Dr Lu’s Work
Cheng Hua
10/2/2021
Counselor Burnout Inventory - Rasch Based Analysis
Preload the R package for analysis
library(haven) # For loading the SPSS data
library(psych) # For descriptive analysis
library(eRm) # For Rasch Analysis
library(TAM) # For Rasch Analysis
library(WrightMap) # For plotting Wright Map
library(tidyr) # Transform the data format
library(dplyr) # For data manipulationLoad the data set
# Import the data from SPSS
Rehabilitation <- read_sav("~/Desktop/Dr. Junfei Lu Work/Rehabilitation counseling burnout_clean data (1).sav")
# Subset the dataset that we need
Rehab_data <- Rehabilitation[,3:22]
# Change the column name
colnames(Rehab_data) <- c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9","Item_10","Item_11","Item_12","Item_13","Item_14","Item_15","Item_16","Item_17","Item_18","Item_19","Item_20")
# Rescale the data to zero
Rehab_data <- Rehab_data-1Descriptive Analysis
# Descriptive Analysis
data_review <- describe(Rehab_data)
data_review## vars n mean sd median trimmed mad min max range skew kurtosis
## Item_1 1 147 2.41 0.96 2 2.43 1.48 0 4 4 -0.08 -0.28
## Item_2 2 147 0.95 0.97 1 0.84 1.48 0 4 4 0.87 0.35
## Item_3 3 147 1.22 1.13 1 1.10 1.48 0 4 4 0.60 -0.43
## Item_4 4 147 0.43 0.87 0 0.22 0.00 0 4 4 2.50 6.44
## Item_5 5 147 0.98 1.14 1 0.83 1.48 0 4 4 0.83 -0.51
## Item_6 6 147 2.21 1.08 2 2.21 1.48 0 4 4 0.03 -0.57
## Item_7 7 147 1.70 1.14 2 1.65 1.48 0 4 4 0.30 -0.62
## Item_8 8 147 1.05 1.21 1 0.88 1.48 0 4 4 0.88 -0.31
## Item_9 9 147 0.41 0.68 0 0.28 0.00 0 3 3 1.60 2.05
## Item_10 10 147 1.65 1.26 2 1.56 1.48 0 4 4 0.27 -0.87
## Item_11 11 147 2.35 1.02 2 2.37 1.48 0 4 4 -0.12 -0.37
## Item_12 12 147 1.21 1.01 1 1.11 1.48 0 4 4 0.61 -0.07
## Item_13 13 147 2.41 1.19 2 2.48 1.48 0 4 4 -0.26 -0.82
## Item_14 14 147 0.50 0.82 0 0.32 0.00 0 4 4 2.03 4.47
## Item_15 15 147 1.30 1.21 1 1.18 1.48 0 4 4 0.63 -0.59
## Item_16 16 147 2.23 1.29 2 2.29 1.48 0 4 4 -0.24 -0.98
## Item_17 17 147 1.44 1.02 1 1.39 1.48 0 4 4 0.25 -0.48
## Item_18 18 147 2.20 1.23 2 2.24 1.48 0 4 4 -0.15 -0.86
## Item_19 19 147 0.22 0.51 0 0.11 0.00 0 2 2 2.19 3.93
## Item_20 20 147 1.10 1.13 1 0.95 1.48 0 4 4 0.91 0.09
## se
## Item_1 0.08
## Item_2 0.08
## Item_3 0.09
## Item_4 0.07
## Item_5 0.09
## Item_6 0.09
## Item_7 0.09
## Item_8 0.10
## Item_9 0.06
## Item_10 0.10
## Item_11 0.08
## Item_12 0.08
## Item_13 0.10
## Item_14 0.07
## Item_15 0.10
## Item_16 0.11
## Item_17 0.08
## Item_18 0.10
## Item_19 0.04
## Item_20 0.09Rasch Analysis
Rating Scale Rasch Analysis
# Prepare the design matrix
design.matrix <- designMatrices(resp=Rehab_data,modeltype = "RSM",constraint="items")$A
# Run the Rating Scale Model
RSM.Rehab <- tam.mml(Rehab_data, irtmodel="RSM", A = design.matrix, constraint = "items", verbose = FALSE)
# Overall summary of the model
summary(RSM.Rehab)## ------------------------------------------------------------
## TAM 3.7-16 (2021-06-24 14:31:37)
## R version 4.1.0 (2021-05-18) x86_64, darwin17.0 | nodename=Chengs-iMac | login=root
##
## Date of Analysis: 2021-10-02 16:08:27
## Time difference of 0.918438 secs
## Computation time: 0.918438
##
## Multidimensional Item Response Model in TAM
##
## IRT Model: PCM2
## Call:
## tam.mml(resp = Rehab_data, irtmodel = "RSM", constraint = "items",
## A = design.matrix, verbose = FALSE)
##
## ------------------------------------------------------------
## Number of iterations = 1000
## Numeric integration with 21 integration points
##
## Deviance = 6866.13
## Log likelihood = -3433.06
## Number of persons = 147
## Number of persons used = 147
## Number of items = 20
## Number of estimated parameters = 24
## Item threshold parameters = 22
## Item slope parameters = 0
## Regression parameters = 1
## Variance/covariance parameters = 1
##
## AIC = 6914 | penalty=48 | AIC=-2*LL + 2*p
## AIC3 = 6938 | penalty=72 | AIC3=-2*LL + 3*p
## BIC = 6986 | penalty=119.77 | BIC=-2*LL + log(n)*p
## aBIC = 6909 | penalty=43.17 | aBIC=-2*LL + log((n-2)/24)*p (adjusted BIC)
## CAIC = 7010 | penalty=143.77 | CAIC=-2*LL + [log(n)+1]*p (consistent AIC)
## AICc = 6924 | penalty=57.84 | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1) (bias corrected AIC)
## GHP = 1.17587 | GHP=( -LL + p ) / (#Persons * #Items) (Gilula-Haberman log penalty)
##
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.912
## ------------------------------------------------------------
## Covariances and Variances
## [,1]
## [1,] 0.823
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
## [,1]
## [1,] 0.907
## ------------------------------------------------------------
## Regression Coefficients
## [,1]
## [1,] -0.84634
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## item N M xsi.item AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4
