=20.57    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## GHP = 1.07711     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 
## 
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.777
## ------------------------------------------------------------
## Covariances and Variances
##       [,1]
## [1,] 2.049
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##       [,1]
## [1,] 1.431
## ------------------------------------------------------------
## Regression Coefficients
##      [,1]
## [1,]    0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##         item  N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1  IDochem08 80 2.550   -2.474     -9.528    -12.191    -12.364     -9.897
## 2  IDochem09 80 2.487   -2.305     -9.359    -11.852    -11.855     -9.218
## 3 FASochem02 80 2.362   -1.965     -9.019    -11.173    -10.836     -7.860
## 4 FASochem03 80 2.900   -3.445    -10.500    -14.133    -15.277    -13.781
## 5 FASochem05 80 2.775   -3.092    -10.147    -13.428    -14.219    -12.370
##   B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
## 1           1           2           3           4
## 2           1           2           3           4
## 3           1           2           3           4
## 4           1           2           3           4
## 5           1           2           3           4
## 
## Item Parameters Xsi
##               xsi se.xsi
## IDochem08  -2.474  0.184
## IDochem09  -2.305  0.184
## FASochem02 -1.965  0.184
## FASochem03 -3.445  0.189
## FASochem05 -3.092  0.187
## Cat1       -7.054  0.174
## Cat2       -0.188  0.134
## Cat3        2.301  0.110
## 
## Item Parameters in IRT parameterization
##         item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1  IDochem08     1 -2.474   -7.054   -0.188    2.301    4.941
## 2  IDochem09     1 -2.305   -7.054   -0.188    2.301    4.941
## 3 FASochem02     1 -1.965   -7.054   -0.188    2.301    4.941
## 4 FASochem03     1 -3.445   -7.054   -0.188    2.301    4.941
## 5 FASochem05     1 -3.092   -7.054   -0.188    2.301    4.941

Wright Map or Variable Map

IRT.WrightMap(rs_model,show.thr.lab=TRUE)

Item Estimates & Fit Statistics

rs_model$xsi # The first column is the item difficulty. In this case, is the rater's rating severity.

##                   xsi    se.xsi
## IDochem08  -2.4741528 0.1844231
## IDochem09  -2.3045698 0.1842312
## FASochem02 -1.9650549 0.1844146
## FASochem03 -3.4452518 0.1891040
## FASochem05 -3.0924898 0.1866949
## Cat1       -7.0542517 0.1735807
## Cat2       -0.1884432 0.1340774
## Cat3        2.3014427 0.1097370

tam.fit(rs_model)

## Item fit calculation based on 100 simulations
## |**********|
## |--------|

## $itemfit
##    parameter    Outfit   Outfit_t     Outfit_p Outfit_pholm     Infit
## 1  IDochem08 1.1783092  1.1455584 2.519779e-01 1.000000e+00 1.1456682
## 2  IDochem09 0.9368175 -0.3968901 6.914485e-01 1.000000e+00 0.9089668
## 3 FASochem02 1.0456928  0.3358555 7.369799e-01 1.000000e+00 1.0575651
## 4 FASochem03 1.1219956  0.8054538 4.205578e-01 1.000000e+00 1.1542231
## 5 FASochem05 0.7105204 -2.0864080 3.694168e-02 2.216501e-01 0.7158746
## 6       Cat1 2.1135397  7.7547176 8.854026e-15 7.083221e-14 1.1685170
## 7       Cat2 1.3420976  3.9041748 9.454742e-05 6.618319e-04 1.3165882
## 8       Cat3 1.0678236  1.8375579 6.612758e-02 3.306379e-01 1.0738598
##      Infit_t      Infit_p Infit_pholm
## 1  0.9549524 0.3396017805 1.000000000
## 2 -0.5863275 0.5576554772 1.000000000
## 3  0.4118674 0.6804366212 1.000000000
## 4  0.9984850 0.3180442342 1.000000000
## 5 -2.0418228 0.0411691144 0.288183801
## 6  1.5011047 0.1333284949 0.666642475
## 7  3.6670527 0.0002453622 0.001962898
## 8  2.0184525 0.0435441532 0.288183801
## 
## $time
## [1] "2022-08-15 19:23:25 EDT" "2022-08-15 19:23:25 EDT"
## 
## $CALL
## tam.fit(tamobj = rs_model)
## 
## attr(,"class")
## [1] "tam.fit"

