CTS_project
Cheng Hua
5/12/2021
Teacher Commitment Scale
Part 1 EFA Analysis
Load the dataset
library(haven)
TCS <- read_sav("Desktop/Current Work/Dr. Sun's Project/Teacher Commitment Scale/Teacher Commitment Scale.sav")Decriptive Data Analysis
library(psych)
TCS_data <- TCS[,1:12]
summary(TCS_data) # TC3 Minimum Mean = 3.48; ## TC1 TC2 TC3 TC4
## Min. :2.000 Min. :3.000 Min. :1.000 Min. :3.000
## 1st Qu.:4.000 1st Qu.:5.000 1st Qu.:2.000 1st Qu.:4.000
## Median :5.000 Median :5.000 Median :3.500 Median :5.000
## Mean :4.667 Mean :5.048 Mean :3.476 Mean :4.738
## 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.000
## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000
## TC5 TC6 TC7 TC8
## Min. :2.000 Min. :2.000 Min. :2.000 Min. :3.000
## 1st Qu.:4.000 1st Qu.:3.250 1st Qu.:3.000 1st Qu.:5.000
## Median :4.000 Median :4.000 Median :4.000 Median :5.000
## Mean :4.286 Mean :4.333 Mean :4.143 Mean :5.024
## 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:5.000 3rd Qu.:6.000
## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000
## TC9 TC10 TC11 TC12
## Min. :3.000 Min. :2.000 Min. :4.000 Min. :3.000
## 1st Qu.:4.250 1st Qu.:4.000 1st Qu.:5.000 1st Qu.:5.000
## Median :5.000 Median :5.000 Median :5.000 Median :5.000
## Mean :5.024 Mean :4.786 Mean :5.119 Mean :5.119
## 3rd Qu.:6.000 3rd Qu.:5.000 3rd Qu.:6.000 3rd Qu.:6.000
## Max. :6.000 Max. :6.000 Max. :6.000 Max. :6.000table(TCS$Gender) # 1: male; 2:female##
## 1 2
## 15 22table(TCS$YTeach) # 1: "1-2 years"; 2: "3-5 years"; 3:"6-10 years"; 4:"11 years+"##
## 1 2 3 4
## 10 1 4 27table(TCS$HstDgreee) # 1: Bachelor; 2: Master; 3: Doctoral; 4: Other##
## 1 2 3 4
## 17 23 1 1Exploratory Factor Analysis (EFA)
library("Hmisc")## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alpha##
## Attaching package: 'Hmisc'## The following object is masked from 'package:psych':
##
## describe## The following objects are masked from 'package:base':
##
## format.pval, units## Check the correlation matrix
cor(TCS_data, method = "pearson", use = "complete.obs")## TC1 TC2 TC3 TC4 TC5 TC6
## TC1 1.00000000 0.66737042 0.08004538 0.24771215 0.5383015 0.03865415
## TC2 0.66737042 1.00000000 -0.17113998 0.31789749 0.2710722 0.12609394
## TC3 0.08004538 -0.17113998 1.00000000 -0.06009972 0.1554789 -0.13295728
## TC4 0.24771215 0.31789749 -0.06009972 1.00000000 0.3854090 0.46803096
## TC5 0.53830146 0.27107224 0.15547888 0.38540897 1.0000000 0.22353289
## TC6 0.03865415 0.12609394 -0.13295728 0.46803096 0.2235329 1.00000000
## TC7 0.26978378 0.21759811 -0.22784870 0.49357783 0.6010427 0.32675219
## TC8 0.25924788 0.38846174 0.02547788 0.38427092 0.3926485 -0.03014318
## TC9 0.49217469 0.48135106 0.07804105 0.30679327 0.4309068 0.06220214
## TC10 -0.11432127 -0.05634904 0.14263249 0.15021084 0.1049378 -0.12461555
## TC11 0.38230298 0.38514481 -0.11437370 0.26924967 0.3675621 -0.19159916
## TC12 0.55355140 0.55696640 0.03284144 0.36241010 0.4114006 -0.10056617
## TC7 TC8 TC9 TC10 TC11 TC12
## TC1 0.2697838 0.25924788 0.49217469 -0.11432127 0.3823030 0.55355140
## TC2 0.2175981 0.38846174 0.48135106 -0.05634904 0.3851448 0.55696640
## TC3 -0.2278487 0.02547788 0.07804105 0.14263249 -0.1143737 0.03284144
## TC4 0.4935778 0.38427092 0.30679327 0.15021084 0.2692497 0.36241010
## TC5 0.6010427 0.39264852 0.43090683 0.10493778 0.3675621 0.41140064
## TC6 0.3267522 -0.03014318 0.06220214 -0.12461555 -0.1915992 -0.10056617
## TC7 1.0000000 0.17218777 0.15504833 -0.13517864 0.2308352 0.24687837
## TC8 0.1721878 1.00000000 0.81275793 0.45171856 0.5736734 0.62104996
## TC9 0.1550483 0.81275793 1.00000000 0.29360561 0.4725758 0.64078565
## TC10 -0.1351786 0.45171856 0.29360561 1.00000000 0.3566939 0.37420006
## TC11 0.2308352 0.57367341 0.47257581 0.35669389 1.0000000 0.76724488
## TC12 0.2468784 0.62104996 0.64078565 0.37420006 0.7672449 1.00000000## Now we reverse code the TC3
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitreversed_TC3 <- recode(TCS_data$TC3,"1=6;2=5;3=4;4=3;5=2;6=1")
recoded_TCS_data <- TCS_data
recoded_TCS_data$TC3 <- reversed_TC3
## Check the correlation matrix
cor(recoded_TCS_data, method = "pearson", use = "complete.obs")## TC1 TC2 TC3 TC4 TC5 TC6