## 1 Item_1 147 2.415 -1.334 -2.482 -4.541 -5.142 -5.334
## 2 Item_2 147 0.946 0.495 -0.654 -0.885 0.342 1.978
## 3 Item_3 147 1.218 0.109 -1.039 -1.656 -0.814 0.436
## 4 Item_4 147 0.429 1.500 0.352 1.126 3.359 6.001
## 5 Item_5 147 0.980 0.443 -0.705 -0.988 0.189 1.773
## 6 Item_6 147 2.211 -1.091 -2.239 -4.055 -4.413 -4.362
## 7 Item_7 147 1.701 -0.492 -1.641 -2.859 -2.619 -1.970
## 8 Item_8 147 1.048 0.344 -0.804 -1.187 -0.110 1.375
## 9 Item_9 147 0.415 1.142 0.374 1.171 3.427 NA
## 10 Item_10 147 1.646 -0.428 -1.576 -2.729 -2.424 -1.710
## 11 Item_11 147 2.354 -1.260 -2.408 -4.394 -4.921 -5.040
## 12 Item_12 147 1.211 0.118 -1.030 -1.638 -0.787 0.473
## 13 Item_13 147 2.415 -1.334 -2.482 -4.541 -5.142 -5.334
## 14 Item_14 147 0.497 1.328 0.180 0.782 2.843 5.313
## 15 Item_15 147 1.299 0.002 -1.146 -1.870 -1.135 0.008
## 16 Item_16 147 2.231 -1.115 -2.263 -4.103 -4.485 -4.458
## 17 Item_17 147 1.435 -0.171 -1.319 -2.215 -1.653 -0.682
## 18 Item_18 147 2.197 -1.075 -2.223 -4.023 -4.365 -4.298
## 19 Item_19 147 0.224 1.230 1.019 2.461 NA NA
## 20 Item_20 147 1.102 0.268 -0.881 -1.339 -0.338 1.071
## 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 0
## 10 1 2 3 4
## 11 1 2 3 4
## 12 1 2 3 4
## 13 1 2 3 4
## 14 1 2 3 4
## 15 1 2 3 4
## 16 1 2 3 4
## 17 1 2 3 4
## 18 1 2 3 4
## 19 1 2 0 0
## 20 1 2 3 4
##
## Item Parameters Xsi
## xsi se.xsi
## Item_1 -1.334 0.066
## Item_2 0.495 0.070
## Item_3 0.109 0.068
## Item_4 1.500 0.079
## Item_5 0.443 0.070
## Item_6 -1.091 0.066
## Item_7 -0.492 0.066
## Item_8 0.344 0.069
## Item_9 1.523 0.080
## Item_10 -0.428 0.066
## Item_11 -1.260 0.066
## Item_12 0.118 0.068
## Item_13 -1.334 0.066
## Item_14 1.328 0.077
## Item_15 0.002 0.068
## Item_16 -1.115 0.066
## Item_17 -0.171 0.067
## Item_18 -1.075 0.066
## Item_19 2.167 0.086
## Cat1 -1.148 0.043
## Cat2 -0.726 0.045
## Cat3 0.733 0.061
##
## Item Parameters in IRT parameterization
## item alpha beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1 Item_1 1 -1.334 -1.148 -0.726 0.733 1.141
## 2 Item_2 1 0.495 -1.148 -0.726 0.733 1.141
## 3 Item_3 1 0.109 -1.148 -0.726 0.733 1.141
## 4 Item_4 1 1.500 -1.148 -0.726 0.733 1.141
## 5 Item_5 1 0.443 -1.148 -0.726 0.733 1.141
## 6 Item_6 1 -1.091 -1.148 -0.726 0.733 1.141
## 7 Item_7 1 -0.492 -1.148 -0.726 0.733 1.141
## 8 Item_8 1 0.344 -1.148 -0.726 0.733 1.141
## 9 Item_9 1 1.142 -0.768 -0.346 1.113 NA
## 10 Item_10 1 -0.428 -1.148 -0.726 0.733 1.141
## 11 Item_11 1 -1.260 -1.148 -0.726 0.733 1.141
## 12 Item_12 1 0.118 -1.148 -0.726 0.733 1.141
## 13 Item_13 1 -1.334 -1.148 -0.726 0.733 1.141
## 14 Item_14 1 1.328 -1.148 -0.726 0.733 1.141
## 15 Item_15 1 0.002 -1.148 -0.726 0.733 1.141
## 16 Item_16 1 -1.115 -1.148 -0.726 0.733 1.141
## 17 Item_17 1 -0.171 -1.148 -0.726 0.733 1.141
## 18 Item_18 1 -1.075 -1.148 -0.726 0.733 1.141
## 19 Item_19 1 1.230 -0.211 0.211 NA NA
## 20 Item_20 1 0.268 -1.148 -0.726 0.733 1.141Item and person parameters
# Obtain the item parameters
items_MMLE <- RSM.Rehab$xsi[1:(ncol(data_review)),]
# View the item parameters
RSM.Rehab$item_irt## item alpha beta tau.Cat1 tau.Cat2 tau.Cat3 tau.Cat4
## 1 Item_1 1 -1.333542523 -1.1483245 -0.7259343 0.7329561 1.141303
## 2 Item_2 1 0.494589403 -1.1483245 -0.7259343 0.7329561 1.141303
## 3 Item_3 1 0.109095374 -1.1483245 -0.7259343 0.7329561 1.141303
## 4 Item_4 1 1.500212916 -1.1483245 -0.7259343 0.7329561 1.141303
## 5 Item_5 1 0.443359234 -1.1483245 -0.7259343 0.7329561 1.141303
## 6 Item_6 1 -1.090541965 -1.1483245 -0.7259343 0.7329561 1.141303
## 7 Item_7 1 -0.492455174 -1.1483245 -0.7259343 0.7329561 1.141303
## 8 Item_8 1 0.343845689 -1.1483245 -0.7259343 0.7329561 1.141303
## 9 Item_9 1 1.142257105 -0.7678903 -0.3455001 1.1133903 NA
## 10 Item_10 1 -0.427594129 -1.1483245 -0.7259343 0.7329561 1.141303
## 11 Item_11 1 -1.259946243 -1.1483245 -0.7259343 0.7329561 1.141303
## 12 Item_12 1 0.118167682 -1.1483245 -0.7259343 0.7329561 1.141303
## 13 Item_13 1 -1.333542523 -1.1483245 -0.7259343 0.7329561 1.141303
## 14 Item_14 1 1.328210981 -1.1483245 -0.7259343 0.7329561 1.141303
## 15 Item_15 1 0.001944817 -1.1483245 -0.7259343 0.7329561 1.141303
## 16 Item_16 1 -1.114584787 -1.1483245 -0.7259343 0.7329561 1.141303
## 17 Item_17 1 -0.170611219 -1.1483245 -0.7259343 0.7329561 1.141303
## 18 Item_18 1 -1.074554674 -1.1483245 -0.7259343 0.7329561 1.141303
## 19 Item_19 1 1.230325035 -0.2111951 0.2111951 NA NA
## 20 Item_20 1 0.267801410 -1.1483245 -0.7259343 0.7329561 1.141303# Check the beta value for item difficulty
# Obtain the detailed item fit statistics
MMLE_fit <- tam.fit(RSM.Rehab)## Item fit calculation based on 100 simulations
## |**********|
## |----------|item.fit_MMLE <- MMLE_fit$itemfit
summary(item.fit_MMLE)## parameter Outfit Outfit_t Outfit_p
## Length:22 Min. :0.6473 Min. :-4.9415 Min. :0.0000000
## Class :character 1st Qu.:0.8702 1st Qu.:-1.5542 1st Qu.:0.0000008
## Mode :character Median :1.0331 Median : 0.4013 Median :0.0271821
## Mean :1.1900 Mean : 5.7541 Mean :0.1200929
## 3rd Qu.:1.2679 3rd Qu.: 3.0145 3rd Qu.:0.1908104
## Max. :3.4499 Max. :75.3702 Max. :0.7242531
## Outfit_pholm Infit Infit_t Infit_p
## Min. :0.0000000 Min. :0.6973 Min. :-4.2555 Min. :0.0000000
## 1st Qu.:0.0000138 1st Qu.:0.8947 1st Qu.:-1.3668 1st Qu.:0.0000241
## Median :0.3116597 Median :1.0333 Median : 0.4373 Median :0.0229333
## Mean :0.4581847 Mean :1.2255 Mean : 6.4715 Mean :0.1874272
## 3rd Qu.:1.0000000 3rd Qu.:1.2805 3rd Qu.: 3.2530 3rd Qu.:0.2346261
## Max. :1.0000000 Max. :3.4930 Max. :76.2945 Max. :0.8700591
## Infit_pholm
## Min. :0.0000000
## 1st Qu.:0.0004034
## Median :0.2592348
## Mean :0.4592205
## 3rd Qu.:1.0000000
## Max. :1.0000000# The Outfit and Infit statistics are the MSE versions and the Outfit_t and Infit_t statistics are the standardized versions of the statistics.
