ＩＲＴ
Liu Yi Jie
2024-12-29
步驟一: 整理資料
讀取A區資料檔案
#讀資料
data <- read.csv(file = "IRT整理檔案.csv",
header = TRUE, stringsAsFactors = TRUE)
head(data)## A1a A1b A2a A2b A2c A2d A2e A2f A2g A2h A3a A3b A3c A3d A3e A3f A3g A3h A3i
## 1 2 5 1 1 1 2 1 1 3 1 6 7 6 5 4 3 3 4 1
## 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 3 6 6 3 3 3 4 2 4 4 4 7 5 7 4 5 4 2 5 7
## 4 7 7 7 7 4 7 1 7 7 NA 7 7 7 6 7 7 7 7 7
## 5 7 7 5 7 5 7 1 5 7 6 6 6 6 4 4 4 3 4 6
## 6 1 3 2 1 2 5 2 3 2 1 3 2 2 2 4 2 3 1 1
## A3j A3k A3l A3m
## 1 3 3 3 4
## 2 1 1 1 1
## 3 7 6 6 7
## 4 7 7 7 7
## 5 5 6 7 7
## 6 3 3 2 2print(nrow(data))## [1] 3881檢查是否有NA值
data |> apply(2, is.na) |> apply(2, sum)## A1a A1b A2a A2b A2c A2d A2e A2f A2g A2h A3a A3b A3c A3d A3e A3f A3g A3h A3i A3j
## 25 87 13 15 26 19 13 26 30 16 11 17 48 34 36 31 33 18 21 22
## A3k A3l A3m
## 30 24 15#因為資料數有3881筆，資料數龐大，因此決定將有NA值得觀察值(受試者)都剔除
data2 <- na.omit(data)
head(data2)## A1a A1b A2a A2b A2c A2d A2e A2f A2g A2h A3a A3b A3c A3d A3e A3f A3g A3h A3i
## 1 2 5 1 1 1 2 1 1 3 1 6 7 6 5 4 3 3 4 1
## 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 3 6 6 3 3 3 4 2 4 4 4 7 5 7 4 5 4 2 5 7
## 5 7 7 5 7 5 7 1 5 7 6 6 6 6 4 4 4 3 4 6
## 6 1 3 2 1 2 5 2 3 2 1 3 2 2 2 4 2 3 1 1
## 7 1 1 2 2 1 1 1 1 1 1 2 2 1 2 2 1 1 2 1
## A3j A3k A3l A3m
## 1 3 3 3 4
## 2 1 1 1 1
## 3 7 6 6 7
## 5 5 6 7 7
## 6 3 3 2 2
## 7 1 1 1 1print(nrow(data2))## [1] 3471#上表與先前的原始資料比較前6筆資料，可以看出原始資料中的第5位受試者已經被剔除，至此確定資料已無NA值
#剩下3471筆資料
本組期中提案中有提到本組資料的一個困境，也就是本組所採用的資料由7點或8典李克特氏量表組成(有的題目是7點，有的題目是8點)，量尺由1:Strongly agree 到 7:Very dissatisfied，而8:Do not know or does not apply
在期中提案報告這點時 陳俊宏老師 建議本組可以將8點量尺剔除，因為代表該受試者在本題沒有反應(可視為沒有作答)
因此我們將剔除填寫8點態度的受試者
# 計算含有 8 分的受試者數量
num_subjects <- sum(apply(data2, 1, function(x) any(x == 8)))
print(num_subjects)## [1] 255#填寫8分的受試者共有255位
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# 使用 dplyr 過濾含有8分的態度的受試者
data3 <- data2 %>%
filter(if_all(everything(), ~ . != 8))
head(data3)## A1a A1b A2a A2b A2c A2d A2e A2f A2g A2h A3a A3b A3c A3d A3e A3f A3g A3h A3i
## 1 2 5 1 1 1 2 1 1 3 1 6 7 6 5 4 3 3 4 1
## 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 3 6 6 3 3 3 4 2 4 4 4 7 5 7 4 5 4 2 5 7
## 4 7 7 5 7 5 7 1 5 7 6 6 6 6 4 4 4 3 4 6
## 5 1 3 2 1 2 5 2 3 2 1 3 2 2 2 4 2 3 1 1
## 6 1 1 2 2 1 1 1 1 1 1 2 2 1 2 2 1 1 2 1
## A3j A3k A3l A3m
## 1 3 3 3 4
## 2 1 1 1 1
## 3 7 6 6 7
## 4 5 6 7 7
## 5 3 3 2 2
## 6 1 1 1 1print(nrow(data3))## [1] 3216#最終的資料共有3216筆資料
將data整理完後的資料data3重新命名為dta，方便後續使用更簡易
dta<-data3步驟二: EFA探索性因素分析
#上過鄭中平老師的「R在行為科學之應用」，在此利用老師教授的package進行探索性因素分析
#整體設定，含載入套件
source("https://raw.githubusercontent.com/ChungPingCheng/R4BS2/main/R4BS_setup.R")## Loading required package: pacman## Loading required package: ggmirt## Loading required package: brolgar## Registered S3 method overwritten by 'tsibble':
## method from
## as_tibble.grouped_df dplyr##
## Attaching package: 'brolgar'## The following object is masked from 'package:insight':
##
## n_obs#平行分析探索因素數
dta |>
EFA.dimensions::RAWPAR() |>
purrr::pluck("eigenvalues") |>
as_tibble() |>
tidyr::pivot_longer(cols=c(2,4),
names_to = "Type",
values_to = "Eigen") |>
ggplot2::ggplot() +
aes(x=Root, y=Eigen, color=Type) +
geom_line()+
geom_point(size=rel(2))+
scale_color_grey(start=.6, end=.1)+
scale_y_continuous(name='特徵值')+
scale_x_continuous(name='因素個數', breaks=seq(0,35,5))+
theme(legend.position='top')
PARALLEL ANALYSIS
Randomization method: generated data
Type of correlations specified for the real data eigenvalues: Pearson
Type of correlations specified for the random data eigenvalues: pearson
Extraction Method: Principal Components
Variables = 23
Cases = 3216
Ndatasets = 100
Percentile = 95
Compare the Real Data eigenvalues below to the correspondingrandom data Mean and Percentile eigenvalues Root Real Data Mean Percentile
1 13.470 1.151 1.172
2 1.581 1.129 1.144
3 1.044 1.112 1.124
4 0.888 1.096 1.109
5 0.794 1.082 1.096
6 0.535 1.069 1.081
7 0.496 1.055 1.064
8 0.458 1.043 1.052
9 0.425 1.031 1.039