Test Information Function

imod1 <- TAM::IRT.informationCurves( rs_model, theta=seq(-5,5,len=100) )
plot(imod1)

Alt (All)

Summary

summary(rs_model)

## ------------------------------------------------------------
## TAM 4.0-16 (2022-05-13 13:23:23) 
## R version 4.1.2 (2021-11-01) x86_64, mingw32 | nodename=DESKTOP-UE2VMI8 | login=hthrp 
## 
## Date of Analysis: 2022-08-15 19:23:26 
## Time difference of 0.8281851 secs
## Computation time: 0.8281851 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: RSM
## Call:
## TAM::tam.mml(resp = d, irtmodel = "RSM")
## 
## ------------------------------------------------------------
## Number of iterations = 1000 
## Numeric integration with 21 integration points
## 
## Deviance = 2280.63 
## Log likelihood = -1140.31 
## Number of persons = 102 
## Number of persons used = 100 
## Number of items = 12 
## Number of estimated parameters = 16 
##     Item threshold parameters = 15 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 1 
## 
## AIC = 2313  | penalty=32    | AIC=-2*LL + 2*p 
## AIC3 = 2329  | penalty=48    | AIC3=-2*LL + 3*p 
## BIC = 2354  | penalty=73.68    | BIC=-2*LL + log(n)*p 
## aBIC = 2303  | penalty=22.51    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 2370  | penalty=89.68    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 2319  | penalty=38.55    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## GHP = 0.97169     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 
## 
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.89
## ------------------------------------------------------------
## Covariances and Variances
##       [,1]
## [1,] 2.546
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##       [,1]
## [1,] 1.596
## ------------------------------------------------------------
## Regression Coefficients
##      [,1]
## [1,]    0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##          item   N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1   IDochem02  99 2.414   -2.411    -10.345    -12.981    -12.680     -9.645
## 2   IDochem03  99 2.313   -2.108    -10.042    -12.375    -11.770     -8.433
## 3   IDochem04  99 2.465   -2.562    -10.496    -13.282    -13.131    -10.248
## 4   IDochem05  99 2.424   -2.442    -10.376    -13.041    -12.770     -9.766
## 5   IDochem06  99 2.545   -2.803    -10.737    -13.763    -13.854    -11.211
## 6   IDochem10  99 2.848   -3.712    -11.646    -15.581    -16.580    -14.846
## 7   IDochem07 100 2.220   -1.825     -9.759    -11.807    -10.919     -7.299
## 8   IDochem08 100 2.310   -2.097    -10.031    -12.352    -11.737     -8.389
## 9   IDochem09  99 2.303   -2.077    -10.011    -12.311    -11.676     -8.307
## 10 FASochem02  99 2.354   -2.230    -10.164    -12.618    -12.135     -8.919
## 11 FASochem03  99 2.869   -3.773    -11.707    -15.704    -16.765    -15.092
## 12 FASochem05  99 2.848   -3.707    -11.641    -15.572    -16.566    -14.828
##    B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
## 1            1           2           3           4
## 2            1           2           3           4
## 3            1           2           3           4
## 4            1           2           3           4
## 5            1           2           3           4
## 6            1           2           3           4
## 7            1           2           3           4
## 8            1           2           3           4
## 9            1           2           3           4
## 10           1           2           3           4
## 11           1           2           3           4
## 12           1           2           3           4
## 
## Item Parameters Xsi
##               xsi se.xsi
## IDochem02  -2.411  0.174
## IDochem03  -2.108  0.174
## IDochem04  -2.562  0.174
## IDochem05  -2.442  0.174
## IDochem06  -2.803  0.173
## IDochem10  -3.712  0.175
## IDochem07  -1.825  0.175
## IDochem08  -2.097  0.174
## IDochem09  -2.077  0.175
## FASochem02 -2.230  0.174
## FASochem03 -3.773  0.176
## FASochem05 -3.707  0.175
## Cat1       -7.934  0.113
## Cat2       -0.224  0.080
## Cat3        2.712  0.067
## 
## Item Parameters in IRT parameterization
##          item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1   IDochem02     1 -2.411   -7.934   -0.224    2.712    5.446
## 2   IDochem03     1 -2.108   -7.934   -0.224    2.712    5.446
## 3   IDochem04     1 -2.562   -7.934   -0.224    2.712    5.446
## 4   IDochem05     1 -2.442   -7.934   -0.224    2.712    5.446
## 5   IDochem06     1 -2.803   -7.934   -0.224    2.712    5.446
## 6   IDochem10     1 -3.712   -7.934   -0.224    2.712    5.446
## 7   IDochem07     1 -1.825   -7.934   -0.224    2.712    5.446
## 8   IDochem08     1 -2.097   -7.934   -0.224    2.712    5.446
## 9   IDochem09     1 -2.077   -7.934   -0.224    2.712    5.446
## 10 FASochem02     1 -2.230   -7.934   -0.224    2.712    5.446
## 11 FASochem03     1 -3.773   -7.934   -0.224    2.712    5.446
## 12 FASochem05     1 -3.707   -7.934   -0.224    2.712    5.446