# Use the tam.wle function to calculate person location parameters:
person.locations.estimate_MMLE <- tam.wle(RSM.Rehab)## Iteration in WLE/MLE estimation 1 | Maximal change 0.3142
## Iteration in WLE/MLE estimation 2 | Maximal change 0.0313
## Iteration in WLE/MLE estimation 3 | Maximal change 4e-04
## Iteration in WLE/MLE estimation 4 | Maximal change 0
## ----
## WLE Reliability= 0.912# Store person parameters and their standard errors in a dataframe object:
person.locations_MMLE <- cbind.data.frame(person.locations.estimate_MMLE$theta,
person.locations.estimate_MMLE$error)
names(person.locations_MMLE) <- c("theta", "SE")
# View summary statistics for person parameters:
summary(person.locations_MMLE)## theta SE
## Min. :-3.6949 Min. :0.2469
## 1st Qu.:-1.4260 1st Qu.:0.2506
## Median :-0.8270 Median :0.2581
## Mean :-0.8485 Mean :0.2788
## 3rd Qu.:-0.2669 3rd Qu.:0.2824
## Max. : 1.9639 Max. :0.6297# Obtain the person fits
person.fit.results_MMLE <- tam.personfit(RSM.Rehab)
summary(person.fit.results_MMLE)## outfitPerson outfitPerson_t infitPerson infitPerson_t
## Min. :0.2571 Min. :-3.1030 Min. :0.2655 Min. :-3.1523
## 1st Qu.:0.5908 1st Qu.:-1.1459 1st Qu.:0.5866 1st Qu.:-1.3227
## Median :0.8038 Median :-0.3713 Median :0.8170 Median :-0.4893
## Mean :0.9697 Mean :-0.1929 Mean :0.9434 Mean :-0.3211
## 3rd Qu.:1.1988 3rd Qu.: 0.6613 3rd Qu.:1.2254 3rd Qu.: 0.8105
## Max. :3.4506 Max. : 3.6696 Max. :2.8691 Max. : 3.7776We will use popular Rasch fit statistics for practical purposes that are based on sums of squared residuals: Unweighted (outfit) and Weighted (infit) mean square error (MSE) statistics. Unstandardized (χ^2 ) & standardized versions (Z or t) are available in most Rasch software programs. In this analysis, we will focus on the Unstandardized (χ^2) versions of these statistics.
Outfit Mean Square Error (MSE), statistics are “unweighted fit” statistics. For items, outfit MSE is the sum of squared residuals for an item divided by the number of persons who responded to the item. For persons, outfit MSE is sum of squared residuals for a person divided by the number of items encountered by the person.
Because it is an unweighted mean, the outfit statistic is sensitive to extreme departures from model expectations. For example, an extreme departure from model expectations would occur when an otherwise high-achieving student provided an incorrect response to a very easy item, or when an otherwise low-achieving student provided a correct response to a very difficult item.
Infit Mean Square Error
Infit stands for “information-weighted fit”, where “information” means variance, such as larger variance for well-targeted observations, or smaller variance for extreme observations. For items, infit MSE statistics are calculated as the sum of squared standardized item residuals, weighted by variance, divided by the number of persons who responded to the item. For persons, infit MSE is the sum of squared standardized person residuals, weighted by variance, divided by the number of items the person encountered.
Infit MSE is sensitive to less-extreme unexpected responses compared to outfit MSE Examples of less-extreme unexpected responses include a student providing an incorrect response to an item that is just below their achievement level, or a student providing a correct response to an item that is just above their achievement level.
Expected Values for MSE Fit Statistics
There is considerable disagreement among measurement scholars about how to classify an infit or outfit MSE statistic as evidence of “misfit” or “fit.” Nonetheless, readers may find it useful to be aware of commonly agreed-upon principles for interpreting these statistics:
The expected value is 1.00 when data fit the model
Less than 1.00: Responses are more predictable than the model expects; responses resemble a Guttman-like (deterministic) pattern (“muted”)
Greater than 1.00: Responses are more haphazard (“noisy”) than the model expects; there is too much variation to interpret that the estimate as a good representation of the response pattern
Some variation is expected, but noisy responses are usually considered more cause for concern than muted responses.
Plots from the Rasch Analysis
Rating scale category probability plots
items.to.plot <- c(1:5)
plot(RSM.Rehab, type="items", items = items.to.plot)## Iteration in WLE/MLE estimation 1 | Maximal change 0.3142
## Iteration in WLE/MLE estimation 2 | Maximal change 0.0313
## Iteration in WLE/MLE estimation 3 | Maximal change 4e-04
## Iteration in WLE/MLE estimation 4 | Maximal change 0
## ----
## WLE Reliability= 0.912
## ....................................................
## Plots exported in png format into folder:
## /Users/chenghua/Desktop/Plots# The x-axis is the logit scale that represents the latent variable, the y-axis is the probability for a rating in each category, and individual lines show the conditional probability for a rating in each category.Wright Map
# Plot the Wright Map
IRT.WrightMap(RSM.Rehab) 
Many-facet Rasch Model [In Facet]
# Add variable "ID" to the previous data
ID <- 1:147
Rehab_data$ID <- ID
# Transform to the long format
Rehab_data_long <- gather(Rehab_data,item_No,rating,Item_1:Item_20,factor_key=TRUE)
Rehab_data_long## ID item_No rating