10 0.386 1.020 1.029
11 0.363 1.008 1.016
12 0.317 0.998 1.007
13 0.296 0.987 0.996
14 0.283 0.976 0.986
15 0.268 0.964 0.973
16 0.240 0.954 0.964
17 0.232 0.943 0.952
18 0.215 0.931 0.941
19 0.207 0.918 0.930
20 0.161 0.907 0.918
21 0.131 0.892 0.903
22 0.126 0.876 0.889
23 0.084 0.857 0.875
The number of factors according to the parallel analysis = 2
#利用探索性分析的特徵值曲線，可知A資料集有2個因素
#設定因素數為 2
fit <-
dta |> lavaan::efa(data=_,nfactors = 2)
fit
f1 f2
A1a 0.636* .*
A1b * 0.816*
A2a 0.871*
A2b 0.560* .*
A2c 0.540* .*
A2d 0.458* 0.320*
A2e 0.816*
A2f 0.370* 0.480*
A2g 0.339* 0.483*
A2h .* 0.509*
A3a * 0.952*
A3b * 0.927*
A3c * 0.926*
A3d 0.695*
A3e 0.733*
A3f 0.696*
A3g 0.561*
A3h * 0.812*
A3i .* 0.651*
A3j .* 0.827*
A3k .* 0.803*
A3l .* 0.729*
A3m 0.893*library(psych)
# 進行探索性因素分析（EFA）
# 根據特徵圖提取2個因素
efa_result <- fa(data, nfactors = 2, rotate = "varimax")
# 顯示結果
print(efa_result)Factor Analysis using method = minres
Call: fa(r = data, nfactors = 2, rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 MR2 h2 u2 com
A1a 0.38 0.68 0.61 0.39 1.6
A1b 0.74 0.42 0.72 0.28 1.6
A2a 0.25 0.81 0.72 0.28 1.2
A2b 0.29 0.64 0.50 0.50 1.4
A2c 0.31 0.63 0.49 0.51 1.5
A2d 0.39 0.59 0.50 0.50 1.7
A2e 0.24 0.74 0.60 0.40 1.2
A2f 0.54 0.55 0.59 0.41 2.0
A2g 0.53 0.49 0.53 0.47 2.0
A2h 0.52 0.42 0.44 0.56 1.9
A3a 0.80 0.33 0.75 0.25 1.3
A3b 0.77 0.33 0.69 0.31 1.4
A3c 0.78 0.34 0.73 0.27 1.4
A3d 0.59 0.27 0.41 0.59 1.4
A3e 0.63 0.30 0.48 0.52 1.4
A3f 0.67 0.24 0.51 0.49 1.2
A3g 0.54 0.19 0.32 0.68 1.2
A3h 0.75 0.24 0.62 0.38 1.2
A3i 0.64 0.38 0.55 0.45 1.6
A3j 0.78 0.45 0.80 0.20 1.6
A3k 0.76 0.46 0.79 0.21 1.6
A3l 0.70 0.42 0.66 0.34 1.6
A3m 0.81 0.39 0.80 0.20 1.4
MR1 MR2
SS loadings 8.58 5.25
Proportion Var 0.37 0.23
Cumulative Var 0.37 0.60
Proportion Explained 0.62 0.38
Cumulative Proportion 0.62 1.00
Mean item complexity = 1.5
Test of the hypothesis that 2 factors are sufficient.
df null model = 253 with the objective function = 20.12 with Chi Square = 77876
df of the model are 208 and the objective function was 2.69
The root mean square of the residuals (RMSR) is 0.04
The df corrected root mean square of the residuals is 0.05
The harmonic n.obs is 3834 with the empirical chi square 3842 with prob < 0
The total n.obs was 3881 with Likelihood Chi Square = 10397 with prob < 0
Tucker Lewis Index of factoring reliability = 0.84
RMSEA index = 0.112 and the 90 % confidence intervals are 0.111 0.114
BIC = 8678
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
MR1 MR2
Correlation of (regression) scores with factors 0.95 0.91
Multiple R square of scores with factors 0.91 0.84
Minimum correlation of possible factor scores 0.81 0.67# 查看載荷矩陣（factor loadings）
efa_result$loadings
Loadings:
MR1 MR2
A1a 0.376 0.684
A1b 0.736 0.419
A2a 0.249 0.811
A2b 0.293 0.641
A2c 0.309 0.627
A2d 0.388 0.594
A2e 0.243 0.737
A2f 0.538 0.550
A2g 0.532 0.492
A2h 0.519 0.418
A3a 0.798 0.331
A3b 0.765 0.329
A3c 0.784 0.338
A3d 0.586 0.266
A3e 0.625 0.303
A3f 0.674 0.237
A3g 0.538 0.187
A3h 0.748 0.241
A3i 0.638 0.381
A3j 0.776 0.447
A3k 0.763 0.457
A3l 0.695 0.421
A3m 0.806 0.390
MR1 MR2
SS loadings 8.576 5.249
Proportion Var 0.373 0.228
Cumulative Var 0.373 0.601# 查看每個變數的共同性（communality）
efa_result$communality A1a A1b A2a A2b A2c A2d A2e A2f A2g A2h A3a
0.6091 0.7176 0.7207 0.4972 0.4886 0.5033 0.6026 0.5921 0.5252 0.4437 0.7466
A3b A3c A3d A3e A3f A3g A3h A3i A3j A3k A3l
0.6942 0.7287 0.4141 0.4828 0.5107 0.3240 0.6175 0.5517 0.8017 0.7913 0.6605
A3m
0.8015 # 查看各因素的解釋變異（variance explained）
efa_result$Vaccounted| MR1 | MR2 | |
|---|---|---|
| SS loadings | 8.5764 | 5.2489 |
| Proportion Var | 0.3729 | 0.2282 |
| Cumulative Var | 0.3729 | 0.6011 |
| Proportion Explained | 0.6203 | 0.3797 |
| Cumulative Proportion | 0.6203 | 1.0000 |
# 可視化因素負載
fa.diagram(efa_result)
步驟三:計算內部一致性
alpha_result <- alpha(dta)
print(alpha_result)
Reliability analysis
Call: alpha(x = dta)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
0.97 0.97 0.98 0.56 29 0.00081 3 1.4 0.55