Wright Map or Variable Map

IRT.WrightMap(rs_model,show.thr.lab=TRUE)

Item Estimates & Fit Statistics

rs_model$xsi # The first column is the item difficulty. In this case, is the rater's rating severity.

##                   xsi     se.xsi
## IDochem02  -2.4113662 0.17378811
## IDochem03  -2.1082904 0.17445828
## IDochem04  -2.5619048 0.17359482
## IDochem05  -2.4415604 0.17374209
## IDochem06  -2.8027421 0.17347279
## IDochem10  -3.7115318 0.17529082
## IDochem07  -1.8246361 0.17453216
## IDochem08  -2.0971948 0.17357415
## IDochem09  -2.0767582 0.17455192
## FASochem02 -2.2298058 0.17414328
## FASochem03 -3.7730779 0.17556890
## FASochem05 -3.7069585 0.17529120
## Cat1       -7.9341245 0.11323448
## Cat2       -0.2237961 0.08018879
## Cat3        2.7123563 0.06667138

tam.fit(rs_model)

## Item fit calculation based on 100 simulations
## |**********|
## |----------|

## $itemfit
##     parameter    Outfit   Outfit_t      Outfit_p  Outfit_pholm     Infit
## 1   IDochem02 1.0148470  0.1460049  8.839175e-01  1.000000e+00 1.0124938
## 2   IDochem03 0.9196587 -0.5625570  5.737366e-01  1.000000e+00 0.9257334
## 3   IDochem04 0.8521753 -1.0891658  2.760808e-01  1.000000e+00 0.8502541
## 4   IDochem05 0.6824897 -2.5587837  1.050391e-02  1.155430e-01 0.6823774
## 5   IDochem06 1.4217589  2.7431529  6.085235e-03  7.302282e-02 1.4145649
## 6   IDochem10 1.1812794  1.2880199  1.977390e-01  1.000000e+00 1.1641244
## 7   IDochem07 1.1495336  1.0737078  2.829537e-01  1.000000e+00 1.0762028
## 8   IDochem08 1.2687094  1.8419473  6.548287e-02  5.893458e-01 1.2408517
## 9   IDochem09 0.7989116 -1.5340552  1.250161e-01  1.000000e+00 0.7934031
## 10 FASochem02 1.0196426  0.1811979  8.562122e-01  1.000000e+00 1.0325590
## 11 FASochem03 1.0626343  0.4881614  6.254356e-01  1.000000e+00 1.0893539
## 12 FASochem05 0.6891032 -2.5243348  1.159175e-02  1.159175e-01 0.6869598
## 13       Cat1 1.9688550 10.9320964  8.095617e-28  1.052430e-26 1.8183229
## 14       Cat2 1.7797058 13.4771927  2.130604e-41  2.982846e-40 1.9428255
## 15       Cat3 1.7512143 25.1320858 2.218755e-139 3.328132e-138 1.8191965
##       Infit_t       Infit_p   Infit_pholm
## 1   0.1291355  8.972504e-01  1.000000e+00
## 2  -0.5154241  6.062567e-01  1.000000e+00
## 3  -1.1047536  2.692664e-01  1.000000e+00
## 4  -2.5599753  1.046796e-02  1.151475e-01
## 5   2.7031249  6.869094e-03  8.242912e-02
## 6   1.1780107  2.387924e-01  1.000000e+00
## 7   0.5824891  5.602373e-01  1.000000e+00
## 8   1.6714840  9.462611e-02  8.516350e-01
## 9  -1.5790698  1.143200e-01  9.145603e-01
## 10  0.2730030  7.848509e-01  1.000000e+00
## 11  0.6748643  4.997620e-01  1.000000e+00
## 12 -2.5432931  1.098131e-02  1.151475e-01
## 13  9.5652014  1.119832e-21  1.455782e-20
## 14 15.7740025  4.697612e-56  6.576657e-55
## 15 27.0758257 1.896937e-161 2.845405e-160
## 
## $time
## [1] "2022-08-15 19:23:27 EDT" "2022-08-15 19:23:27 EDT"
## 
## $CALL
## tam.fit(tamobj = rs_model)
## 
## attr(,"class")
## [1] "tam.fit"