## 1 1 Item_1 2
## 2 2 Item_1 2
## 3 3 Item_1 3
## 4 4 Item_1 4
## 5 5 Item_1 2
## 6 6 Item_1 4
## 7 7 Item_1 2
## 8 8 Item_1 2
## 9 9 Item_1 2
## 10 10 Item_1 4
## 11 11 Item_1 2
## 12 12 Item_1 4
## 13 13 Item_1 2
## 14 14 Item_1 2
## 15 15 Item_1 3
## 16 16 Item_1 2
## 17 17 Item_1 2
## 18 18 Item_1 3
## 19 19 Item_1 1
## 20 20 Item_1 3
## 21 21 Item_1 4
## 22 22 Item_1 4
## 23 23 Item_1 1
## 24 24 Item_1 2
## 25 25 Item_1 1
## 26 26 Item_1 2
## 27 27 Item_1 3
## 28 28 Item_1 3
## 29 29 Item_1 4
## 30 30 Item_1 2
## 31 31 Item_1 2
## 32 32 Item_1 3
## 33 33 Item_1 3
## 34 34 Item_1 3
## 35 35 Item_1 2
## 36 36 Item_1 2
## 37 37 Item_1 2
## 38 38 Item_1 2
## 39 39 Item_1 4
## 40 40 Item_1 3
## 41 41 Item_1 2
## 42 42 Item_1 3
## 43 43 Item_1 2
## 44 44 Item_1 2
## 45 45 Item_1 1
## 46 46 Item_1 4
## 47 47 Item_1 0
## 48 48 Item_1 3
## 49 49 Item_1 4
## 50 50 Item_1 4
## 51 51 Item_1 3
## 52 52 Item_1 2
## 53 53 Item_1 3
## 54 54 Item_1 3
## 55 55 Item_1 3
## 56 56 Item_1 0
## 57 57 Item_1 3
## 58 58 Item_1 2
## 59 59 Item_1 2
## 60 60 Item_1 3
## 61 61 Item_1 3
## 62 62 Item_1 1
## 63 63 Item_1 1
## 64 64 Item_1 1
## 65 65 Item_1 4
## 66 66 Item_1 3
## 67 67 Item_1 3
## 68 68 Item_1 2
## 69 69 Item_1 3
## 70 70 Item_1 3
## 71 71 Item_1 2
## 72 72 Item_1 3
## 73 73 Item_1 2
## 74 74 Item_1 2
## 75 75 Item_1 2
## 76 76 Item_1 4
## 77 77 Item_1 2
## 78 78 Item_1 2
## 79 79 Item_1 2
## 80 80 Item_1 3
## 81 81 Item_1 2
## 82 82 Item_1 2
## 83 83 Item_1 3
## 84 84 Item_1 2
## 85 85 Item_1 3
## 86 86 Item_1 4
## 87 87 Item_1 4
## 88 88 Item_1 3
## 89 89 Item_1 2
## 90 90 Item_1 4
## 91 91 Item_1 2
## 92 92 Item_1 1
## 93 93 Item_1 3
## 94 94 Item_1 2
## 95 95 Item_1 3
## 96 96 Item_1 4
## 97 97 Item_1 4
## 98 98 Item_1 4
## 99 99 Item_1 2
## 100 100 Item_1 2
## 101 101 Item_1 2
## 102 102 Item_1 3
## 103 103 Item_1 1
## 104 104 Item_1 2
## 105 105 Item_1 4
## 106 106 Item_1 2
## 107 107 Item_1 1
## 108 108 Item_1 2
## 109 109 Item_1 1
## 110 110 Item_1 3
## 111 111 Item_1 3
## 112 112 Item_1 3
## 113 113 Item_1 2
## 114 114 Item_1 0
## 115 115 Item_1 1
## 116 116 Item_1 2
## 117 117 Item_1 2
## 118 118 Item_1 2
## 119 119 Item_1 2
## 120 120 Item_1 2
## 121 121 Item_1 3
## 122 122 Item_1 3
## 123 123 Item_1 2
## 124 124 Item_1 1
## 125 125 Item_1 2
## 126 126 Item_1 4
## 127 127 Item_1 1
## 128 128 Item_1 2
## 129 129 Item_1 3
## 130 130 Item_1 2
## 131 131 Item_1 2
## 132 132 Item_1 2
## 133 133 Item_1 1
## 134 134 Item_1 2
## 135 135 Item_1 3
## 136 136 Item_1 2
## 137 137 Item_1 2
## 138 138 Item_1 3
## 139 139 Item_1 4
## 140 140 Item_1 0
## 141 141 Item_1 1
## 142 142 Item_1 2
## 143 143 Item_1 3
## 144 144 Item_1 2
## 145 145 Item_1 3
## 146 146 Item_1 2
## 147 147 Item_1 2
## 148 1 Item_2 1
## 149 2 Item_2 2
## 150 3 Item_2 1
## 151 4 Item_2 3
## 152 5 Item_2 2
## 153 6 Item_2 3
## 154 7 Item_2 0
## 155 8 Item_2 0
## 156 9 Item_2 1
## 157 10 Item_2 0
## 158 11 Item_2 0
## 159 12 Item_2 0
## 160 13 Item_2 2
## 161 14 Item_2 2
## 162 15 Item_2 0
## 163 16 Item_2 1
## 164 17 Item_2 0
## 165 18 Item_2 0
## 166 19 Item_2 0
## 167 20 Item_2 1
## 168 21 Item_2 2
## 169 22 Item_2 0
## 170 23 Item_2 2
## 171 24 Item_2 2
## 172 25 Item_2 0
## 173 26 Item_2 1
## 174 27 Item_2 2
## 175 28 Item_2 1
## 176 29 Item_2 2
## 177 30 Item_2 0
## 178 31 Item_2 1
## 179 32 Item_2 1
## 180 33 Item_2 3
## 181 34 Item_2 3
## 182 35 Item_2 3
## 183 36 Item_2 0
## 184 37 Item_2 1
## 185 38 Item_2 0
## 186 39 Item_2 1
## 187 40 Item_2 2
## 188 41 Item_2 0
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## 2703 57 Item_19 0
## 2704 58 Item_19 0
## 2705 59 Item_19 0
## 2706 60 Item_19 0
## 2707 61 Item_19 1
## 2708 62 Item_19 0
## 2709 63 Item_19 0
## 2710 64 Item_19 0
## 2711 65 Item_19 0
## 2712 66 Item_19 0
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## 2741 95 Item_19 0
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## 2744 98 Item_19 2
## 2745 99 Item_19 0
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## 2748 102 Item_19 2
## 2749 103 Item_19 0
## 2750 104 Item_19 1
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## 2753 107 Item_19 0
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## 2756 110 Item_19 1
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## 2758 112 Item_19 0
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## 2761 115 Item_19 0
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## 2763 117 Item_19 0
## 2764 118 Item_19 0
## 2765 119 Item_19 0
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## 2794 1 Item_20 1
## 2795 2 Item_20 1
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## 2816 23 Item_20 0
## 2817 24 Item_20 0
## 2818 25 Item_20 0
## 2819 26 Item_20 0
## 2820 27 Item_20 1
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## 2822 29 Item_20 2
## 2823 30 Item_20 0
## 2824 31 Item_20 0
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## 2850 57 Item_20 0
## 2851 58 Item_20 1
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## 2858 65 Item_20 1
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## 2860 67 Item_20 1
## 2861 68 Item_20 3
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## 2863 70 Item_20 3
## 2864 71 Item_20 1
## 2865 72 Item_20 1
## 2866 73 Item_20 1
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## 2868 75 Item_20 0
## 2869 76 Item_20 4
## 2870 77 Item_20 2
## 2871 78 Item_20 2
## 2872 79 Item_20 1
## 2873 80 Item_20 3
## 2874 81 Item_20 0
## 2875 82 Item_20 2
## 2876 83 Item_20 3
## 2877 84 Item_20 2
## 2878 85 Item_20 0
## 2879 86 Item_20 1
## 2880 87 Item_20 0
## 2881 88 Item_20 3
## 2882 89 Item_20 2
## 2883 90 Item_20 0
## 2884 91 Item_20 1
## 2885 92 Item_20 0
## 2886 93 Item_20 0
## 2887 94 Item_20 0
## 2888 95 Item_20 1
## 2889 96 Item_20 1
## 2890 97 Item_20 2
## 2891 98 Item_20 4
## 2892 99 Item_20 0
## 2893 100 Item_20 0
## 2894 101 Item_20 3
## 2895 102 Item_20 3
## 2896 103 Item_20 3
## 2897 104 Item_20 1
## 2898 105 Item_20 3
## 2899 106 Item_20 2
## 2900 107 Item_20 0
## 2901 108 Item_20 0
## 2902 109 Item_20 1
## 2903 110 Item_20 1
## 2904 111 Item_20 0
## 2905 112 Item_20 2
## 2906 113 Item_20 1
## 2907 114 Item_20 0
## 2908 115 Item_20 0
## 2909 116 Item_20 1
## 2910 117 Item_20 0
## 2911 118 Item_20 2
## 2912 119 Item_20 2
## 2913 120 Item_20 2
## 2914 121 Item_20 1
## 2915 122 Item_20 0
## 2916 123 Item_20 1
## 2917 124 Item_20 1
## 2918 125 Item_20 1
## 2919 126 Item_20 0
## 2920 127 Item_20 2
## 2921 128 Item_20 1
## 2922 129 Item_20 0
## 2923 130 Item_20 1
## 2924 131 Item_20 1
## 2925 132 Item_20 1
## 2926 133 Item_20 0
## 2927 134 Item_20 1
## 2928 135 Item_20 2
## 2929 136 Item_20 1
## 2930 137 Item_20 0
## 2931 138 Item_20 1
## 2932 139 Item_20 1
## 2933 140 Item_20 0
## 2934 141 Item_20 1
## 2935 142 Item_20 1
## 2936 143 Item_20 2
## 2937 144 Item_20 1
## 2938 145 Item_20 2
## 2939 146 Item_20 0
## 2940 147 Item_20 0# Sort the data by ID
sorted_data <- arrange(Rehab_data_long,ID)
# Build a variable "Facet"
Facet <- rep(rep(c(1,2,3,4,5),4),147)