## TC1 1.00000000 0.66737042 -0.08004538 0.24771215 0.5383015 0.03865415
## TC2 0.66737042 1.00000000 0.17113998 0.31789749 0.2710722 0.12609394
## TC3 -0.08004538 0.17113998 1.00000000 0.06009972 -0.1554789 0.13295728
## TC4 0.24771215 0.31789749 0.06009972 1.00000000 0.3854090 0.46803096
## TC5 0.53830146 0.27107224 -0.15547888 0.38540897 1.0000000 0.22353289
## TC6 0.03865415 0.12609394 0.13295728 0.46803096 0.2235329 1.00000000
## TC7 0.26978378 0.21759811 0.22784870 0.49357783 0.6010427 0.32675219
## TC8 0.25924788 0.38846174 -0.02547788 0.38427092 0.3926485 -0.03014318
## TC9 0.49217469 0.48135106 -0.07804105 0.30679327 0.4309068 0.06220214
## TC10 -0.11432127 -0.05634904 -0.14263249 0.15021084 0.1049378 -0.12461555
## TC11 0.38230298 0.38514481 0.11437370 0.26924967 0.3675621 -0.19159916
## TC12 0.55355140 0.55696640 -0.03284144 0.36241010 0.4114006 -0.10056617
## TC7 TC8 TC9 TC10 TC11 TC12
## TC1 0.2697838 0.25924788 0.49217469 -0.11432127 0.3823030 0.55355140
## TC2 0.2175981 0.38846174 0.48135106 -0.05634904 0.3851448 0.55696640
## TC3 0.2278487 -0.02547788 -0.07804105 -0.14263249 0.1143737 -0.03284144
## TC4 0.4935778 0.38427092 0.30679327 0.15021084 0.2692497 0.36241010
## TC5 0.6010427 0.39264852 0.43090683 0.10493778 0.3675621 0.41140064
## TC6 0.3267522 -0.03014318 0.06220214 -0.12461555 -0.1915992 -0.10056617
## TC7 1.0000000 0.17218777 0.15504833 -0.13517864 0.2308352 0.24687837
## TC8 0.1721878 1.00000000 0.81275793 0.45171856 0.5736734 0.62104996
## TC9 0.1550483 0.81275793 1.00000000 0.29360561 0.4725758 0.64078565
## TC10 -0.1351786 0.45171856 0.29360561 1.00000000 0.3566939 0.37420006
## TC11 0.2308352 0.57367341 0.47257581 0.35669389 1.0000000 0.76724488
## TC12 0.2468784 0.62104996 0.64078565 0.37420006 0.7672449 1.00000000library(ltm)## Loading required package: MASS## Loading required package: msm## Loading required package: polycor##
## Attaching package: 'polycor'## The following object is masked from 'package:psych':
##
## polyserial##
## Attaching package: 'ltm'## The following object is masked from 'package:psych':
##
## factor.scorescronbach.alpha(recoded_TCS_data) # Report Internal Consistency (reliability)##
## Cronbach's alpha for the 'recoded_TCS_data' data-set
##
## Items: 12
## Sample units: 42
## alpha: 0.758# Principal Components Analysis
# Run a PCA to determine the number of factors
fit <- princomp(recoded_TCS_data, cor=TRUE)
summary(fit) # print variance accounted for## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 2.1288240 1.4068458 1.1421142 1.07498539 0.94372257
## Proportion of Variance 0.3776576 0.1649346 0.1087021 0.09629947 0.07421769
## Cumulative Proportion 0.3776576 0.5425922 0.6512943 0.74759378 0.82181147
## Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## Standard deviation 0.77511270 0.67327343 0.58944641 0.51957123 0.48001132
## Proportion of Variance 0.05006664 0.03777476 0.02895392 0.02249619 0.01920091
## Cumulative Proportion 0.87187811 0.90965287 0.93860679 0.96110298 0.98030389
## Comp.11 Comp.12
## Standard deviation 0.37419558 0.310372390
## Proportion of Variance 0.01166853 0.008027585
## Cumulative Proportion 0.99197241 1.000000000loadings(fit) # pc loadings##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## TC1 0.318 0.115 0.474 0.270 0.143 0.233 0.116 0.427 0.267
## TC2 0.314 0.109 0.425 -0.126 0.361 0.187 0.342 -0.440 -0.419
## TC3 0.228 0.120 -0.822 -0.217 0.260 0.113 0.307
## TC4 0.270 0.304 -0.369 0.156 0.419 -0.503 0.196 0.421
## TC5 0.316 0.210 0.377 -0.377 -0.221 0.341 0.204 -0.389
## TC6 0.505 -0.329 0.448 0.387 -0.473 -0.165
## TC7 0.220 0.454 -0.128 -0.499 -0.141 -0.152 0.211 -0.457 0.280
## TC8 0.365 -0.226 -0.214 0.167 -0.437 -0.257 -0.290
## TC9 0.375 -0.152 0.316 -0.509 0.364
## TC10 0.150 -0.411 -0.502 0.258 0.515 0.412
## TC11 0.345 -0.216 -0.251 -0.336 0.231 -0.565 -0.313
## TC12 0.401 -0.187 0.283 -0.222 -0.249 0.443
## Comp.11 Comp.12
## TC1 0.336 0.362
## TC2 -0.198
## TC3 -0.164
## TC4 -0.148
## TC5 -0.417 -0.166
## TC6 0.149
## TC7 0.318
## TC8 0.624
## TC9 0.125 -0.558
## TC10 0.191
## TC11 0.389 -0.170
## TC12 -0.609 0.160
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083
## Cumulative Var 0.083 0.167 0.250 0.333 0.417 0.500 0.583 0.667 0.750
## Comp.10 Comp.11 Comp.12
## SS loadings 1.000 1.000 1.000
## Proportion Var 0.083 0.083 0.083
## Cumulative Var 0.833 0.917 1.000plot(fit,type="lines") # scree plot
# From the plot we can see there are 4 primary factors contributing to the total variance
# Varimax Rotated Principal Components
scale_fa <- factanal(recoded_TCS_data,factors=4,rotation="varimax")