Test Information Function

imod1 <- TAM::IRT.informationCurves( rs_model, theta=seq(-5,5,len=100) )
plot(imod1)

Alt (1F)

Summary

summary(rs_model)

## ------------------------------------------------------------
## TAM 4.0-16 (2022-05-13 13:23:23) 
## R version 4.1.2 (2021-11-01) x86_64, mingw32 | nodename=DESKTOP-UE2VMI8 | login=hthrp 
## 
## Date of Analysis: 2022-08-15 19:23:28 
## Time difference of 0.857192 secs
## Computation time: 0.857192 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: RSM
## Call:
## TAM::tam.mml(resp = d1, irtmodel = "RSM")
## 
## ------------------------------------------------------------
## Number of iterations = 1000 
## Numeric integration with 21 integration points
## 
## Deviance = 872.1 
## Log likelihood = -436.05 
## Number of persons = 102 
## Number of persons used = 99 
## Number of items = 5 
## Number of estimated parameters = 9 
##     Item threshold parameters = 8 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 1 
## 
## AIC = 890  | penalty=18    | AIC=-2*LL + 2*p 
## AIC3 = 899  | penalty=27    | AIC3=-2*LL + 3*p 
## BIC = 913  | penalty=41.36    | BIC=-2*LL + log(n)*p 
## aBIC = 885  | penalty=12.57    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 922  | penalty=50.36    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 892  | penalty=20.02    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## GHP = 0.89909     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 
## 
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.886
## ------------------------------------------------------------
## Covariances and Variances
##       [,1]
## [1,] 7.431
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##       [,1]
## [1,] 2.726
## ------------------------------------------------------------
## Regression Coefficients
##      [,1]
## [1,]    0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##        item  N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1 IDochem02 99 2.414   -2.998    -13.099    -16.370    -16.121    -11.992
## 2 IDochem03 99 2.313   -2.588    -12.689    -15.550    -14.891    -10.352
## 3 IDochem04 99 2.465   -3.203    -13.304    -16.780    -16.735    -12.811
## 4 IDochem05 99 2.424   -3.039    -13.140    -16.452    -16.243    -12.156
## 5 IDochem06 99 2.545   -3.530    -13.631    -17.434    -17.716    -14.120
##   B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
## 1           1           2           3           4
## 2           1           2           3           4
## 3           1           2           3           4
## 4           1           2           3           4
## 5           1           2           3           4
## 
## Item Parameters Xsi
##               xsi se.xsi
## IDochem02  -2.998  0.202
## IDochem03  -2.588  0.203
## IDochem04  -3.203  0.202
## IDochem05  -3.039  0.202
## IDochem06  -3.530  0.202
## Cat1      -10.101  0.202
## Cat2       -0.273  0.136
## Cat3        3.248  0.114
## 
## Item Parameters in IRT parameterization
##        item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1 IDochem02     1 -2.998  -10.101   -0.273    3.248    7.127
## 2 IDochem03     1 -2.588  -10.101   -0.273    3.248    7.127
## 3 IDochem04     1 -3.203  -10.101   -0.273    3.248    7.127
## 4 IDochem05     1 -3.039  -10.101   -0.273    3.248    7.127
## 5 IDochem06     1 -3.530  -10.101   -0.273    3.248    7.127

Wright Map or Variable Map

IRT.WrightMap(rs_model,show.thr.lab=TRUE)

Item Estimates & Fit Statistics

rs_model$xsi # The first column is the item difficulty. In this case, is the rater's rating severity.