sorted_data$Facet <- Facet
# Transform the Item_No.
sorted_data$item_No <- rep(1:20,147)
#
write.csv(sorted_data,"Lu_BO_data.csv", row.names = FALSE)Mediation Test Rasch Analysis
Load the data
# Import the data
mediation_test <- read_sav("~/Desktop/Dr. Junfei Lu Work/mediation_test.sav")Descriptive Analysis
# Select the target data
Medi_data <- mediation_test[,27:37]
# Describe the data
describe(Medi_data)## vars n mean sd median trimmed mad min max range skew kurtosis
## Decenter_1 1 191 3.55 0.81 4 3.54 1.48 1 5 4 -0.10 -0.19
## Decenter_2 2 191 3.16 0.82 3 3.18 1.48 1 5 4 -0.13 -0.11
## Decenter_3 3 191 2.84 0.94 3 2.81 1.48 1 5 4 0.25 -0.40
## Decenter_4 4 191 3.68 0.84 4 3.70 1.48 1 5 4 -0.26 -0.24
## Decenter_5 5 191 3.08 0.95 3 3.09 1.48 1 5 4 -0.12 -0.23
## Decenter_6 6 191 3.62 0.82 4 3.63 1.48 1 5 4 -0.17 -0.23
## Decenter_7 7 191 3.01 0.97 3 3.01 1.48 1 5 4 -0.05 -0.27
## Decenter_8 8 191 3.07 0.97 3 3.06 1.48 1 5 4 0.00 -0.16
## Decenter_9 9 191 3.43 0.98 3 3.46 1.48 1 5 4 -0.31 -0.27
## Decenter_10 10 191 3.39 0.84 3 3.39 1.48 1 5 4 -0.07 -0.17
## Decenter_11 11 191 3.72 0.85 4 3.74 1.48 1 5 4 -0.24 -0.34
## se
## Decenter_1 0.06
## Decenter_2 0.06
## Decenter_3 0.07
## Decenter_4 0.06
## Decenter_5 0.07
## Decenter_6 0.06
## Decenter_7 0.07
## Decenter_8 0.07
## Decenter_9 0.07
## Decenter_10 0.06
## Decenter_11 0.06Medi_data <- Medi_data-1Rasch Rating Scale Analysis
# Run a Rasch Rating Scale Model
Medi_RSM <- RSM(Medi_data)Plot the wright map
plotPImap(Medi_RSM, main = "Mediation Rating Scale Model Wright Map")
Item Parameters
# Obtain Item locations
item.locations <- Medi_RSM$etapar
item.locations## Decenter_2 Decenter_3 Decenter_4 Decenter_5 Decenter_6 Decenter_7
## 0.3124396 0.8902153 -0.6750616 0.4555666 -0.5624306 0.5884371
## Decenter_8 Decenter_9 Decenter_10 Decenter_11 Cat 2 Cat 3
## 0.4745873 -0.2019576 -0.1134441 -0.7474657 1.3604576 4.5972779
## Cat 4
## 9.6350309summary(item.locations)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.7475 -0.2020 0.4556 1.2318 0.8902 9.6350n.items <- ncol(Medi_data)
# Obtain Item 1's location
i1 <- 0 - sum(item.locations[1:(n.items - 1)])
item.locations.all <- c(i1, item.locations[c(1:(n.items - 1))])
item.locations.all## Decenter_2 Decenter_3 Decenter_4 Decenter_5 Decenter_6
## -0.4208863 0.3124396 0.8902153 -0.6750616 0.4555666 -0.5624306
## Decenter_7 Decenter_8 Decenter_9 Decenter_10 Decenter_11
## 0.5884371 0.4745873 -0.2019576 -0.1134441 -0.7474657# Apply thresholds() function to the model object in order to obtain item locations (not centered at zero logits):
items.and.taus <- thresholds(Medi_RSM)
items.and.taus.table <- as.data.frame(items.and.taus$threshtable)
uncentered.item.locations <- items.and.taus.table$X1.Location
# Set the mean of the item locations to zero logits:
centered.item.locations <- scale(uncentered.item.locations, scale = FALSE)
summary(centered.item.locations)## V1
## Min. :-0.7475
## 1st Qu.:-0.4917
## Median :-0.1134
## Mean : 0.0000
## 3rd Qu.: 0.4651
## Max. : 0.8902centered.item.locations## [,1]
## [1,] -0.4208863
## [2,] 0.3124396
## [3,] 0.8902153
## [4,] -0.6750616
## [5,] 0.4555666
## [6,] -0.5624306
## [7,] 0.5884371
## [8,] 0.4745873
## [9,] -0.2019576
## [10,] -0.1134441
## [11,] -0.7474657
## attr(,"scaled:center")
## [1] 2.408758Plot Item Response Function
# items.to.plot <- c(1:11)
plotICC(Medi_RSM, ask = FALSE)
Person parameter
# Calculate person parameters:
person.locations.estimate <- person.parameter(Medi_RSM)
# Store person parameters and their standard errors in a dataframe object:
person.locations <- cbind.data.frame(person.locations.estimate$thetapar,
person.locations.estimate$se.theta)
names(person.locations) <- c("theta", "SE")
# View summary statistics for person parameters:
summary(person.locations)## theta SE
## Min. :0.5826 Min. :0.3956
## 1st Qu.:2.3342 1st Qu.:0.4012
## Median :2.9897 Median :0.4086
## Mean :2.9124 Mean :0.4133
## 3rd Qu.:3.4989 3rd Qu.:0.4159
## Max. :6.2395 Max. :0.6455Item and person fit
# Exam Item fit
item.fit.results <- itemfit(person.locations.estimate)
item.fit <- cbind.data.frame(item.fit.results$i.infitMSQ,
item.fit.results$i.outfitMSQ,
item.fit.results$i.infitZ,
item.fit.results$i.outfitZ)
names(item.fit) <- c("infit_MSE", "outfit_MSE", "std_infit", "std_outfit")
summary(item.fit)## infit_MSE outfit_MSE std_infit std_outfit
## Min. :0.6736 Min. :0.6737 Min. :-3.6492 Min. :-3.6569
## 1st Qu.:0.8259 1st Qu.:0.8268 1st Qu.:-1.8316 1st Qu.:-1.8285
## Median :0.9124 Median :0.9122 Median :-0.8721 Median :-0.8816
## Mean :0.9121 Mean :0.9135 Mean :-0.9497 Mean :-0.9349
## 3rd Qu.:0.9806 3rd Qu.:0.9843 3rd Qu.:-0.1639 3rd Qu.:-0.1267
## Max. :1.1647 Max. :1.1638 Max. : 1.5938 Max. : 1.5932item.fit## infit_MSE outfit_MSE std_infit std_outfit
## Decenter_1 0.7268730 0.7419581 -2.9938349 -2.8265134
## Decenter_2 0.6735916 0.6736770 -3.6491864 -3.6568735
## Decenter_3 0.9124301 0.9108674 -0.8720733 -0.8906467
## Decenter_4 0.9094132 0.9122409 -0.9050739 -0.8816013
## Decenter_5 0.9509940 0.9458656 -0.4625791 -0.5166380
## Decenter_6 1.0101662 1.0154013 0.1348078 0.1876684
## Decenter_7 0.9498165 0.9532564 -0.4755053 -0.4409914
## Decenter_8 0.8905554 0.8905278 -1.0986197 -1.1012185
## Decenter_9 1.1647317 1.1638264 1.5937960 1.5932181
## Decenter_10 0.7612899 0.7630038 -2.5646016 -2.5557383
## Decenter_11 1.0831533 1.0782461 0.8465551 0.8049873# Exam person fit
person.fit.results <- personfit(person.locations.estimate)