scale_fa # Check the factor loadings in here.##
## Call:
## factanal(x = recoded_TCS_data, factors = 4, rotation = "varimax")
##
## Uniquenesses:
## TC1 TC2 TC3 TC4 TC5 TC6 TC7 TC8 TC9 TC10 TC11 TC12
## 0.005 0.503 0.902 0.624 0.427 0.735 0.096 0.108 0.168 0.628 0.119 0.235
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4
## TC1 0.992
## TC2 0.657 0.219 0.111
## TC3 -0.109 0.229 0.172
## TC4 0.196 0.276 0.510
## TC5 0.484 0.203 0.544
## TC6 0.406 -0.314
## TC7 0.177 0.929
## TC8 0.235 0.897 0.157
## TC9 0.483 0.764 0.101
## TC10 -0.118 0.533 -0.115 0.247
## TC11 0.341 0.456 0.126 0.736
## TC12 0.523 0.510 0.130 0.462
##
## Factor1 Factor2 Factor3 Factor4
## SS loadings 2.424 2.313 1.740 0.974
## Proportion Var 0.202 0.193 0.145 0.081
## Cumulative Var 0.202 0.395 0.540 0.621
##
## Test of the hypothesis that 4 factors are sufficient.
## The chi square statistic is 32.45 on 24 degrees of freedom.
## The p-value is 0.116According to the factor loading, we can conclude that: D1: TC1, TC2 or (TC12) D2: TC8, TC9, TC10 or (TC12) D3: TC3(weak), TC4, TC5, TC6, TC7 D4: TC11 or (TC12)
One-level CFA
# Load the R packages that needed for the analysis
library(foreign)
library(lavaan)## This is lavaan 0.6-7## lavaan is BETA software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2cov# Establish our model
model <-'TC=~Student_Learning+Change+School+Teaching_profession
Student_Learning=~TC1+TC2+TC12
Change=~TC8+TC9+TC10
School=~TC3+TC4+TC5+TC6+TC7
Teaching_profession=~TC11'
# Factor 1 = Commitment to Student_Learning
# Factor 2 = Commitment to Change
# Factor 3 = Commitment to School
# Factor 4 = Commitment to Teaching_profession
# Fit the CFA model
# test_data <- recoded_TCS_data[,c(-3,-7)]
fit_cfa <- cfa(model, data=recoded_TCS_data)
# Check the model summary
summary(fit_cfa,fit.measure=TRUE)## lavaan 0.6-7 ended normally after 80 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 27
##
## Number of observations 42
##
## Model Test User Model:
##
## Test statistic 100.726
## Degrees of freedom 51
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 292.017
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.780
## Tucker-Lewis Index (TLI) 0.715
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -591.948
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 1237.895
## Bayesian (BIC) 1284.812
## Sample-size adjusted Bayesian (BIC) 1200.261
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.152
## 90 Percent confidence interval - lower 0.108
## 90 Percent confidence interval - upper 0.196
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.125
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## TC =~
## Student_Lernng 1.000
## Change 1.229 0.374 3.283 0.001
## School 0.146 0.263 0.556 0.578
## Teachng_prfssn 1.129 0.320 3.526 0.000
## Student_Learning =~
## TC1 1.000
## TC2 0.808 0.247 3.265 0.001
## TC12 1.369 0.327 4.191 0.000
## Change =~
## TC8 1.000
## TC9 0.909 0.129 7.041 0.000
## TC10 0.516 0.176 2.931 0.003
## School =~
## TC3 1.000
## TC4 3.772 6.636 0.568 0.570
## TC5 4.881 8.570 0.570 0.569
## TC6 3.036 5.434 0.559 0.576
## TC7 6.131 10.753 0.570 0.569
## Teaching_profession =~
## TC11 1.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .TC1 0.486 0.111 4.365 0.000
## .TC2 0.304 0.070 4.354 0.000
## .TC12 0.046 0.052 0.883 0.377
## .TC8 0.106 0.072 1.467 0.142
## .TC9 0.176 0.069 2.566 0.010
## .TC10 0.750 0.167 4.478 0.000
## .TC3 2.558 0.560 4.571 0.000
## .TC4 0.503 0.136 3.694 0.000
## .TC5 0.558 0.175 3.185 0.001
## .TC6 1.181 0.272 4.349 0.000
## .TC7 0.560 0.227 2.465 0.014
## .TC11 0.000
## TC 0.248 0.131 1.889 0.059
## .Student_Lernng 0.013 0.038 0.332 0.740
## .Change 0.305 0.106 2.872 0.004
## .School 0.020 0.069 0.286 0.775
## .Teachng_prfssn 0.170 0.054 3.175 0.001# Print out the paramarter Estimates
parameterEstimates(fit_cfa)## lhs op rhs est se z pvalue