##                   xsi    se.xsi
## IDochem02  -2.9979613 0.2024478
## IDochem03  -2.5879838 0.2026120
## IDochem04  -3.2027677 0.2023320
## IDochem05  -3.0389410 0.2024269
## IDochem06  -3.5299110 0.2021136
## Cat1      -10.1014249 0.2020765
## Cat2       -0.2729292 0.1361224
## Cat3        3.2476835 0.1140024

tam.fit(rs_model)

## Item fit calculation based on 100 simulations
## |**********|
## |--------|

## $itemfit
##   parameter    Outfit   Outfit_t     Outfit_p Outfit_pholm     Infit
## 1 IDochem02 0.7112591 -2.1748680 2.964001e-02 1.185600e-01 0.7519496
## 2 IDochem03 0.9779041 -0.1297933 8.967300e-01 8.967300e-01 0.9924659
## 3 IDochem04 0.6114910 -3.0899850 2.001666e-03 1.000833e-02 0.6494035
## 4 IDochem05 0.5045984 -4.1802121 2.912373e-05 1.747424e-04 0.5129991
## 5 IDochem06 1.3232156  2.0748979 3.799599e-02 1.185600e-01 1.3572953
## 6      Cat1 0.8277787 -1.9593744 5.006896e-02 1.185600e-01 1.5312932
## 7      Cat2 1.6972193  6.7720035 1.270111e-11 8.890774e-11 1.7026460
## 8      Cat3 1.9886507 14.0227517 1.131411e-44 9.051292e-44 1.5388750
##       Infit_t      Infit_p  Infit_pholm
## 1 -1.83111287 6.708370e-02 1.341674e-01
## 2 -0.01649472 9.868397e-01 9.868397e-01
## 3 -2.73507238 6.236656e-03 2.494662e-02
## 4 -4.07893172 4.524312e-05 2.714587e-04
## 5  2.27184130 2.309610e-02 6.928829e-02
## 6  3.69449522 2.203240e-04 1.101620e-03
## 7  7.03282719 2.023900e-12 1.416730e-11
## 8  9.00154560 2.225620e-19 1.780496e-18
## 
## $time
## [1] "2022-08-15 19:23:29 EDT" "2022-08-15 19:23:29 EDT"
## 
## $CALL
## tam.fit(tamobj = rs_model)
## 
## attr(,"class")
## [1] "tam.fit"

Test Information Function

imod1 <- TAM::IRT.informationCurves( rs_model, theta=seq(-5,5,len=100) )
plot(imod1)

Alt (2F)

Summary

summary(rs_model)

## ------------------------------------------------------------
## TAM 4.0-16 (2022-05-13 13:23:23) 
## R version 4.1.2 (2021-11-01) x86_64, mingw32 | nodename=DESKTOP-UE2VMI8 | login=hthrp 
## 
## Date of Analysis: 2022-08-15 19:23:30 
## Time difference of 0.693157 secs
## Computation time: 0.693157 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: RSM
## Call:
## TAM::tam.mml(resp = d2, irtmodel = "RSM")
## 
## ------------------------------------------------------------
## Number of iterations = 1000 
## Numeric integration with 21 integration points
## 
## Deviance = 737.7 
## Log likelihood = -368.85 
## Number of persons = 102 
## Number of persons used = 100 
## Number of items = 4 
## Number of estimated parameters = 8 
##     Item threshold parameters = 7 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 1 
## 
## AIC = 754  | penalty=16    | AIC=-2*LL + 2*p 
## AIC3 = 762  | penalty=24    | AIC3=-2*LL + 3*p 
## BIC = 775  | penalty=36.84    | BIC=-2*LL + log(n)*p 
## aBIC = 749  | penalty=11.26    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 783  | penalty=44.84    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 755  | penalty=17.58    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## GHP = 0.95164     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 
## 
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.835
## ------------------------------------------------------------
## Covariances and Variances
##      [,1]
## [1,] 5.64
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##       [,1]
## [1,] 2.375
## ------------------------------------------------------------
## Regression Coefficients
##      [,1]
## [1,]    0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##         item  N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1  IDochem10 99 2.848   -4.133    -12.768    -17.322    -19.035    -16.531
## 2 FASochem02 99 2.354   -2.249    -10.884    -13.554    -13.383     -8.995
## 3 FASochem03 99 2.869   -4.215    -12.850    -17.486    -19.282    -16.860
## 4 FASochem05 99 2.848   -4.095    -12.729    -17.246    -18.921    -16.378
##   B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
## 1           1           2           3           4
## 2           1           2           3           4
## 3           1           2           3           4
## 4           1           2           3           4
## 
## Item Parameters Xsi
##               xsi se.xsi
## IDochem10  -4.133  0.202
## FASochem02 -2.249  0.192
## FASochem03 -4.215  0.203
## FASochem05 -4.095  0.202
## Cat1       -8.635  0.189
## Cat2       -0.422  0.149
## Cat3        2.420  0.120
## 
## Item Parameters in IRT parameterization
##         item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1  IDochem10     1 -4.133   -8.635   -0.422     2.42    6.637
## 2 FASochem02     1 -2.249   -8.635   -0.422     2.42    6.637
## 3 FASochem03     1 -4.215   -8.635   -0.422     2.42    6.637
## 4 FASochem05     1 -4.095   -8.635   -0.422     2.42    6.637