95% confidence boundaries
lower alpha upper
Feldt 0.97 0.97 0.97
Duhachek 0.97 0.97 0.97
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
A1a 0.97 0.97 0.97 0.56 28 0.00084 0.014 0.55
A1b 0.96 0.96 0.97 0.55 27 0.00087 0.013 0.54
A2a 0.97 0.97 0.97 0.56 28 0.00083 0.014 0.55
A2b 0.97 0.97 0.97 0.57 29 0.00082 0.014 0.56
A2c 0.97 0.97 0.97 0.57 29 0.00083 0.014 0.56
A2d 0.97 0.97 0.98 0.56 28 0.00083 0.014 0.55
A2e 0.97 0.97 0.97 0.57 29 0.00082 0.013 0.56
A2f 0.97 0.97 0.97 0.56 28 0.00085 0.014 0.54
A2g 0.97 0.97 0.97 0.56 28 0.00085 0.014 0.55
A2h 0.97 0.97 0.98 0.56 29 0.00083 0.014 0.56
A3a 0.96 0.96 0.97 0.55 27 0.00087 0.013 0.55
A3b 0.97 0.96 0.97 0.55 27 0.00087 0.013 0.55
A3c 0.96 0.96 0.97 0.55 27 0.00087 0.013 0.55
A3d 0.97 0.97 0.98 0.57 29 0.00083 0.014 0.56
A3e 0.97 0.97 0.97 0.56 28 0.00085 0.014 0.55
A3f 0.97 0.97 0.97 0.56 28 0.00083 0.014 0.55
A3g 0.97 0.97 0.97 0.57 29 0.00081 0.012 0.56
A3h 0.97 0.97 0.97 0.56 28 0.00085 0.014 0.55
A3i 0.97 0.97 0.97 0.56 28 0.00084 0.014 0.55
A3j 0.96 0.96 0.97 0.55 27 0.00088 0.013 0.54
A3k 0.96 0.96 0.97 0.55 27 0.00088 0.013 0.54
A3l 0.97 0.96 0.97 0.55 27 0.00086 0.013 0.55
A3m 0.96 0.96 0.97 0.55 27 0.00088 0.013 0.54
Item statistics
n raw.r std.r r.cor r.drop mean sd
A1a 3216 0.72 0.73 0.71 0.69 2.5 1.6
A1b 3216 0.85 0.84 0.84 0.83 3.1 1.9
A2a 3216 0.70 0.71 0.70 0.67 2.4 1.6
A2b 3216 0.64 0.66 0.64 0.61 2.2 1.5
A2c 3216 0.64 0.66 0.64 0.61 1.9 1.3
A2d 3216 0.71 0.71 0.70 0.68 2.6 1.8
A2e 3216 0.66 0.67 0.65 0.63 2.6 1.8
A2f 3216 0.79 0.79 0.78 0.76 3.3 1.9
A2g 3216 0.77 0.76 0.75 0.74 3.9 2.1
A2h 3216 0.69 0.69 0.67 0.66 2.4 1.5
A3a 3216 0.85 0.85 0.85 0.83 3.5 2.0
A3b 3216 0.83 0.82 0.82 0.81 3.9 2.0
A3c 3216 0.85 0.85 0.84 0.83 3.6 2.0
A3d 3216 0.68 0.68 0.66 0.65 3.4 1.8
A3e 3216 0.77 0.76 0.75 0.74 3.7 1.9
A3f 3216 0.72 0.72 0.71 0.69 3.0 1.8
A3g 3216 0.61 0.61 0.60 0.58 2.6 1.7
A3h 3216 0.77 0.77 0.76 0.75 3.0 1.8
A3i 3216 0.76 0.76 0.75 0.73 3.1 1.8
A3j 3216 0.89 0.89 0.89 0.88 3.5 1.8
A3k 3216 0.89 0.88 0.89 0.87 3.4 1.8
A3l 3216 0.82 0.82 0.82 0.80 2.9 1.7
A3m 3216 0.88 0.88 0.88 0.87 3.3 1.9
Non missing response frequency for each item
1 2 3 4 5 6 7 miss
A1a 0.27 0.40 0.16 0.04 0.05 0.05 0.03 0
A1b 0.20 0.31 0.16 0.06 0.10 0.08 0.08 0
A2a 0.33 0.34 0.16 0.03 0.04 0.05 0.04 0
A2b 0.41 0.33 0.11 0.03 0.04 0.04 0.03 0
A2c 0.47 0.33 0.11 0.04 0.03 0.02 0.02 0
A2d 0.30 0.33 0.15 0.04 0.06 0.05 0.06 0
A2e 0.31 0.30 0.16 0.06 0.06 0.05 0.06 0
A2f 0.19 0.25 0.21 0.09 0.08 0.07 0.10 0
A2g 0.13 0.19 0.16 0.12 0.11 0.10 0.18 0
A2h 0.38 0.26 0.13 0.14 0.03 0.03 0.03 0
A3a 0.14 0.27 0.19 0.08 0.10 0.10 0.12 0
A3b 0.09 0.22 0.20 0.09 0.14 0.11 0.15 0
A3c 0.14 0.24 0.18 0.11 0.10 0.10 0.13 0
A3d 0.14 0.25 0.22 0.13 0.10 0.08 0.08 0
A3e 0.12 0.22 0.16 0.16 0.12 0.09 0.13 0
A3f 0.24 0.28 0.18 0.09 0.08 0.06 0.07 0
A3g 0.30 0.29 0.18 0.06 0.06 0.05 0.06 0
A3h 0.24 0.26 0.18 0.12 0.07 0.06 0.07 0
A3i 0.21 0.24 0.19 0.17 0.06 0.06 0.07 0
A3j 0.14 0.22 0.22 0.15 0.11 0.07 0.09 0
A3k 0.15 0.23 0.20 0.15 0.10 0.07 0.09 0
A3l 0.27 0.24 0.17 0.17 0.05 0.05 0.06 0
A3m 0.20 0.22 0.17 0.16 0.08 0.07 0.10 0#Cronbach’s Alpha=0.9672
步驟四:CFA驗證性因素分析
model <- '
#latent variable
Approval_of_the_Environment_and_Workplace_Culture=~ A3m + A3a + A3c + A3j + A3b + A3k + A3h + A1b + A3l + A3f + A3i + A3e + A3d + A3g + A2h + A2g
Organizational_Commitment_and_Satisfaction =~ A2a+ A2e + A1a + A2b + A2c + A2d +A2f
#residual covariances
A3f ~~ A3g
A3j ~~ A3k
A3a ~~ A3b
A3a ~~ A3c
A2a ~~ A2e
A3c ~~ A3b
A3l ~~ A2h
A3h ~~ A3f
A3h ~~ A3g
'#跑CFA
library(lavaan)
fit <- cfa(model, data = dta)
#檢視結果
summary(fit, fit.measures = TRUE, standardized = TRUE)lavaan 0.6-18 ended normally after 48 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 56
Number of observations 3216
Model Test User Model:
Test statistic 4543.836
Degrees of freedom 220
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 69219.455
Degrees of freedom 253