## 1 TC =~ Student_Learning 1.000 0.000 NA NA
## 2 TC =~ Change 1.229 0.374 3.283 0.001
## 3 TC =~ School 0.146 0.263 0.556 0.578
## 4 TC =~ Teaching_profession 1.129 0.320 3.526 0.000
## 5 Student_Learning =~ TC1 1.000 0.000 NA NA
## 6 Student_Learning =~ TC2 0.808 0.247 3.265 0.001
## 7 Student_Learning =~ TC12 1.369 0.327 4.191 0.000
## 8 Change =~ TC8 1.000 0.000 NA NA
## 9 Change =~ TC9 0.909 0.129 7.041 0.000
## 10 Change =~ TC10 0.516 0.176 2.931 0.003
## 11 School =~ TC3 1.000 0.000 NA NA
## 12 School =~ TC4 3.772 6.636 0.568 0.570
## 13 School =~ TC5 4.881 8.570 0.570 0.569
## 14 School =~ TC6 3.036 5.434 0.559 0.576
## 15 School =~ TC7 6.131 10.753 0.570 0.569
## 16 Teaching_profession =~ TC11 1.000 0.000 NA NA
## 17 TC1 ~~ TC1 0.486 0.111 4.365 0.000
## 18 TC2 ~~ TC2 0.304 0.070 4.354 0.000
## 19 TC12 ~~ TC12 0.046 0.052 0.883 0.377
## 20 TC8 ~~ TC8 0.106 0.072 1.467 0.142
## 21 TC9 ~~ TC9 0.176 0.069 2.566 0.010
## 22 TC10 ~~ TC10 0.750 0.167 4.478 0.000
## 23 TC3 ~~ TC3 2.558 0.560 4.571 0.000
## 24 TC4 ~~ TC4 0.503 0.136 3.694 0.000
## 25 TC5 ~~ TC5 0.558 0.175 3.185 0.001
## 26 TC6 ~~ TC6 1.181 0.272 4.349 0.000
## 27 TC7 ~~ TC7 0.560 0.227 2.465 0.014
## 28 TC11 ~~ TC11 0.000 0.000 NA NA
## 29 TC ~~ TC 0.248 0.131 1.889 0.059
## 30 Student_Learning ~~ Student_Learning 0.013 0.038 0.332 0.740
## 31 Change ~~ Change 0.305 0.106 2.872 0.004
## 32 School ~~ School 0.020 0.069 0.286 0.775
## 33 Teaching_profession ~~ Teaching_profession 0.170 0.054 3.175 0.001
## ci.lower ci.upper
## 1 1.000 1.000
## 2 0.495 1.963
## 3 -0.369 0.661
## 4 0.501 1.756
## 5 1.000 1.000
## 6 0.323 1.292
## 7 0.729 2.009
## 8 1.000 1.000
## 9 0.656 1.162
## 10 0.171 0.861
## 11 1.000 1.000
## 12 -9.234 16.778
## 13 -11.915 21.677
## 14 -7.614 13.686
## 15 -14.945 27.206
## 16 1.000 1.000
## 17 0.268 0.704
## 18 0.167 0.441
## 19 -0.056 0.148
## 20 -0.036 0.247
## 21 0.042 0.310
## 22 0.421 1.078
## 23 1.461 3.654
## 24 0.236 0.769
## 25 0.215 0.902
## 26 0.649 1.714
## 27 0.115 1.004
## 28 0.000 0.000
## 29 -0.009 0.505
## 30 -0.061 0.086
## 31 0.097 0.514
## 32 -0.116 0.156
## 33 0.065 0.276modificationindices(fit_cfa)## lhs op rhs mi epc sepc.lv sepc.all
## 34 TC =~ TC1 1.621 -5.175 -2.575 -2.981
## 35 TC =~ TC2 0.820 -2.964 -1.475 -2.142
## 36 TC =~ TC12 11.343 28.938 14.400 19.715
## 37 TC =~ TC8 3.124 -1.117 -0.556 -0.627
## 38 TC =~ TC9 2.139 0.803 0.400 0.466
## 39 TC =~ TC10 0.121 0.167 0.083 0.086
## 40 TC =~ TC3 0.097 -0.191 -0.095 -0.059
## 41 TC =~ TC4 1.210 0.342 0.170 0.183
## 42 TC =~ TC5 3.540 0.678 0.337 0.314
## 43 TC =~ TC6 5.427 -1.001 -0.498 -0.419
## 44 TC =~ TC7 2.287 -0.641 -0.319 -0.260
## 46 Student_Learning =~ TC8 4.696 -1.229 -0.627 -0.708
## 47 Student_Learning =~ TC9 3.446 0.919 0.468 0.546
## 48 Student_Learning =~ TC10 0.094 0.134 0.068 0.071
## 49 Student_Learning =~ TC3 0.146 -0.223 -0.114 -0.071
## 50 Student_Learning =~ TC4 1.193 0.323 0.165 0.178
## 51 Student_Learning =~ TC5 3.309 0.624 0.318 0.296
## 52 Student_Learning =~ TC6 5.090 -0.923 -0.471 -0.396
## 53 Student_Learning =~ TC7 2.183 -0.596 -0.304 -0.248
## 54 Student_Learning =~ TC11 0.236 4.091 2.086 2.993
## 55 Change =~ TC1 0.704 -0.199 -0.164 -0.190
## 56 Change =~ TC2 0.029 0.032 0.026 0.038
## 57 Change =~ TC12 0.071 0.060 0.049 0.067
## 58 Change =~ TC3 0.357 -0.204 -0.168 -0.105
## 59 Change =~ TC4 2.039 0.241 0.199 0.214
## 60 Change =~ TC5 3.898 0.378 0.311 0.290
## 61 Change =~ TC6 1.865 -0.325 -0.268 -0.226
## 62 Change =~ TC7 3.696 -0.418 -0.344 -0.281
## 63 Change =~ TC11 0.001 -0.009 -0.008 -0.011
## 64 School =~ TC1 2.255 1.374 0.218 0.252
## 65 School =~ TC2 0.467 0.496 0.079 0.114
## 66 School =~ TC12 1.086 -0.603 -0.096 -0.131
## 67 School =~ TC8 0.072 0.165 0.026 0.029
## 68 School =~ TC9 0.235 0.300 0.048 0.055
## 69 School =~ TC10 1.357 -1.213 -0.192 -0.199
## 70 School =~ TC11 0.127 -0.222 -0.035 -0.051
## 71 Teaching_profession =~ TC1 1.790 -0.418 -0.292 -0.337
## 72 Teaching_profession =~ TC2 1.997 -0.353 -0.246 -0.357
## 73 Teaching_profession =~ TC12 6.264 0.890 0.620 0.849
## 74 Teaching_profession =~ TC8 0.784 0.177 0.123 0.139
## 75 Teaching_profession =~ TC9 1.669 -0.240 -0.167 -0.195
## 76 Teaching_profession =~ TC10 0.774 0.220 0.153 0.159
## 77 Teaching_profession =~ TC3 0.329 0.223 0.156 0.097
## 78 Teaching_profession =~ TC4 0.218 0.090 0.063 0.068
## 79 Teaching_profession =~ TC5 2.112 0.321 0.223 0.208
## 80 Teaching_profession =~ TC6 7.113 -0.726 -0.506 -0.426
## 81 Teaching_profession =~ TC7 0.540 -0.185 -0.129 -0.105
## 82 TC1 ~~ TC2 11.343 0.214 0.214 0.556
## 83 TC1 ~~ TC12 0.820 -0.063 -0.063 -0.421
## 84 TC1 ~~ TC8 5.804 -0.129 -0.129 -0.568
## 85 TC1 ~~ TC9 8.559 0.158 0.158 0.541
## 86 TC1 ~~ TC10 7.232 -0.258 -0.258 -0.427
## 87 TC1 ~~ TC3 0.561 -0.131 -0.131 -0.118
## 88 TC1 ~~ TC4 0.602 -0.065 -0.065 -0.132
## 89 TC1 ~~ TC5 5.297 0.213 0.213 0.409
## 90 TC1 ~~ TC6 0.059 0.030 0.030 0.039
## 91 TC1 ~~ TC7 0.003 -0.005 -0.005 -0.010
## 92 TC1 ~~ TC11 1.693 -0.073 -0.073 NA
## 93 TC2 ~~ TC12 1.621 -0.072 -0.072 -0.606
## 94 TC2 ~~ TC8 0.164 -0.017 -0.017 -0.096
## 95 TC2 ~~ TC9 2.062 0.061 0.061 0.266
## 96 TC2 ~~ TC10 6.149 -0.188 -0.188 -0.394
## 97 TC2 ~~ TC3 1.931 0.193 0.193 0.219
## 98 TC2 ~~ TC4 0.330 0.038 0.038 0.098
## 99 TC2 ~~ TC5 0.338 -0.043 -0.043 -0.104
## 100 TC2 ~~ TC6 1.792 0.129 0.129 0.215
## 101 TC2 ~~ TC7 0.002 0.004 0.004 0.009
## 102 TC2 ~~ TC11 1.999 -0.064 -0.064 NA
## 103 TC12 ~~ TC8 0.548 -0.026 -0.026 -0.372
## 104 TC12 ~~ TC9 0.020 0.005 0.005 0.053
## 105 TC12 ~~ TC10 4.041 0.106 0.106 0.572
## 106 TC12 ~~ TC3 1.176 -0.104 -0.104 -0.304
## 107 TC12 ~~ TC4 0.239 0.023 0.023 0.150
## 108 TC12 ~~ TC5 0.206 -0.023 -0.023 -0.147
## 109 TC12 ~~ TC6 0.991 -0.067 -0.067 -0.286
## 110 TC12 ~~ TC7 0.101 -0.018 -0.018 -0.114
## 111 TC12 ~~ TC11 5.683 0.147 0.147 NA
## 112 TC8 ~~ TC9 0.121 0.073 0.073 0.536
## 113 TC8 ~~ TC10 2.139 0.113 0.113 0.402
## 114 TC8 ~~ TC3 0.144 0.045 0.045 0.087
## 115 TC8 ~~ TC4 1.478 0.069 0.069 0.300
## 116 TC8 ~~ TC5 0.065 -0.016 -0.016 -0.066
## 117 TC8 ~~ TC6 0.353 -0.049 -0.049 -0.138
## 118 TC8 ~~ TC7 0.000 0.000 0.000 0.002
## 119 TC8 ~~ TC11 2.826 0.063 0.063 NA
## 120 TC9 ~~ TC10 3.124 -0.130 -0.130 -0.358
## 121 TC9 ~~ TC3 0.435 -0.080 -0.080 -0.119
## 122 TC9 ~~ TC4 0.544 -0.043 -0.043 -0.144
## 123 TC9 ~~ TC5 1.292 0.073 0.073 0.232
## 124 TC9 ~~ TC6 1.254 0.094 0.094 0.206
## 125 TC9 ~~ TC7 0.379 -0.043 -0.043 -0.137
## 126 TC9 ~~ TC11 4.373 -0.075 -0.075 NA
## 127 TC10 ~~ TC3 0.657 -0.175 -0.175 -0.126
## 128 TC10 ~~ TC4 0.526 0.075 0.075 0.122
## 129 TC10 ~~ TC5 0.023 0.017 0.017 0.027
## 130 TC10 ~~ TC6 0.285 -0.080 -0.080 -0.085
## 131 TC10 ~~ TC7 2.648 -0.203 -0.203 -0.313
## 132 TC10 ~~ TC11 0.938 0.059 0.059 NA
## 133 TC3 ~~ TC4 0.001 -0.006 -0.006 -0.006
## 134 TC3 ~~ TC5 6.253 -0.543 -0.543 -0.455
## 135 TC3 ~~ TC6 0.464 0.188 0.188 0.108
## 136 TC3 ~~ TC7 4.539 0.524 0.524 0.438
## 137 TC3 ~~ TC11 1.796 0.150 0.150 NA
## 138 TC4 ~~ TC5 2.983 -0.255 -0.255 -0.482
## 139 TC4 ~~ TC6 5.036 0.312 0.312 0.405
## 140 TC4 ~~ TC7 0.300 -0.103 -0.103 -0.194
## 141 TC4 ~~ TC11 0.251 -0.027 -0.027 NA
## 142 TC5 ~~ TC6 0.775 -0.141 -0.141 -0.173
## 143 TC5 ~~ TC7 1.960 0.355 0.355 0.636
## 144 TC5 ~~ TC11 0.058 0.014 0.014 NA
## 145 TC6 ~~ TC7 0.011 0.020 0.020 0.024
## 146 TC6 ~~ TC11 2.793 -0.129 -0.129 NA
## 147 TC7 ~~ TC11 0.183 0.028 0.028 NA
## 152 Student_Learning ~~ Change 0.127 -0.033 -0.532 -0.532
## 153 Student_Learning ~~ School 0.001 0.000 -0.019 -0.019
## 154 Student_Learning ~~ Teaching_profession 0.236 0.051 1.109 1.109
## 155 Change ~~ School 0.236 0.008 0.105 0.105
## 156 Change ~~ Teaching_profession 0.001 -0.003 -0.013 -0.013
## 157 School ~~ Teaching_profession 0.127 -0.004 -0.076 -0.076
## sepc.nox
## 34 -2.981
## 35 -2.142
## 36 19.715
## 37 -0.627
## 38 0.466
## 39 0.086
## 40 -0.059
## 41 0.183
## 42 0.314
## 43 -0.419
## 44 -0.260
## 46 -0.708
## 47 0.546
## 48 0.071
## 49 -0.071
## 50 0.178
## 51 0.296
## 52 -0.396
## 53 -0.248
## 54 2.993
## 55 -0.190
## 56 0.038
## 57 0.067
## 58 -0.105
## 59 0.214
## 60 0.290
## 61 -0.226
## 62 -0.281
## 63 -0.011
## 64 0.252
## 65 0.114
## 66 -0.131
## 67 0.029
## 68 0.055
## 69 -0.199
## 70 -0.051
## 71 -0.337
## 72 -0.357
## 73 0.849
## 74 0.139
## 75 -0.195
## 76 0.159
## 77 0.097
## 78 0.068
## 79 0.208
## 80 -0.426
## 81 -0.105
## 82 0.556
## 83 -0.421
## 84 -0.568
## 85 0.541
## 86 -0.427
## 87 -0.118
## 88 -0.132
## 89 0.409
## 90 0.039
## 91 -0.010
## 92 NA
## 93 -0.606
## 94 -0.096
## 95 0.266
## 96 -0.394
## 97 0.219
## 98 0.098
## 99 -0.104
## 100 0.215
## 101 0.009
## 102 NA
## 103 -0.372
## 104 0.053
## 105 0.572
## 106 -0.304
## 107 0.150
## 108 -0.147
## 109 -0.286
## 110 -0.114
## 111 NA
## 112 0.536
## 113 0.402
## 114 0.087
## 115 0.300
## 116 -0.066
## 117 -0.138
## 118 0.002
## 119 NA
## 120 -0.358
## 121 -0.119
## 122 -0.144
## 123 0.232
## 124 0.206
## 125 -0.137
## 126 NA
## 127 -0.126
## 128 0.122
## 129 0.027
## 130 -0.085
## 131 -0.313
## 132 NA
## 133 -0.006
## 134 -0.455
## 135 0.108
## 136 0.438
## 137 NA
## 138 -0.482
## 139 0.405
## 140 -0.194
## 141 NA
## 142 -0.173
## 143 0.636
## 144 NA
## 145 0.024
## 146 NA
## 147 NA
## 152 -0.532
## 153 -0.019
## 154 1.109
## 155 0.105
## 156 -0.013
## 157 -0.076library("lavaanPlot")
lavaanPlot(model=fit_cfa,node_options=list(shape="box",fontname="Helvetica"),edge_options=list(color="blue"),coefs=TRUE, covs=TRUE, stars=c("regress"),stand = FALSE)Based on the results, we do not use the CFA’s result due to the small sample size.