Wright Map or Variable Map

IRT.WrightMap(rs_model,show.thr.lab=TRUE)

Item Estimates & Fit Statistics

rs_model$xsi # The first column is the item difficulty. In this case, is the rater's rating severity.

##                   xsi    se.xsi
## IDochem10  -4.1327884 0.2023837
## FASochem02 -2.2487719 0.1916396
## FASochem03 -4.2149540 0.2030029
## FASochem05 -4.0945485 0.2024161
## Cat1       -8.6348873 0.1886333
## Cat2       -0.4215771 0.1489548
## Cat3        2.4195937 0.1198912

tam.fit(rs_model)

## Item fit calculation based on 100 simulations
## |**********|
## |-------|

## $itemfit
##    parameter    Outfit   Outfit_t     Outfit_p Outfit_pholm     Infit
## 1  IDochem10 1.1112994  0.7505225 4.529401e-01 1.000000e+00 1.1631204
## 2 FASochem02 0.9102145 -0.6532151 5.136176e-01 1.000000e+00 0.8927270
## 3 FASochem03 0.9410709 -0.3812735 7.030003e-01 1.000000e+00 0.9877355
## 4 FASochem05 0.7120409 -2.1752301 2.961287e-02 1.480644e-01 0.7380063
## 5       Cat1 3.3222647 11.3982177 4.267663e-30 2.987364e-29 1.1663350
## 6       Cat2 1.1339004  1.3884729 1.649931e-01 6.599723e-01 1.2206534
## 7       Cat3 1.1676169  2.8431646 4.466800e-03 2.680080e-02 1.1371277
##       Infit_t    Infit_p Infit_pholm
## 1  1.08265405 0.27896201   0.8368860
## 2 -0.78192341 0.43425959   0.8685192
## 3 -0.05625828 0.95513605   0.9551361
## 4 -1.93308131 0.05322618   0.2661309
## 5  1.37426387 0.16935978   0.6774391
## 6  2.29674968 0.02163305   0.1297983
## 7  2.44373005 0.01453630   0.1017541
## 
## $time
## [1] "2022-08-15 19:23:30 EDT" "2022-08-15 19:23:30 EDT"
## 
## $CALL
## tam.fit(tamobj = rs_model)
## 
## attr(,"class")
## [1] "tam.fit"

Test Information Function

imod1 <- TAM::IRT.informationCurves( rs_model, theta=seq(-5,5,len=100) )
plot(imod1)

Alt (3F)

Summary

summary(rs_model)

## ------------------------------------------------------------
## TAM 4.0-16 (2022-05-13 13:23:23) 
## R version 4.1.2 (2021-11-01) x86_64, mingw32 | nodename=DESKTOP-UE2VMI8 | login=hthrp 
## 
## Date of Analysis: 2022-08-15 19:23:31 
## Time difference of 0.8391879 secs
## Computation time: 0.8391879 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: RSM
## Call:
## TAM::tam.mml(resp = d3, irtmodel = "RSM")
## 
## ------------------------------------------------------------
## Number of iterations = 1000 
## Numeric integration with 21 integration points
## 
## Deviance = 486.9 
## Log likelihood = -243.45 
## Number of persons = 102 
## Number of persons used = 100 
## Number of items = 3 
## Number of estimated parameters = 7 
##     Item threshold parameters = 6 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 1 
## 
## AIC = 501  | penalty=14    | AIC=-2*LL + 2*p 
## AIC3 = 508  | penalty=21    | AIC3=-2*LL + 3*p 
## BIC = 519  | penalty=32.24    | BIC=-2*LL + log(n)*p 
## aBIC = 497  | penalty=9.85    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 526  | penalty=39.24    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 502  | penalty=15.22    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## GHP = 0.83763     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 
## 
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.694
## ------------------------------------------------------------
## Covariances and Variances
##       [,1]
## [1,] 4.184
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##       [,1]
## [1,] 2.045
## ------------------------------------------------------------
## Regression Coefficients
##      [,1]
## [1,]    0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##        item   N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1 IDochem07 100 2.220   -2.282    -11.434    -15.429    -13.599     -9.127
## 2 IDochem08 100 2.310   -2.716    -11.868    -16.298    -14.903    -10.865
## 3 IDochem09  99 2.303   -2.707    -11.859    -16.280    -14.876    -10.829
##   B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
## 1           1           2           3           4
## 2           1           2           3           4
## 3           1           2           3           4
## 
## Item Parameters Xsi
##              xsi se.xsi
## IDochem07 -2.282  0.223
## IDochem08 -2.716  0.216
## IDochem09 -2.707  0.218
## Cat1      -9.152  0.332
## Cat2      -1.714  0.219
## Cat3       4.112  0.157
## 
## Item Parameters in IRT parameterization
##        item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1 IDochem07     1 -2.282   -9.152   -1.714    4.112    6.754
## 2 IDochem08     1 -2.716   -9.152   -1.714    4.112    6.754
## 3 IDochem09     1 -2.707   -9.152   -1.714    4.112    6.754