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.937
Tucker-Lewis Index (TLI) 0.928
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -114905.246
Loglikelihood unrestricted model (H1) -112633.328
Akaike (AIC) 229922.492
Bayesian (BIC) 230262.742
Sample-size adjusted Bayesian (SABIC) 230084.805
Root Mean Square Error of Approximation:
RMSEA 0.078
90 Percent confidence interval - lower 0.076
90 Percent confidence interval - upper 0.080
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 0.066
Standardized Root Mean Square Residual:
SRMR 0.042
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err
Approval_of_the_Environment_and_Workplace_Culture =~
A3m 1.000
A3a 0.957 0.013
A3c 0.957 0.013
A3j 0.929 0.011
A3b 0.917 0.014
A3k 0.933 0.011
A3h 0.779 0.014
A1b 0.916 0.012
A3l 0.829 0.012
A3f 0.710 0.015
A3i 0.774 0.013
A3e 0.834 0.015
A3d 0.679 0.015
A3g 0.546 0.015
A2h 0.587 0.013
A2g 0.859 0.016
Organizational_Commitment_and_Satisfaction =~
A2a 1.000
A2e 0.981 0.018
A1a 0.957 0.021
A2b 0.872 0.020
A2c 0.727 0.017
A2d 1.049 0.024
A2f 1.178 0.026
z-value P(>|z|) Std.lv Std.all
1.754 0.913
73.554 0.000 1.678 0.855
71.812 0.000 1.679 0.847
84.534 0.000 1.630 0.903
67.170 0.000 1.609 0.822
82.064 0.000 1.637 0.893
57.349 0.000 1.367 0.759
73.800 0.000 1.607 0.856
70.720 0.000 1.454 0.841
47.624 0.000 1.246 0.680
58.406 0.000 1.358 0.766
57.157 0.000 1.463 0.757
45.819 0.000 1.190 0.663
35.252 0.000 0.958 0.551
46.195 0.000 1.030 0.667
53.091 0.000 1.508 0.726
1.263 0.776
55.388 0.000 1.238 0.706
46.274 0.000 1.209 0.776
43.056 0.000 1.100 0.730
42.188 0.000 0.918 0.718
44.587 0.000 1.325 0.752
46.137 0.000 1.488 0.774
Covariances:
Estimate Std.Err
.A3f ~~
.A3g 1.246 0.042
.A3j ~~
.A3k 0.351 0.016
.A3a ~~
.A3b 0.550 0.025
.A3c 0.517 0.024
.A2a ~~
.A2e 0.565 0.029
.A3c ~~
.A3b 0.538 0.026
.A3l ~~
.A2h 0.404 0.022
.A3h ~~
.A3f 0.636 0.032
.A3g 0.681 0.034
Approval_of_the_Environment_and_Workplace_Culture ~~
Orgnztnl_Cm__S 1.857 0.061
z-value P(>|z|) Std.lv Std.all
29.730 0.000 1.246 0.640
22.173 0.000 0.351 0.549
22.024 0.000 0.550 0.485
21.693 0.000 0.517 0.483
19.537 0.000 0.565 0.445
21.068 0.000 0.538 0.457
18.538 0.000 0.404 0.375
20.178 0.000 0.636 0.404
20.267 0.000 0.681 0.400
30.591 0.000 0.838 0.838
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.A3m 0.611 0.019 32.650 0.000 0.611 0.166
.A3a 1.033 0.029 35.925 0.000 1.033 0.268
.A3c 1.113 0.031 36.194 0.000 1.113 0.283
.A3j 0.603 0.018 33.351 0.000 0.603 0.185
.A3b 1.245 0.034 36.837 0.000 1.245 0.325
.A3k 0.679 0.020 33.950 0.000 0.679 0.202
.A3h 1.379 0.036 38.094 0.000 1.379 0.425
.A1b 0.940 0.026 36.056 0.000 0.940 0.267
.A3l 0.877 0.024 36.539 0.000 0.877 0.293
.A3f 1.803 0.046 38.804 0.000 1.803 0.537
.A3i 1.299 0.034 38.018 0.000 1.299 0.413
.A3e 1.594 0.042 38.131 0.000 1.594 0.427
.A3d 1.804 0.046 38.950 0.000 1.804 0.560
.A3g 2.099 0.053 39.432 0.000 2.099 0.696
.A2h 1.321 0.034 38.846 0.000 1.321 0.555
.A2g 2.036 0.053 38.464 0.000 2.036 0.472
.A2a 1.050 0.031 34.008 0.000 1.050 0.397
.A2e 1.539 0.043 35.901 0.000 1.539 0.501
.A1a 0.965 0.028 34.170 0.000 0.965 0.398
.A2b 1.059 0.030 35.640 0.000 1.059 0.467
.A2c 0.792 0.022 35.957 0.000 0.792 0.485
.A2d 1.346 0.038 35.006 0.000 1.346 0.434
.A2f 1.479 0.043 34.244 0.000 1.479 0.401
Apprv___E__W_C 3.078 0.091 33.685 0.000 1.000 1.000
Orgnztnl_Cm__S 1.594 0.063 25.429 0.000 1.000 1.000#檢查看是否有修改指數 (如有需要會加入residual covariance)
modificationIndices(fit, maximum.number = 10, sort=TRUE, op="~~")| lhs | op | rhs | mi | epc | sepc.lv | sepc.all | sepc.nox | |
|---|---|---|---|---|---|---|---|---|
| 320 | A2b | ~~ | A2c | 388.3 | 0.3652 | 0.3652 | 0.3985 | 0.3985 |
| 89 | A3m | ~~ | A3l | 275.8 | 0.2339 | 0.2339 | 0.3195 | 0.3195 |
| 225 | A3l | ~~ | A3i | 196.7 | 0.2614 | 0.2614 | 0.2449 | 0.2449 |
| 305 | A2g | ~~ | A2f | 187.7 | 0.4591 | 0.4591 | 0.2646 | 0.2646 |
| 107 | A3a | ~~ | A1b | 145.5 | 0.1863 | 0.1863 | 0.1891 | 0.1891 |
| 219 | A1b | ~~ | A1a | 139.9 | 0.2247 | 0.2247 | 0.2360 | 0.2360 |