Part 2 Rasch Analysis
Prepare the package
## Running the Rasch Rating Scale Model
library(TAM) # For running the Rating Scale Rasch Model## Loading required package: CDM## Loading required package: mvtnorm## **********************************
## ** CDM 7.5-15 (2020-03-10 14:19:21)
## ** Cognitive Diagnostic Models **
## **********************************##
## Attaching package: 'CDM'## The following object is masked from 'package:car':
##
## deltaMethod## * TAM 3.5-19 (2020-05-05 22:45:39)library(plyr) # For plot the Item characteristic curves##
## Attaching package: 'plyr'## The following objects are masked from 'package:Hmisc':
##
## is.discrete, summarizelibrary(WrightMap)# For plot the variable map
library(eRm) # For another example##
## Attaching package: 'eRm'## The following object is masked from 'package:psych':
##
## sim.raschRun the Partial Credit Model
# Run the Partial Credit Model
recoded_TCS_data1 <- recoded_TCS_data[-7,]
PC_model <- PCM(recoded_TCS_data1)## Warning:
## The following items have no 0-responses:
## TC1 TC2 TC3 TC4 TC5 TC6 TC7 TC8 TC9 TC10 TC11 TC12
## Responses are shifted such that lowest category is 0.# Check the result
summary(PC_model)##
## Results of PCM estimation:
##
## Call: PCM(X = recoded_TCS_data1)
##
## Conditional log-likelihood: -484.9877
## Number of iterations: 49
## Number of parameters: 41
##
## Item (Category) Difficulty Parameters (eta): with 0.95 CI:
## Estimate Std. Error lower CI upper CI
## TC1.c2 -1.769 1.037 -3.802 0.263
## TC1.c3 -1.852 1.001 -3.815 0.110
## TC1.c4 0.792 1.085 -1.334 2.918
## TC2.c1 -1.526 1.069 -3.622 0.570
## TC2.c2 -2.321 1.008 -4.298 -0.345
## TC2.c3 -0.454 1.041 -2.495 1.586
## TC3.c1 0.352 0.583 -0.791 1.495
## TC3.c2 0.601 0.567 -0.510 1.713
## TC3.c3 1.570 0.622 0.352 2.788
## TC3.c4 2.654 0.689 1.304 4.004
## TC3.c5 3.971 0.790 2.422 5.519
## TC4.c1 -0.242 0.558 -1.336 0.853
## TC4.c2 -0.085 0.553 -1.169 0.998
## TC4.c3 1.621 0.654 0.339 2.903
## TC5.c1 -0.407 0.710 -1.799 0.985
## TC5.c2 -0.627 0.663 -1.928 0.673
## TC5.c3 0.211 0.691 -1.142 1.565
## TC5.c4 2.397 0.835 0.761 4.034
## TC6.c1 -0.681 0.679 -2.012 0.651
## TC6.c2 -0.365 0.675 -1.688 0.958
## TC6.c3 0.390 0.698 -0.977 1.758
## TC6.c4 1.867 0.774 0.349 3.385
## TC7.c1 0.388 0.586 -0.762 1.537
## TC7.c2 0.472 0.555 -0.616 1.560
## TC7.c3 1.101 0.587 -0.050 2.252
## TC7.c4 3.301 0.766 1.800 4.802
## TC8.c1 0.339 0.716 -1.065 1.743
## TC8.c2 -0.650 0.596 -1.818 0.517
## TC8.c3 0.768 0.663 -0.531 2.067
## TC9.c1 -1.180 0.783 -2.714 0.355
## TC9.c2 -1.150 0.765 -2.650 0.349
## TC9.c3 -0.023 0.798 -1.586 1.541
## TC10.c1 -1.042 1.141 -3.279 1.194
## TC10.c2 -1.804 1.037 -3.837 0.230
## TC10.c3 -1.656 1.008 -3.632 0.320
## TC10.c4 -0.073 1.026 -2.084 1.938
## TC11.c1 -0.353 0.432 -1.199 0.494
## TC11.c2 1.044 0.513 0.039 2.049
## TC12.c1 -1.543 1.070 -3.640 0.553
## TC12.c2 -2.225 1.012 -4.210 -0.241
## TC12.c3 -0.782 1.030 -2.800 1.237
##
## Item Easiness Parameters (beta) with 0.95 CI:
## Estimate Std. Error lower CI upper CI
## beta TC1.c1 1.028 1.141 -1.209 3.265
## beta TC1.c2 1.769 1.037 -0.263 3.802
## beta TC1.c3 1.852 1.001 -0.110 3.815
## beta TC1.c4 -0.792 1.085 -2.918 1.334
## beta TC2.c1 1.526 1.069 -0.570 3.622
## beta TC2.c2 2.321 1.008 0.345 4.298
## beta TC2.c3 0.454 1.041 -1.586 2.495
## beta TC3.c1 -0.352 0.583 -1.495 0.791
## beta TC3.c2 -0.601 0.567 -1.713 0.510
## beta TC3.c3 -1.570 0.622 -2.788 -0.352
## beta TC3.c4 -2.654 0.689 -4.004 -1.304
## beta TC3.c5 -3.971 0.790 -5.519 -2.422
## beta TC4.c1 0.242 0.558 -0.853 1.336
## beta TC4.c2 0.085 0.553 -0.998 1.169
## beta TC4.c3 -1.621 0.654 -2.903 -0.339
## beta TC5.c1 0.407 0.710 -0.985 1.799
## beta TC5.c2 0.627 0.663 -0.673 1.928
## beta TC5.c3 -0.211 0.691 -1.565 1.142
## beta TC5.c4 -2.397 0.835 -4.034 -0.761
## beta TC6.c1 0.681 0.679 -0.651 2.012
## beta TC6.c2 0.365 0.675 -0.958 1.688
## beta TC6.c3 -0.390 0.698 -1.758 0.977
## beta TC6.c4 -1.867 0.774 -3.385 -0.349
## beta TC7.c1 -0.388 0.586 -1.537 0.762
## beta TC7.c2 -0.472 0.555 -1.560 0.616
## beta TC7.c3 -1.101 0.587 -2.252 0.050
## beta TC7.c4 -3.301 0.766 -4.802 -1.800
## beta TC8.c1 -0.339 0.716 -1.743 1.065
## beta TC8.c2 0.650 0.596 -0.517 1.818
## beta TC8.c3 -0.768 0.663 -2.067 0.531
## beta TC9.c1 1.180 0.783 -0.355 2.714
## beta TC9.c2 1.150 0.765 -0.349 2.650
## beta TC9.c3 0.023 0.798 -1.541 1.586
## beta TC10.c1 1.042 1.141 -1.194 3.279
## beta TC10.c2 1.804 1.037 -0.230 3.837
## beta TC10.c3 1.656 1.008 -0.320 3.632
## beta TC10.c4 0.073 1.026 -1.938 2.084
## beta TC11.c1 0.353 0.432 -0.494 1.199
## beta TC11.c2 -1.044 0.513 -2.049 -0.039
## beta TC12.c1 1.543 1.070 -0.553 3.640
## beta TC12.c2 2.225 1.012 0.241 4.210
## beta TC12.c3 0.782 1.030 -1.237 2.800# Plot the Variable Map
plotPImap(PC_model)
### Examine item difficulty values:
item.estimates <- thresholds(PC_model)
item.estimates##