Wright Map or Variable Map

IRT.WrightMap(rs_model,show.thr.lab=TRUE)

Item Estimates & Fit Statistics

rs_model$xsi # The first column is the item difficulty. In this case, is the rater's rating severity.

##                 xsi    se.xsi
## IDochem07 -2.281813 0.2232262
## IDochem08 -2.716182 0.2162951
## IDochem09 -2.707272 0.2180768
## Cat1      -9.151757 0.3318448
## Cat2      -1.713982 0.2186850
## Cat3       4.111730 0.1566069

tam.fit(rs_model)

## Item fit calculation based on 100 simulations
## |**********|
## |------|

## $itemfit
##   parameter    Outfit   Outfit_t     Outfit_p Outfit_pholm    Infit     Infit_t
## 1 IDochem07 0.7146352 -1.9248897 0.0542431582  0.271215791 0.750262 -1.64321061
## 2 IDochem08 1.1502120  0.9084775 0.3636260076  1.000000000 1.123535  0.77120580
## 3 IDochem09 1.0647806  0.4109376 0.6811182622  1.000000000 1.010063  0.09406038
## 4      Cat1 0.4531484 -3.6808690 0.0002324404  0.001394642 1.027586  0.07647897
## 5      Cat2 0.9293489 -0.6017011 0.5473730937  1.000000000 1.038002  0.21587128
## 6      Cat3 0.9983428 -0.3424275 0.7320291655  1.000000000 1.019869  0.17442287
##     Infit_p Infit_pholm
## 1 0.1003394   0.6020362
## 2 0.4405850   1.0000000
## 3 0.9250612   1.0000000
## 4 0.9390380   1.0000000
## 5 0.8290881   1.0000000
## 6 0.8615331   1.0000000
## 
## $time
## [1] "2022-08-15 19:23:32 EDT" "2022-08-15 19:23:32 EDT"
## 
## $CALL
## tam.fit(tamobj = rs_model)
## 
## attr(,"class")
## [1] "tam.fit"

Test Information Function

imod1 <- TAM::IRT.informationCurves( rs_model, theta=seq(-5,5,len=100) )
plot(imod1)

Organic Chemistry Survey: Identity RSM

Heather Perkins

2022-08-15

Prepare Data

Identity

Items

EFA & 1PL

Rasch Rating Scale Models

Orig (All)

Summary

Wright Map or Variable Map

Item Estimates & Fit Statistics

Test Information Function

Orig (1F)

Summary

Wright Map or Variable Map

Item Estimates & Fit Statistics

Test Information Function

Orig (2F)

Summary

Wright Map or Variable Map

Item Estimates & Fit Statistics

Test Information Function

Alt (All)

Summary

Wright Map or Variable Map

Item Estimates & Fit Statistics

Test Information Function

Alt (1F)

Summary

Wright Map or Variable Map

Item Estimates & Fit Statistics

Test Information Function

Alt (2F)

Summary

Wright Map or Variable Map

Item Estimates & Fit Statistics

Test Information Function

Alt (3F)

Summary

Wright Map or Variable Map

Item Estimates & Fit Statistics

Test Information Function