| 264 | A3e | ~~ | A2g | 139.3 | 0.3940 | 0.3940 | 0.2187 | 0.2187 |
| 300 | A2g | ~~ | A2e | 132.6 | 0.3323 | 0.3323 | 0.1877 | 0.1877 |
#載入圖表套件
library(semPlot)
#將CFA模型給視覺化
semPaths(fit, "std", layout = "circle", title = FALSE)
步驟五:IRT分析
#該資料我們先假設是2參數模型，先用2參數模型
(一)擬合模型
#本組是7點量表 GRM 模型
library(mirt)Loading required package: stats4Loading required package: lattice
Attaching package: 'lattice'The following object is masked from 'package:boot':
melanoma
Attaching package: 'mirt'The following object is masked from 'package:nlme':
fixefThe following objects are masked from 'package:eRm':
itemfit, personfitThe following object is masked from 'package:lme4':
fixef#前面因素分析分析出2因子，因此使用多維度假設 mirt(,2)
md1<-mirt(dta,2, itemtype = 'graded')Iteration: 1, Log-Lik: -117772.571, Max-Change: 3.51778Iteration: 2, Log-Lik: -102784.242, Max-Change: 1.25245Iteration: 3, Log-Lik: -100881.466, Max-Change: 0.54929Iteration: 4, Log-Lik: -100345.053, Max-Change: 0.18883Iteration: 5, Log-Lik: -99990.262, Max-Change: 0.19263Iteration: 6, Log-Lik: -99741.401, Max-Change: 0.12281Iteration: 7, Log-Lik: -99537.351, Max-Change: 0.17925Iteration: 8, Log-Lik: -99385.125, Max-Change: 0.17226Iteration: 9, Log-Lik: -99260.191, Max-Change: 0.23415Iteration: 10, Log-Lik: -99155.180, Max-Change: 0.23224Iteration: 11, Log-Lik: -99068.488, Max-Change: 0.22710Iteration: 12, Log-Lik: -98991.556, Max-Change: 0.23736Iteration: 13, Log-Lik: -98924.193, Max-Change: 0.20492Iteration: 14, Log-Lik: -98864.211, Max-Change: 0.22268Iteration: 15, Log-Lik: -98808.133, Max-Change: 0.20894Iteration: 16, Log-Lik: -98755.282, Max-Change: 0.16403Iteration: 17, Log-Lik: -98705.748, Max-Change: 0.16231Iteration: 18, Log-Lik: -98666.901, Max-Change: 0.20837Iteration: 19, Log-Lik: -98574.329, Max-Change: 0.19876Iteration: 20, Log-Lik: -98500.952, Max-Change: 0.12134Iteration: 21, Log-Lik: -98451.079, Max-Change: 0.08350Iteration: 22, Log-Lik: -98415.316, Max-Change: 0.08127Iteration: 23, Log-Lik: -98387.451, Max-Change: 0.07109Iteration: 24, Log-Lik: -98366.898, Max-Change: 0.05698Iteration: 25, Log-Lik: -98350.593, Max-Change: 0.05341Iteration: 26, Log-Lik: -98338.018, Max-Change: 0.04545Iteration: 27, Log-Lik: -98328.057, Max-Change: 0.04137Iteration: 28, Log-Lik: -98320.011, Max-Change: 0.03489Iteration: 29, Log-Lik: -98313.549, Max-Change: 0.03666Iteration: 30, Log-Lik: -98308.069, Max-Change: 0.02569Iteration: 31, Log-Lik: -98303.484, Max-Change: 0.02166Iteration: 32, Log-Lik: -98300.308, Max-Change: 0.01998Iteration: 33, Log-Lik: -98297.523, Max-Change: 0.01882Iteration: 34, Log-Lik: -98284.137, Max-Change: 0.01507Iteration: 35, Log-Lik: -98282.569, Max-Change: 0.02252Iteration: 36, Log-Lik: 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Log-Lik: -98257.303, Max-Change: 0.00058Iteration: 269, Log-Lik: -98257.303, Max-Change: 0.00029Iteration: 270, Log-Lik: -98257.302, Max-Change: 0.00045Iteration: 271, Log-Lik: -98257.302, Max-Change: 0.00036Iteration: 272, Log-Lik: -98257.302, Max-Change: 0.00056Iteration: 273, Log-Lik: -98257.302, Max-Change: 0.00028Iteration: 274, Log-Lik: -98257.301, Max-Change: 0.00022Iteration: 275, Log-Lik: -98257.301, Max-Change: 0.00034Iteration: 276, Log-Lik: -98257.301, Max-Change: 0.00016Iteration: 277, Log-Lik: -98257.301, Max-Change: 0.00013Iteration: 278, Log-Lik: -98257.301, Max-Change: 0.00021Iteration: 279, Log-Lik: -98257.300, Max-Change: 0.00050Iteration: 280, Log-Lik: -98257.300, Max-Change: 0.00025Iteration: 281, Log-Lik: -98257.300, Max-Change: 0.00039Iteration: 282, Log-Lik: -98257.300, Max-Change: 0.00020Iteration: 283, Log-Lik: -98257.300, Max-Change: 0.00015Iteration: 284, Log-Lik: -98257.299, Max-Change: 0.00025Iteration: 285, Log-Lik: -98257.299, Max-Change: 0.00011Iteration: 286, Log-Lik: -98257.299, Max-Change: 0.00046Iteration: 287, Log-Lik: -98257.299, Max-Change: 0.00023Iteration: 288, Log-Lik: -98257.299, Max-Change: 0.00036Iteration: 289, Log-Lik: -98257.298, Max-Change: 