person.fit <- cbind.data.frame(person.fit.results$p.infitMSQ,
person.fit.results$p.outfitMSQ,
person.fit.results$p.infitZ,
person.fit.results$p.outfitZ)
names(person.fit) <- c("infit_MSE", "outfit_MSE", "std_infit", "std_outfit")
person.fit## infit_MSE outfit_MSE std_infit std_outfit
## P1 0.9067225 0.9268917 -0.100339364 -0.04943769
## P2 1.2618795 1.2876543 0.709981972 0.76161647
## P3 1.7815786 1.7575408 1.640209628 1.60347333
## P4 0.4875167 0.4829200 -1.396079690 -1.41901655
## P5 0.5874628 0.5876735 -1.110901418 -1.11264806
## P6 0.9041745 0.8914858 -0.090585311 -0.12297481
## P7 1.4918152 1.5122967 1.146915386 1.18385930
## P8 0.9314514 0.9128359 -0.054734224 -0.10778062
## P9 0.8223777 0.8178739 -0.303840020 -0.31681198
## P10 0.7074835 0.7100907 -0.675941643 -0.66650900
## P11 0.7434115 0.7540076 -0.547709897 -0.51948578
## P12 0.5753849 0.5774170 -1.062075625 -1.05830145
## P13 0.6322997 0.6391987 -0.903763455 -0.87844362
## P14 0.5310833 0.5249628 -1.211930647 -1.23223250
## P15 0.7134800 0.7178589 -0.670040512 -0.65628337
## P16 0.6670526 0.6723606 -0.751042508 -0.73423079
## P17 0.7351201 0.7293961 -0.633573021 -0.65663928
## P18 0.4914207 0.4984623 -1.380978775 -1.35881603
## P19 0.9392846 0.9310584 -0.006337431 -0.02634163
## P20 0.4910838 0.4888173 -1.382279003 -1.39602452
## P21 0.6523622 0.6466739 -0.795225731 -0.81467582
## P22 1.2626119 1.2715204 0.711454749 0.72945548
## P23 1.4692489 1.4850919 1.167037580 1.20638194
## P24 0.5835617 0.5839038 -1.015502528 -1.01556880
## P25 1.2258873 1.2633440 0.665578193 0.75270512
## P26 0.6679778 0.6818348 -0.748188077 -0.70529093
## P27 0.4188734 0.4197483 -1.716503262 -1.72206791
## P28 1.1198124 1.1258298 0.428308309 0.44378814
## P29 0.5034115 0.5011152 -1.313748227 -1.32034437
## P30 1.2958820 1.3186864 0.799831357 0.84933386
## P31 0.5390465 0.5363595 -1.202884059 -1.21709738
## P32 0.5827700 0.5915450 -1.072745957 -1.03928959
## P33 0.4365742 0.4280545 -1.619869230 -1.66325388
## P34 0.7440002 0.7541288 -0.519153602 -0.49104821
## P35 1.1544782 1.1576170 0.490372006 0.49768145
## P36 0.8609360 0.8672962 -0.227721756 -0.20967319
## P37 0.3094481 0.3070328 -2.307858730 -2.32116654
## P38 0.8101126 0.8073450 -0.349797436 -0.35935324
## P39 0.1657179 0.1651526 -3.044831298 -3.04770828
## P40 0.3953662 0.4014363 -1.863479518 -1.85126144
## P41 1.9774754 1.9629038 1.955360909 1.93130109
## P42 1.0050483 1.0095097 0.153513554 0.16378712
## P43 2.4339666 2.4233903 2.595278351 2.57850625
## P44 0.2322449 0.2371497 -2.571896816 -2.54427907
## P45 0.8730046 0.8898043 -0.182952871 -0.13783424
## P46 1.1846732 1.1782751 0.556260320 0.54206175
## P47 0.7420940 0.7490278 -0.543354830 -0.52548628
## P48 0.4318197 0.4274191 -1.590985715 -1.61290210
## P49 2.9008862 2.9369119 3.239893064 3.29395591
## P50 0.6329649 0.6342226 -0.891948122 -0.89216081
## P51 1.0287207 1.0026797 0.208601394 0.14775648
## P52 0.6637510 0.6669610 -0.764865390 -0.75690215
## P53 0.3480896 0.3511700 -2.040377970 -2.02023128
## P54 0.3405194 0.3392975 -2.024538220 -2.02605919
## P55 1.1625685 1.0982521 0.521674710 0.37307938
## P56 0.3772076 0.3723307 -1.842192523 -1.86969486
## P57 2.4928259 2.4433318 2.728282419 2.67145909
## P58 0.3372035 0.3402515 -2.166431193 -2.17271349
## P59 1.0743761 1.0790797 0.313548736 0.32460122
## P60 0.7199009 0.7101362 -0.673304534 -0.70839495
## P61 0.4125516 0.4079913 -1.662503350 -1.68481207
## P62 0.4384554 0.4358514 -1.679581190 -1.69094713
## P63 0.8263747 0.8248482 -0.291811977 -0.29642699
## P64 0.6653534 0.6598611 -0.754850796 -0.77339787
## P65 1.2009847 1.1875332 0.586461215 0.55817401
## P66 2.0393503 2.0243925 2.169993787 2.16609530
## P67 0.9229291 0.9141675 -0.068819569 -0.09599444
## P68 0.4432358 0.4422672 -1.537840245 -1.54092413
## P69 0.1456386 0.1475760 -3.451300343 -3.46757359
## P70 1.1954988 1.1917417 0.576766911 0.56848957
## P71 0.3087551 0.3086762 -2.158234173 -2.16334126
## P72 0.8490620 0.8581451 -0.253348631 -0.22757031
## P73 1.3858417 1.3745288 0.970968608 0.94736573
## P74 1.8460109 1.8412004 1.759634025 1.75555880
## P75 2.4732016 2.4628723 2.728179395 2.72587856
## P76 0.1745557 0.1777207 -2.964968066 -2.94434121
## P77 1.7013932 1.6958969 1.507547956 1.49883834
## P78 0.4366604 0.4428753 -1.639662198 -1.62223023
## P79 1.4819228 1.5047082 1.176552465 1.21847657
## P80 0.7924499 0.8138872 -0.393041406 -0.33543528
## P81 0.4047885 0.4087505 -1.719333661 -1.70691761
## P82 0.2352147 0.2335029 -2.712377287 -2.71938899
## P83 0.4769672 0.4839924 -1.437293309 -1.41482159
## P84 0.5121261 0.5063068 -1.449666094 -1.48060807
## P85 1.4542526 1.4482200 1.112107344 1.09880606
## P86 0.8693023 0.8617977 -0.223550621 -0.24673751
## P87 3.4018852 3.3694394 3.716019268 3.68853971
## P88 0.8616349 0.8507889 -0.199113784 -0.22783276
## P89 0.7038746 0.6955723 -0.657352111 -0.68552561
## P90 1.0682440 1.0699096 0.299336556 0.30331061
## P91 0.4561275 0.4593118 -1.504750709 -1.49624748
## P92 0.7887639 0.8119493 -0.423587731 -0.36060251
## P93 0.5487238 0.5536791 -1.138316004 -1.12302368
## P94 0.7122054 0.7215053 -0.614705707 -0.58694288
## P95 1.0042974 1.0072859 0.138101440 0.14549425
## P96 1.7669583 1.7724553 1.669884978 1.67604100
## P98 0.4047885 0.4087505 -1.719333661 -1.70691761
## P99 0.7579087 0.7521367 -0.485104946 -0.50307344
## P100 0.4939251 0.4832271 -1.460358850 -1.52244242
## P101 0.3951156 0.3942916 -1.800525350 -1.81202130
## P102 0.2593238 