## Design Matrix Block 1:
## Location Threshold 1 Threshold 2 Threshold 3 Threshold 4 Threshold 5
## TC1 0.19805 -1.02791 -0.74138 -0.08310 2.64459 NA
## TC2 -0.15148 -1.52601 -0.79518 1.86674 NA NA
## TC3 0.79411 0.35194 0.24929 0.96874 1.08393 1.31666
## TC4 0.54035 -0.24174 0.15661 1.70618 NA NA
## TC5 0.59934 -0.40724 -0.22002 0.83859 2.18605 NA
## TC6 0.46674 -0.68062 0.31570 0.75530 1.47660 NA
## TC7 0.82521 0.38756 0.08481 0.62866 2.19982 NA
## TC8 0.25602 0.33866 -0.98916 1.41855 NA NA
## TC9 -0.00756 -1.17958 0.02919 1.12771 NA NA
## TC10 -0.01822 -1.04234 -0.76118 0.14749 1.58312 NA
## TC11 0.52187 -0.35264 1.39638 NA NA NA
## TC12 -0.26055 -1.54339 -0.68201 1.44375 NA NA## Get threshold SEs values:
item.se <- item.estimates$se.thresh
item.se## thresh beta TC1.c1 thresh beta TC1.c2 thresh beta TC1.c3 thresh beta TC1.c4
## 1.1413654 0.6802707 0.4015551 0.5534176
## thresh beta TC2.c1 thresh beta TC2.c2 thresh beta TC2.c3 thresh beta TC3.c1
## 1.0693218 0.4775345 0.4080593 0.5831876
## thresh beta TC3.c2 thresh beta TC3.c3 thresh beta TC3.c4 thresh beta TC3.c5
## 0.5458626 0.5033656 0.5343557 0.6002664
## thresh beta TC4.c1 thresh beta TC4.c2 thresh beta TC4.c3 thresh beta TC5.c1
## 0.5584964 0.4171829 0.4433559 0.7102064
## thresh beta TC5.c2 thresh beta TC5.c3 thresh beta TC5.c4 thresh beta TC6.c1
## 0.5089525 0.3997560 0.5791396 0.6792984
## thresh beta TC6.c2 thresh beta TC6.c3 thresh beta TC6.c4 thresh beta TC7.c1
## 0.4854199 0.4376947 0.4926988 0.5864065
## thresh beta TC7.c2 thresh beta TC7.c3 thresh beta TC7.c4 thresh beta TC8.c1
## 0.5268677 0.4242842 0.5793449 0.7163118
## thresh beta TC8.c2 thresh beta TC8.c3 thresh beta TC9.c1 thresh beta TC9.c2
## 0.5659673 0.3837813 0.7828900 0.4352110
## thresh beta TC9.c3 thresh beta TC10.c1 thresh beta TC10.c2 thresh beta TC10.c3
## 0.3905283 1.1411925 0.6806943 0.4164053
## thresh beta TC10.c4 thresh beta TC11.c1 thresh beta TC11.c2 thresh beta TC12.c1
## 0.4272984 0.4320528 0.3840091 1.0697657
## thresh beta TC12.c2 thresh beta TC12.c3
## 0.4835519 0.3806361# Standard errors for theta estimates:
person.locations.estimate <- person.parameter(PC_model)
summary(person.locations.estimate)##
## Estimation of Ability Parameters
##
## Collapsed log-likelihood: -220.7884
## Number of iterations: 7
## Number of parameters: 16
##
## ML estimated ability parameters (without spline interpolated values):
## Estimate Std. Err. 2.5 % 97.5 %
## theta P1 0.20720166 0.3064184 -0.39336740 0.8077707
## theta P2 0.88190897 0.3215480 0.25168643 1.5121315
## theta P3 1.33622888 0.3568839 0.63674928 2.0357085
## theta P4 1.46847406 0.3708533 0.74161498 2.1953331
## theta P5 0.39482394 0.3066165 -0.20613334 0.9957812
## theta P6 1.21309601 0.3452815 0.53635678 1.8898352
## theta P7 0.20720166 0.3064184 -0.39336740 0.8077707
## theta P8 -0.27558916 0.3180247 -0.89890604 0.3477277
## theta P9 -0.27558916 0.3180247 -0.89890604 0.3477277
## theta P10 0.88190897 0.3215480 0.25168643 1.5121315
## theta P11 0.11306122 0.3073366 -0.48930751 0.7154300
## theta P12 1.33622888 0.3568839 0.63674928 2.0357085
## theta P13 0.39482394 0.3066165 -0.20613334 0.9957812
## theta P14 1.09726443 0.3357044 0.43929581 1.7552330
## theta P15 1.21309601 0.3452815 0.53635678 1.8898352
## theta P16 0.68127579 0.3126566 0.06848016 1.2940714
## theta P17 1.21309601 0.3452815 0.53635678 1.8898352
## theta P18 0.88190897 0.3215480 0.25168643 1.5121315
## theta P19 0.11306122 0.3073366 -0.48930751 0.7154300
## theta P20 0.68127579 0.3126566 0.06848016 1.2940714
## theta P21 0.88190897 0.3215480 0.25168643 1.5121315
## theta P22 0.88190897 0.3215480 0.25168643 1.5121315
## theta P23 0.88190897 0.3215480 0.25168643 1.5121315
## theta P24 1.33622888 0.3568839 0.63674928 2.0357085
## theta P25 0.58446795 0.3097829 -0.02269541 1.1916313
## theta P26 -0.48417652 0.3285324 -1.12808822 0.1597352
## theta P27 -0.07795328 0.3112001 -0.68789422 0.5319877
## theta P28 -1.10262678 0.3833805 -1.85403883 -0.3512147
## theta P29 1.46847406 0.3708533 0.74161498 2.1953331
## theta P30 1.09726443 0.3357044 0.43929581 1.7552330
## theta P31 1.77006026 0.4077880 0.97081050 2.5693100
## theta P32 0.58446795 0.3097829 -0.02269541 1.1916313
## theta P33 1.09726443 0.3357044 0.43929581 1.7552330
## theta P34 0.88190897 0.3215480 0.25168643 1.5121315
## theta P35 0.68127579 0.3126566 0.06848016 1.2940714
## theta P36 1.33622888 0.3568839 0.63674928 2.0357085
## theta P37 1.46847406 0.3708533 0.74161498 2.1953331
## theta P38 0.88190897 0.3215480 0.25168643 1.5121315
## theta P39 0.78018832 0.3165323 0.15979639 1.4005803
## theta P40 1.46847406 0.3708533 0.74161498 2.1953331
## theta P41 0.58446795 0.3097829 -0.02269541 1.1916313# Build a table for person locations
person_theta <- person.locations.estimate$theta.table
person_theta## Person Parameter NAgroup Interpolated