0.00027Iteration: 290, Log-Lik: -98257.298, Max-Change: 0.00042Iteration: 291, Log-Lik: -98257.298, Max-Change: 0.00021Iteration: 292, Log-Lik: -98257.298, Max-Change: 0.00016Iteration: 293, Log-Lik: -98257.298, Max-Change: 0.00026Iteration: 294, Log-Lik: -98257.297, Max-Change: 0.00012Iteration: 295, Log-Lik: -98257.297, Max-Change: 0.00048Iteration: 296, Log-Lik: -98257.297, Max-Change: 0.00024Iteration: 297, Log-Lik: -98257.297, Max-Change: 0.00038Iteration: 298, Log-Lik: -98257.297, Max-Change: 0.00029Iteration: 299, Log-Lik: -98257.296, Max-Change: 0.00046Iteration: 300, Log-Lik: -98257.296, Max-Change: 0.00023Iteration: 301, Log-Lik: -98257.296, Max-Change: 0.00018Iteration: 302, Log-Lik: -98257.296, Max-Change: 0.00028Iteration: 303, Log-Lik: -98257.296, Max-Change: 0.00013Iteration: 304, Log-Lik: -98257.296, Max-Change: 0.00052Iteration: 305, Log-Lik: -98257.296, Max-Change: 0.00026Iteration: 306, Log-Lik: -98257.295, Max-Change: 0.00041Iteration: 307, Log-Lik: -98257.295, Max-Change: 0.00033Iteration: 308, Log-Lik: -98257.295, Max-Change: 0.00051Iteration: 309, Log-Lik: -98257.295, Max-Change: 0.00025Iteration: 310, Log-Lik: -98257.295, Max-Change: 0.00020Iteration: 311, Log-Lik: -98257.295, Max-Change: 0.00031Iteration: 312, Log-Lik: -98257.294, Max-Change: 0.00015Iteration: 313, Log-Lik: -98257.294, Max-Change: 0.00012Iteration: 314, Log-Lik: -98257.294, Max-Change: 0.00019Iteration: 315, Log-Lik: -98257.294, Max-Change: 0.00045Iteration: 316, Log-Lik: -98257.294, Max-Change: 0.00023Iteration: 317, Log-Lik: -98257.294, Max-Change: 0.00035Iteration: 318, Log-Lik: -98257.293, Max-Change: 0.00018Iteration: 319, Log-Lik: -98257.293, Max-Change: 0.00014Iteration: 320, Log-Lik: -98257.293, Max-Change: 0.00022Iteration: 321, Log-Lik: -98257.293, Max-Change: 0.00010Iteration: 322, Log-Lik: -98257.293, Max-Change: 0.00041Iteration: 323, Log-Lik: -98257.293, Max-Change: 0.00020Iteration: 324, Log-Lik: -98257.293, Max-Change: 0.00032Iteration: 325, Log-Lik: -98257.292, Max-Change: 0.00024Iteration: 326, Log-Lik: -98257.292, Max-Change: 0.00038Iteration: 327, Log-Lik: -98257.292, Max-Change: 0.00019Iteration: 328, Log-Lik: -98257.292, Max-Change: 0.00015Iteration: 329, Log-Lik: -98257.292, Max-Change: 0.00024Iteration: 330, Log-Lik: -98257.292, Max-Change: 0.00011Iteration: 331, Log-Lik: -98257.292, Max-Change: 0.00044Iteration: 332, Log-Lik: -98257.292, Max-Change: 0.00022Iteration: 333, Log-Lik: -98257.291, Max-Change: 0.00034Iteration: 334, Log-Lik: -98257.291, Max-Change: 0.00026Iteration: 335, Log-Lik: -98257.291, Max-Change: 0.00041Iteration: 336, Log-Lik: -98257.291, Max-Change: 0.00020Iteration: 337, Log-Lik: -98257.291, Max-Change: 0.00016Iteration: 338, Log-Lik: -98257.291, Max-Change: 0.00026Iteration: 339, Log-Lik: -98257.290, Max-Change: 0.00012Iteration: 340, Log-Lik: -98257.290, Max-Change: 0.00009summary(md1)
Rotation: oblimin
Rotated factor loadings:
F1 F2 h2
A1a 0.2136 0.675001 0.709
A1b 0.8618 0.050595 0.808
A2a -0.0501 0.948504 0.834
A2b 0.1516 0.643813 0.578
A2c 0.1716 0.650217 0.613
A2d 0.2930 0.537495 0.602
A2e -0.0798 0.925373 0.756
A2f 0.4587 0.429095 0.679
A2g 0.4469 0.424347 0.654
A2h 0.5067 0.287450 0.550
A3a 0.9878 -0.092598 0.852
A3b 0.9639 -0.093251 0.808
A3c 0.9591 -0.061576 0.838
A3d 0.7647 -0.029614 0.553
A3e 0.7765 0.046705 0.658
A3f 0.7634 -0.011045 0.571
A3g 0.6387 0.015466 0.422
A3h 0.8838 -0.079138 0.686
A3i 0.6824 0.172572 0.666
A3j 0.8337 0.138625 0.881
A3k 0.8122 0.157150 0.869
A3l 0.7691 0.141221 0.768
A3m 0.9348 0.000632 0.875
Rotated SS loadings: 10.67 3.912
Factor correlations:
F1 F2
F1 1.000
F2 0.722 1(二)參數資訊
#估計檢別度a，難易度b
coef(md1)$A1a
a1 a2 d1 d2 d3 d4 d5 d6
par -2.214 -1.474 2.009 -1.266 -2.835 -3.43 -4.401 -5.849
$A1b
a1 a2 d1 d2 d3 d4 d5 d6
par -3.49 -0.134 3.339 -0.099 -1.757 -2.476 -3.875 -5.544
$A2a
a1 a2 d1 d2 d3 d4 d5 d6
par -2.65 -2.737 1.839 -1.736 -3.949 -4.572 -5.588 -7.359
$A2b
a1 a2 d1 d2 d3 d4 d5 d6