0.2592143 -2.472410993 -2.48127490
## P103 1.2667206 1.2812019 0.752335014 0.78815800
## P104 0.4185427 0.4233448 -1.637186197 -1.61984576
## P105 1.4556743 1.4714817 1.082860558 1.11292796
## P106 0.4357384 0.4343284 -1.562379510 -1.56869421
## P107 0.9533302 0.9102377 0.012674975 -0.10407891
## P108 0.3315537 0.3309127 -2.031774303 -2.03831409
## P109 1.1686492 1.2117948 0.533432858 0.63228765
## P110 0.5266141 0.5343181 -1.219089001 -1.19070302
## P111 0.8170387 0.8166551 -0.325360756 -0.32786446
## P112 1.3196602 1.3204384 0.824470156 0.82614905
## P113 1.2540379 1.2422416 0.695517542 0.67135902
## P114 0.4982467 0.5050183 -1.442893268 -1.43321290
## P115 1.2837691 1.2609186 0.760297911 0.71500043
## P116 0.6055527 0.6162396 -1.032151582 -1.00624831
## P117 0.8097160 0.8140898 -0.338821587 -0.32669667
## P118 1.3858031 1.3096467 1.005020872 0.85294723
## P119 1.4329995 1.4341083 1.050188028 1.05412444
## P120 0.4247757 0.4253111 -1.625151025 -1.62050825
## P121 0.8093631 0.8260620 -0.358194869 -0.31404879
## P122 2.0841274 2.1120544 2.099555434 2.14236824
## P123 0.5753338 0.5807793 -1.062251605 -1.04674942
## P124 0.4322153 0.4476939 -1.721688143 -1.67388224
## P125 1.5777229 1.5647177 1.355496151 1.33016166
## P126 1.2998755 1.3200065 0.818891507 0.86544429
## P127 1.3093293 1.3031362 0.833323569 0.82379721
## P128 2.6317352 2.6719444 3.023700512 3.10619469
## P129 0.4787953 0.4773767 -1.407507803 -1.41087513
## P130 0.4491035 0.4505809 -1.540437368 -1.53090492
## P131 0.4161403 0.4074894 -1.670388085 -1.71238903
## P132 0.5644981 0.5762007 -1.083456907 -1.04535467
## P133 0.5937027 0.5911464 -1.037766036 -1.05289434
## P134 0.6162995 0.6146976 -0.907436560 -0.91375507
## P135 0.8270644 0.8423571 -0.295555337 -0.25398654
## P136 0.7958670 0.8393933 -0.425189729 -0.30494744
## P137 0.3985316 0.4500191 -1.865256698 -1.65009652
## P139 0.4714177 0.4684817 -1.495330549 -1.51566468
## P140 1.2702794 1.2742186 0.729831724 0.73864301
## P141 1.3917241 1.4383474 1.017075363 1.11970947
## P142 0.2605948 0.2662445 -2.408666887 -2.38020189
## P143 0.2195901 0.2284397 -3.001123141 -2.95091363
## P144 0.3499806 0.3538241 -2.036543943 -2.02847211
## P145 0.9984113 1.0692634 0.171715408 0.31012741
## P146 0.8600185 0.8925791 -0.224764573 -0.13949464
## P147 0.2447640 0.2497757 -2.535192323 -2.51159986
## P148 1.6287074 1.5773534 1.458343583 1.37282467
## P149 0.4979852 0.4887523 -1.355766431 -1.39627677
## P150 0.7715171 0.7523613 -0.451771396 -0.50834560
## P151 0.1456386 0.1475760 -3.451300343 -3.46757359
## P152 0.4832853 0.4811863 -1.374746084 -1.38325477
## P153 0.5237857 0.5220178 -1.229327460 -1.23504306
## P154 1.2524187 1.2585284 0.704542261 0.71893981
## P155 1.5561674 1.5234363 1.260630453 1.20386265
## P156 0.8454152 0.8471843 -0.246543174 -0.24119715
## P157 0.3579751 0.3483375 -1.973437039 -2.02883462
## P158 0.8994981 0.8702890 -0.119302113 -0.19924057
## P159 0.6105633 0.6095036 -0.934771000 -0.94060365
## P160 0.4726545 0.4537087 -1.471744530 -1.55536929
## P161 1.7349981 1.7176738 1.580319574 1.55471372
## P162 3.3290035 3.3715902 3.755852790 3.79476767
## P163 0.8004144 0.8169385 -0.366388948 -0.32253453
## P164 1.0958499 1.0868719 0.364829542 0.34429479
## P165 0.4111091 0.4121787 -1.664133215 -1.66141583
## P166 0.9879469 1.0021542 0.109678707 0.14352544
## P167 0.5147590 0.4997364 -1.292333574 -1.35393704
## P168 0.5480078 0.5500684 -1.197152439 -1.18647655
## P169 1.2362008 1.2933008 0.688332337 0.81783339
## P170 0.3662549 0.3696256 -1.901406821 -1.88151478
## P171 0.9992921 0.9929290 0.140256409 0.12522522
## P172 0.4673802 0.4686849 -1.436084346 -1.43150663
## P173 0.5377619 0.5380347 -1.194513596 -1.19707711
## P174 0.5128243 0.4992801 -1.349178076 -1.41206668
## P175 0.7177602 0.7189833 -0.668915376 -0.66672751
## P176 4.4103746 4.3705313 4.659205798 4.63058496
## P177 0.7047669 0.7066869 -0.646459179 -0.64290632
## P178 0.6129356 0.6157122 -0.971702833 -0.96812129
## P179 1.3170071 1.3289965 0.843182760 0.87040488
## P180 1.1958387 1.2071772 0.574635080 0.59848286
## P181 0.2687137 0.2670147 -2.393951143 -2.41014541
## P182 0.4231978 0.4345742 -1.697624050 -1.65765678
## P183 2.6948798 2.7117347 3.016979774 3.05138418
## P184 0.6035413 0.6622033 -1.022123417 -0.82467316
## P185 0.7761558 0.7888465 -0.435436060 -0.39914892
## P186 0.5162667 0.5177047 -1.319219902 -1.32125077
## P187 1.8605529 1.8641849 1.866584864 1.87261764
## P188 0.5633041 0.5626505 -1.087573621 -1.09183668
## P189 2.4366625 2.3388804 2.845701328 2.71575864
## P190 0.7484399 0.7610158 -0.509409128 -0.47330921
## P191 0.7872073 0.7871042 -0.397927392 -0.39885002Item/Person separation reliability
## Person separation reliability
person.separation.reliability <- SepRel(person.locations.estimate)
person.separation.reliability## Separation Reliability: 0.8234## Item separation reliability:
# Get Item scores
ItemScores <- colSums(Medi_data)
# Get Item SD
ItemSD <- apply(Medi_data,2,sd)
# Calculate the se of the Item
ItemSE <- ItemSD/sqrt(length(ItemSD))
# compute the Observed Variance (also known as Total Person Variability or Squared Standard Deviation)
SSD.ItemScores <- var(ItemScores)
# compute the Mean Square Measurement error (also known as Model Error variance)
Item.MSE <- sum((ItemSE)^2) / length(ItemSE)
# compute the Item Separation Reliability
item.separation.reliability <- (SSD.ItemScores-Item.MSE) / SSD.ItemScores
item.separation.reliability## [1] 0.9999787Summarize the result