## P1 0.20720166 1 FALSE
## P2 0.88190897 1 FALSE
## P3 1.33622888 1 FALSE
## P4 1.46847406 1 FALSE
## P5 0.39482394 1 FALSE
## P6 1.21309601 1 FALSE
## P7 0.20720166 1 FALSE
## P8 -0.27558916 1 FALSE
## P9 -0.27558916 1 FALSE
## P10 0.88190897 1 FALSE
## P11 0.11306122 1 FALSE
## P12 1.33622888 1 FALSE
## P13 0.39482394 1 FALSE
## P14 1.09726443 1 FALSE
## P15 1.21309601 1 FALSE
## P16 0.68127579 1 FALSE
## P17 1.21309601 1 FALSE
## P18 0.88190897 1 FALSE
## P19 0.11306122 1 FALSE
## P20 0.68127579 1 FALSE
## P21 0.88190897 1 FALSE
## P22 0.88190897 1 FALSE
## P23 0.88190897 1 FALSE
## P24 1.33622888 1 FALSE
## P25 0.58446795 1 FALSE
## P26 -0.48417652 1 FALSE
## P27 -0.07795328 1 FALSE
## P28 -1.10262678 1 FALSE
## P29 1.46847406 1 FALSE
## P30 1.09726443 1 FALSE
## P31 1.77006026 1 FALSE
## P32 0.58446795 1 FALSE
## P33 1.09726443 1 FALSE
## P34 0.88190897 1 FALSE
## P35 0.68127579 1 FALSE
## P36 1.33622888 1 FALSE
## P37 1.46847406 1 FALSE
## P38 0.88190897 1 FALSE
## P39 0.78018832 1 FALSE
## P40 1.46847406 1 FALSE
## P41 0.58446795 1 FALSEitem.fit <- itemfit(person.locations.estimate)
item.fit##
## Itemfit Statistics:
## Chisq df p-value Outfit MSQ Infit MSQ Outfit t Infit t Discrim
## TC1 37.837 40 0.568 0.923 0.905 -0.217 -0.310 0.580
## TC2 32.833 40 0.782 0.801 0.771 -0.833 -0.980 0.613
## TC3 74.449 40 0.001 1.816 1.627 3.226 2.774 -0.011
## TC4 31.673 40 0.824 0.773 0.740 -1.163 -1.388 0.584
## TC5 33.417 40 0.760 0.815 0.768 -0.867 -1.140 0.621
## TC6 54.251 40 0.066 1.323 1.283 1.555 1.408 0.143
## TC7 36.148 40 0.644 0.882 0.867 -0.501 -0.622 0.482
## TC8 29.336 40 0.893 0.716 0.713 -1.196 -1.304 0.736
## TC9 29.727 40 0.883 0.725 0.708 -1.454 -1.581 0.743
## TC10 58.231 40 0.031 1.420 1.307 1.740 1.334 0.193
## TC11 31.385 40 0.833 0.765 0.771 -1.383 -1.353 0.662
## TC12 27.339 40 0.936 0.667 0.674 -1.663 -1.605 0.795item.fit.table <- cbind(item.fit[["i.outfitMSQ"]],item.fit[["i.infitMSQ"]],item.fit[["i.infitMSQ"]],item.fit[["i.infitZ"]])
pfit <- personfit(person.locations.estimate)
pfit##
## Personfit Statistics:
## Chisq df p-value Outfit MSQ Infit MSQ Outfit t Infit t
## P1 7.456 11 0.761 0.621 0.697 -1.09 -0.77
## P2 2.839 11 0.993 0.237 0.432 -2.70 -1.64
## P3 24.373 11 0.011 2.031 1.902 2.02 1.71
## P4 16.355 11 0.128 1.363 1.317 0.90 0.77
## P5 3.192 11 0.988 0.266 0.347 -2.74 -2.19
## P6 3.873 11 0.973 0.323 0.389 -2.10 -1.67
## P7 9.466 11 0.579 0.789 0.855 -0.50 -0.28
## P8 5.892 11 0.880 0.491 0.479 -1.64 -1.63
## P9 28.227 11 0.003 2.352 2.624 2.86 3.18
## P10 12.877 11 0.301 1.073 1.131 0.31 0.44
## P11 9.071 11 0.615 0.756 0.781 -0.62 -0.51
## P12 8.354 11 0.681 0.696 0.751 -0.66 -0.44
## P13 9.131 11 0.610 0.761 0.662 -0.57 -0.88
## P14 14.464 11 0.208 1.205 1.819 0.60 1.67
## P15 1.582 11 1.000 0.132 0.140 -3.37 -3.09
## P16 9.146 11 0.608 0.762 0.886 -0.53 -0.17
## P17 20.200 11 0.043 1.683 2.397 1.49 2.43
## P18 4.638 11 0.947 0.387 0.359 -1.88 -1.97
## P19 21.816 11 0.026 1.818 1.930 1.95 2.08
## P20 1.937 11 0.999 0.161 0.252 -3.36 -2.65
## P21 4.555 11 0.951 0.380 0.458 -1.92 -1.53
## P22 3.729 11 0.977 0.311 0.316 -2.26 -2.18
## P23 13.063 11 0.289 1.089 1.356 0.35 0.91
## P24 29.209 11 0.002 2.434 3.175 2.58 3.22
## P25 29.776 11 0.002 2.481 1.747 2.88 1.69
## P26 13.865 11 0.241 1.155 1.073 0.52 0.31
## P27 10.024 11 0.528 0.835 0.890 -0.37 -0.18
## P28 7.019 11 0.798 0.585 0.605 -0.88 -0.93
## P29 23.539 11 0.015 1.962 2.090 1.90 1.93
## P30 23.380 11 0.016 1.948 1.825 1.94 1.68
## P31 11.729 11 0.384 0.977 0.873 0.10 -0.10
## P32 4.931 11 0.934 0.411 0.323 -1.87 -2.27
## P33 11.874 11 0.373 0.990 1.788 0.11 1.63
## P34 9.712 11 0.556 0.809 0.873 -0.37 -0.18
## P35 1.654 11 0.999 0.138 0.137 -3.57 -3.52
## P36 8.399 11 0.677 0.700 0.798 -0.65 -0.32
## P37 19.566 11 0.052 1.630 1.586 1.38 1.21
## P38 5.865 11 0.882 0.489 0.490 -1.44 -1.40
## P39 8.535 11 0.665 0.711 0.738 -0.68 -0.58
## P40 5.095 11 0.926 0.425 0.489 -1.59 -1.19
## P41 16.217 11 0.133 1.351 1.498 0.95 1.23person.fit.table <- cbind(pfit[["p.outfitMSQ"]],pfit[["p.outfitMSQ"]],pfit[["p.outfitMSQ"]],pfit[["p.outfitMSQ"]])
# ===================================
# compute item separation reliability
# ===================================
# Get Item scores
ItemScores <- colSums(recoded_TCS_data)
# Get Item SD
ItemSD <- apply(recoded_TCS_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] 0.9997966# ===================================
# compute person separation reliability
# ===================================
# Get Person scores
PersonScores <- rowSums(recoded_TCS_data)
# Get Person SD
PersonSD <- apply(recoded_TCS_data,1,sd)
# Calculate the se of the Person
PersonSE <- PersonSD/sqrt(length(PersonSD))
# compute the Observed Variance (also known as Total Person Variability or Squared Standard Deviation)
SSD.PersonScores <- var(PersonScores)
# compute the Mean Square Measurement error (also known as Model Error variance)
Person.MSE <- sum((PersonSE)^2) / length(PersonSE)
# compute the Person Separation Reliability
person.separation.reliability <- (SSD.PersonScores-Person.MSE) / SSD.PersonScores
person.separation.reliability## [1] 0.9993899