par -1.616 -1.167 0.64 -1.583 -2.705 -3.174 -3.965 -5.216
$A2c
a1 a2 d1 d2 d3 d4 d5 d6
par -1.756 -1.231 0.266 -2.128 -3.403 -4.17 -5.03 -6.105
$A2d
a1 a2 d1 d2 d3 d4 d5 d6
par -1.838 -1.003 1.426 -0.795 -2.009 -2.445 -3.272 -4.27
$A2e
a1 a2 d1 d2 d3 d4 d5 d6
par -2.028 -2.205 1.742 -0.875 -2.441 -3.263 -4.188 -5.508
$A2f
a1 a2 d1 d2 d3 d4 d5 d6
par -2.309 -0.891 2.668 0.522 -1.08 -1.855 -2.701 -3.732
$A2g
a1 a2 d1 d2 d3 d4 d5 d6
par -2.179 -0.848 3.271 1.304 0.109 -0.757 -1.608 -2.582
$A2h
a1 a2 d1 d2 d3 d4 d5 d6
par -1.812 -0.504 0.861 -0.757 -1.725 -3.26 -3.932 -4.883
$A3a
a1 a2 d1 d2 d3 d4 d5 d6
par -4.077 0.286 4.937 1.08 -1.07 -2.068 -3.366 -5.163
$A3b
a1 a2 d1 d2 d3 d4 d5 d6
par -3.483 0.252 5.438 1.973 -0.162 -1.022 -2.452 -3.942
$A3c
a1 a2 d1 d2 d3 d4 d5 d6
par -3.872 0.182 4.741 1.349 -0.616 -1.767 -3.003 -4.685
$A3d
a1 a2 d1 d2 d3 d4 d5 d6
par -1.892 0.053 2.851 0.722 -0.722 -1.613 -2.451 -3.467
$A3e
a1 a2 d1 d2 d3 d4 d5 d6
par -2.357 -0.093 3.512 1.213 0.012 -1.139 -2.106 -3.187
$A3f
a1 a2 d1 d2 d3 d4 d5 d6
par -1.962 0.021 1.948 -0.014 -1.232 -1.94 -2.808 -3.734
$A3g
a1 a2 d1 d2 d3 d4 d5 d6
par -1.456 -0.023 1.191 -0.503 -1.613 -2.127 -2.777 -3.548
$A3h
a1 a2 d1 d2 d3 d4 d5 d6
par -2.512 0.168 2.24 0.051 -1.372 -2.482 -3.402 -4.476
$A3i
a1 a2 d1 d2 d3 d4 d5 d6
par -2.375 -0.35 2.519 0.542 -0.902 -2.366 -3.166 -4.191
$A3j
a1 a2 d1 d2 d3 d4 d5 d6
par -4.612 -0.472 5.583 1.829 -0.927 -2.933 -4.703 -6.384
$A3k
a1 a2 d1 d2 d3 d4 d5 d6
par -4.347 -0.509 4.941 1.477 -0.954 -2.871 -4.419 -6.152
$A3l
a1 a2 d1 d2 d3 d4 d5 d6
par -3.08 -0.344 2.316 0.039 -1.486 -3.443 -4.26 -5.49
$A3m
a1 a2 d1 d2 d3 d4 d5 d6
par -4.498 0 4.161 0.993 -1.089 -3.109 -4.355 -5.995
$GroupPars
MEAN_1 MEAN_2 COV_11 COV_21 COV_22
par 0 0 1 0 1(三)能力參數 #估計能力參數
theta <- fscores(md1)
head(theta)| F1 | F2 |
|---|---|
| 0.6987 | -1.2708 |
| -3.3767 | -2.7996 |
| 2.1434 | 1.3790 |
| 1.9933 | 2.3286 |
| -0.6031 | -0.3177 |
| -2.2475 | -1.6727 |
# 繪製能力分佈
hist(theta[,1], main="Dimension 1 Ability Distribution", xlab="Ability")
hist(theta[,2], main="Dimension 2 Ability Distribution", xlab="Ability")
(四)繪製特徵曲線
# 設定繪圖區域分為3行1列
par(mfrow=c(3,1))
# 分別繪製特徵曲線，每次3個題目
plot(md1, type = "trace", which.items = 1:3, facet = TRUE)
plot(md1, type = "trace", which.items = 4:6, facet = TRUE)
plot(md1, type = "trace", which.items = 7:9, facet = TRUE)
plot(md1, type = "trace", which.items = 10:12, facet = TRUE)
plot(md1, type = "trace", which.items = 13:15, facet = TRUE)
plot(md1, type = "trace", which.items = 16:18, facet = TRUE)
plot(md1, type = "trace", which.items = 19:20, facet = TRUE)
#library(magick)
# 讀取圖片
#img <- image_read("C:/Users/user/Desktop/IRT/sustainability-14-05532-i001a.png")
# 顯示圖片
#print(img)(五) 適配度檢定
md.fit <- M2(md1)
md.fit| M2 | df | p | RMSEA | RMSEA_5 | RMSEA_95 | SRMSR | TLI | CFI | |
|---|---|---|---|---|---|---|---|---|---|
| stats | 1561 | 93 | 0 | 0.0701 | 0.067 | 0.0731 | 0.0462 | 0.9614 | 0.974 |
#RMSEA: 0.0701。通常，0.05以下被認為是良好的適配度，0.05到0.08之間是可以接受的適配度。
步驟7: ANOVA
#載入套件
library(lavaan)
#編制模型
model <-
'
# 第一個淺在因子(對職場環境與文化的認可)
LatentVar1 =~ A3m + A3a + A3c + A3j + A3b + A3k + A3h + A1b + A3l + A3f + A3i + A3e + A3d + A3g + A2h + A2g
# 第二個淺在因子(組職投入與滿意)
LatentVar2 =~ A2a+ A2e + A1a + A2b + A2c + A2d +A2f
'#萃取Factor Score ltnv2 ~ ltnv1
CFAfit <- cfa(model, estimator="MLR", data = dta)
factor_scores <- lavPredict(CFAfit)
#把滿意度分成低與高
dta$group <- ifelse(dta$A1a <= 3, "Low", "High")
dta$aov <- as.factor(dta$group)
combined_df <- cbind(factor_scores, dta)#跑ANOVA
anova1<- aov(LatentVar1~group, data =combined_df)
anova2<- aov(LatentVar2~group, data =combined_df)
summary(anova1) Df Sum Sq Mean Sq F value Pr(>F)
group 1 2593 2593 1213 <2e-16
Residuals 3214 6870 2 summary(anova2) Df Sum Sq Mean Sq F value Pr(>F)
group 1 2342 2342 2643 <2e-16
Residuals 3214 2847 1 #跑DIF
library(readxl)
data4 <- read_excel(path = "Job data.xlsx", sheet = 2)
A4 <- data4[[24]]data_DIF <- cbind(data, A4)
data2_DIF <- na.omit(data_DIF)
library(dplyr)