RSM_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",
"Separation.reliability")
delta.se <- Medi_RSM$se.eta
RSM_item.summary.results <- rbind(mean(centered.item.locations),
sd(centered.item.locations),
mean(delta.se),
sd(delta.se),
mean(item.fit.results$i.outfitMSQ),
sd(item.fit.results$i.outfitMSQ),
mean(item.fit.results$i.infitMSQ),
sd(item.fit.results$i.infitMSQ),
mean(item.fit.results$i.outfitZ),
sd(item.fit.results$i.outfitZ),
mean(item.fit.results$i.infitZ),
sd(item.fit.results$i.infitZ),
item.separation.reliability)
RSM_person.summary.results <- rbind(mean(person.locations$theta),
sd(person.locations$theta),
mean(person.locations$SE),
sd(person.locations$SE),
mean(person.fit$outfit_MSE),
sd(person.fit$outfit_MSE),
mean(person.fit$infit_MSE),
sd(person.fit$infit_MSE),
mean(person.fit$std_outfit),
sd(person.fit$std_outfit),
mean(person.fit$std_infit),
sd(person.fit$std_infit),
as.numeric(person.separation.reliability))
# Round the values for presentation in a table:
RSM_item.summary.results_rounded <- round(RSM_item.summary.results, digits = 2)
RSM_person.summary.results_rounded <- round(RSM_person.summary.results, digits = 2)
RSM_Table1 <- cbind.data.frame(RSM_summary.table.statistics,
RSM_item.summary.results_rounded,
RSM_person.summary.results_rounded)
# Add descriptive column labels:
names(RSM_Table1) <- c("Statistic", "Items", "Persons")
# Print the table to the console:
RSM_Table1## Statistic Items Persons NA NA
## X Logit Scale Location Mean 0.00 2.91 2.91 2.91
## X.1 Logit Scale Location SD 0.57 0.98 0.98 0.98
## X.2 Standard Error Mean 0.16 0.41 0.41 0.41
## X.3 Standard Error SD 0.14 0.02 0.02 0.02
## X.4 Outfit MSE Mean 0.91 0.91 0.91 0.91
## X.5 Outfit MSE SD 0.15 0.65 0.65 0.65
## X.6 Infit MSE Mean 0.91 0.91 0.91 0.91
## X.7 Infit MSE SD 0.15 0.65 0.65 0.65
## X.8 Std. Outfit Mean -0.93 -0.39 -0.39 -0.39
## X.9 Std. Outfit SD 1.57 1.45 1.45 1.45
## X.10 Std. Infit Mean -0.95 -0.39 -0.39 -0.39
## X.11 Std. Infit SD 1.59 1.45 1.45 1.45
## item.separation.reliability Separation.reliability 1.00 0.82 0.97 0.17Table 1 is an overall model summary table that provides an overview of the logit scale locations, standard errors, fit statistics, and reliability statistics for items and persons. This type of table is useful for reporting the results from Rasch model analyses because it provides a quick overview of the location estimates and numeric model-data fit statistics for the items and persons in the analysis.
# Calculate the average rating for each item:
Avg_Rating <- apply(Medi_data, 2, mean)
delta.se <- delta.se[1:11]
# Combine item calibration results in a table:
RSM_Table2 <- cbind.data.frame(c(1:ncol(Medi_data)),
Avg_Rating,
centered.item.locations,
delta.se,
item.fit$outfit_MSE,
item.fit$std_outfit,
item.fit$infit_MSE,
item.fit$std_infit)
# Add meaningful column names:
names(RSM_Table2) <- c("Task ID", "Average Rating", "Item Location","Item SE","Outfit MSE","Std. Outfit", "Infit MSE","Std. Infit")
# Sort Table 2 by Item difficulty:
RSM_Table2 <- RSM_Table2[order(-RSM_Table2$`Item Location`),]
# Round the numeric values (all columns except the first one) to 2 digits:
RSM_Table2[, -1] <- round(RSM_Table2[,-1], digits = 2)
# Print the table to the console:
RSM_Table2## Task ID Average Rating Item Location Item SE Outfit MSE Std. Outfit
## Decenter_3 3 1.84 0.89 0.10 0.91 -0.89
## Decenter_7 7 2.01 0.59 0.09 0.95 -0.44
## Decenter_8 8 2.07 0.47 0.09 0.89 -1.10
## Decenter_5 5 2.08 0.46 0.10 0.95 -0.52
## Decenter_2 2 2.16 0.31 0.10 0.67 -3.66
## Decenter_10 10 2.39 -0.11 0.10 0.76 -2.56
## Decenter_9 9 2.43 -0.20 0.09 1.16 1.59
## Decenter_1 1 2.55 -0.42 0.09 0.74 -2.83
## Decenter_6 6 2.62 -0.56 0.09 1.02 0.19
## Decenter_4 4 2.68 -0.68 0.09 0.91 -0.88
## Decenter_11 11 2.72 -0.75 0.19 1.08 0.80
## Infit MSE Std. Infit
## Decenter_3 0.91 -0.87
## Decenter_7 0.95 -0.48
## Decenter_8 0.89 -1.10
## Decenter_5 0.95 -0.46
## Decenter_2 0.67 -3.65
## Decenter_10 0.76 -2.56
## Decenter_9 1.16 1.59
## Decenter_1 0.73 -2.99
## Decenter_6 1.01 0.13
## Decenter_4 0.91 -0.91
## Decenter_11 1.08 0.85Table 2 is a table that summarizes the overall calibrations of individual items. For data sets with manageable sample sizes such as the Liking for Science data example in this chapter, we recommend reporting details about each item in a table similar to this one.
# Calculate the average rating for persons who did not have extreme scores
Person_Avg_Rating <- apply(person.locations.estimate$X.ex,1, mean)
# Combine person calibration results in a table:
RSM_Table3 <- cbind.data.frame(rownames(person.locations),
Person_Avg_Rating,
person.locations$theta,
person.locations$SE,
person.fit$outfit_MSE,
person.fit$std_outfit,
person.fit$infit_MSE,
person.fit$std_infit)
# Add meaningful column names:
names(RSM_Table3) <- c("ID", "Average Rating", "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:
RSM_Table3[, -1] <- round(RSM_Table3[,-1], digits = 2)
# Print the first six rows of the table to the console:
head(RSM_Table3)## ID Average Rating Person Location Person SE Outfit MSE Std. Outfit Infit MSE
## P1 P1 2.73 3.67 0.42 0.93 -0.05 0.91
## P2 P2 2.09 2.50 0.40 1.29 0.76 1.26
## P3 P3 2.27 2.82 0.41 1.76 1.60 1.78
## P4 P4 2.55 3.33 0.41 0.48 -1.42 0.49
## P5 P5 1.36 1.23 0.40 0.59 -1.11 0.59
## P6 P6 2.18 2.66 0.40 0.89 -0.12 0.90
## Std. Infit
## P1 -0.10
## P2 0.71
## P3 1.64
## P4 -1.40
## P5 -1.11
## P6 -0.09