data3_DIF <- data2_DIF %>% filter(if_all(everything(), ~ . != 8))
head(data3_DIF)| A1a | A1b | A2a | A2b | A2c | A2d | A2e | A2f | A2g | A2h | A3a | A3b | A3c | A3d | A3e | A3f | A3g | A3h | A3i | A3j | A3k | A3l | A3m | A4 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 5 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 1 | 6 | 7 | 6 | 5 | 4 | 3 | 3 | 4 | 1 | 3 | 3 | 3 | 4 | 3 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 |
| 6 | 6 | 3 | 3 | 3 | 4 | 2 | 4 | 4 | 4 | 7 | 5 | 7 | 4 | 5 | 4 | 2 | 5 | 7 | 7 | 6 | 6 | 7 | 3 |
| 7 | 7 | 5 | 7 | 5 | 7 | 1 | 5 | 7 | 6 | 6 | 6 | 6 | 4 | 4 | 4 | 3 | 4 | 6 | 5 | 6 | 7 | 7 | 1 |
| 1 | 3 | 2 | 1 | 2 | 5 | 2 | 3 | 2 | 1 | 3 | 2 | 2 | 2 | 4 | 2 | 3 | 1 | 1 | 3 | 3 | 2 | 2 | 3 |
| 4 | 4 | 3 | 2 | 2 | 3 | 1 | 4 | 5 | 4 | 3 | 5 | 3 | 3 | 6 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 3 |
print(nrow(data3_DIF))[1] 3137library(lordif)Loading required package: rms
Attaching package: 'rms'The following object is masked from 'package:mlogit':
lrtestThe following object is masked from 'package:metafor':
vif
Attaching package: 'lordif'The following object is masked from 'package:nlme':
collapseThe following objects are masked from 'package:tidyr':
extract, separateThe following objects are masked from 'package:dplyr':
collapse, recodelibrary(mirt)
items <- data3_DIF[, c("A1a", "A1b", "A2a", "A2b", "A2c", "A2d", "A2e",
"A2f", "A2g", "A2h", "A3a", "A3b", "A3c", "A3d",
"A3e", "A3f", "A3g", "A3h", "A3i", "A3j", "A3k",
"A3l", "A3m")]
group_dif <- data3_DIF$A4
head(group_dif)[1] 3 3 3 1 3 3results_dif <- lordif(items, group_dif)Iteration: 1, Log-Lik: -106181.578, Max-Change: 2.35075Iteration: 2, Log-Lik: -101352.793, Max-Change: 1.77146Iteration: 3, Log-Lik: -99637.778, Max-Change: 0.65267Iteration: 4, Log-Lik: -99232.211, Max-Change: 0.26375Iteration: 5, Log-Lik: -99054.549, Max-Change: 0.19831Iteration: 6, Log-Lik: -98900.650, Max-Change: 0.16633Iteration: 7, Log-Lik: -98795.058, Max-Change: 0.17753Iteration: 8, Log-Lik: -98709.312, Max-Change: 0.33514Iteration: 9, Log-Lik: -98625.104, Max-Change: 0.31924Iteration: 10, Log-Lik: -98563.297, Max-Change: 0.28127Iteration: 11, Log-Lik: -98497.013, Max-Change: 0.33976Iteration: 12, Log-Lik: -98451.185, Max-Change: 0.23747Iteration: 13, Log-Lik: -98406.366, Max-Change: 0.26800Iteration: 14, Log-Lik: -98368.645, Max-Change: 0.25637Iteration: 15, Log-Lik: -98334.106, Max-Change: 0.41230Iteration: 16, Log-Lik: -98244.885, Max-Change: 0.30709Iteration: 17, Log-Lik: -98182.329, Max-Change: 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(mirt) | Iteration: 2, 7 items flagged for DIF (1,3,7,9,17,18,19)
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(mirt) | Iteration: 3, 8 items flagged for DIF (1,3,7,9,17,18,19,23)
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0.00017Iteration: 500, Log-Lik: -97725.791, Max-Change: 0.00026EM cycles terminated after 500 iterations. (mirt) | Iteration: 4, 8 items flagged for DIF (1,3,7,9,17,18,19,23)print(results_dif)Call:
lordif(resp.data = items, group = group_dif)
Number of DIF groups: 3
Number of items flagged for DIF: 8 of 23
Items flagged: 1, 3, 7, 9, 17, 18, 19, 23
Number of iterations for purification: 4 of 10
Detection criterion: Chisqr
Threshold: alpha = 0.01
item ncat chi12 chi13 chi23
1 1 7 0.0000 0.0000 0.2297
2 2 7 0.0154 0.0259 0.2569
3 3 7 0.0000 0.0001 0.4130
4 4 7 0.5128 0.4611 0.3205
5 5 7 0.4795 0.3266 0.2053
6 6 7 0.1139 0.1006 0.1809
7 7 7 0.0000 0.0000 0.0418
8 8 7 0.2853 0.3598 0.3968
9 9 7 0.0000 0.0000 0.3535
10 10 7 0.0228 0.0981 0.8764
11 11 7 0.1394 0.1321 0.2089
12 12 7 0.0872 0.1612 0.4319
13 13 7 0.5532 0.5249 0.3650
14 14 7 0.1501 0.0703 0.0879
15 15 7 0.0184 0.0485 0.4572
16 16 7 0.1799 0.1432 0.1796
17 17 7 0.4787 0.0000 0.0000
18 18 7 0.0003 0.0002 0.0642
19 19 7 0.0000 0.0000 0.1506
20 20 7 0.7255 0.5817 0.3301
21 21 7 0.8871 0.9575 0.8150
22 22 7 0.0895 0.1200 0.2877
23 23 7 0.0008 0.0014 0.1785plot(results_dif)