健康測量問卷實作課程
Ruei-Ning Su
2021-11-28
安裝Package {lavaan}
https://lavaan.ugent.be/tutorial/index.html
SEM和CFA
SEM和CFA都要看適配度指標fit index，包括：CFI、TLI、MSEA、SRMR，(HU & Bentler, 1998/1999)，有提供cut off point，CFI、TLI:>0.95，後面很多人抓0.9；MSEA和SRMR抓<0.08。這些適配度指標在SEM裡面都要一起看，其中一個表現不好，模型就視為不成立。 CFA是SEM的一個特殊的例子。
CFA
knitr::include_graphics("cfa.png")
https://lavaan.ugent.be/tutorial/cfa.html 雙箭頭表示相關，方框X1.X2…是真實資料，圓形是跑出來的概念(潛在變項) visual =~ x1 + x2 + x3 (CFA的語法) visual潛在變項是X1.X2.X3具合起來的
CFA與EFA
若是自己做的問卷，並不會知道甚麼是適合的模型，可以先做EPA，在依照EFA結果，做CFA模型。若是前人已經開發的問卷，可以依照前人的EFA來建構CFA模。
CFA實作
#依然用老師的資料GSdata做例子
#讀檔案存成dta
dta<-read.csv("D://GSdata_20211113.csv", head=T, fileEncoding = "UTF-8-BOM")
#看資料
summary(dta) Placeofliving Age Gender Weight
Min. :1.000 Min. :17.0 Min. :1.000 Min. : 40.00
1st Qu.:1.000 1st Qu.:20.0 1st Qu.:1.000 1st Qu.: 52.00
Median :1.000 Median :21.0 Median :2.000 Median : 58.00
Mean :1.241 Mean :21.6 Mean :1.612 Mean : 61.74
3rd Qu.:1.000 3rd Qu.:23.0 3rd Qu.:2.000 3rd Qu.: 70.00
Max. :3.000 Max. :30.0 Max. :2.000 Max. :135.00
NA's :105
Height BMI Major TFEQ1r
Min. :145.0 Min. :15.35 Min. :1.000 Min. :1.000
1st Qu.:159.0 1st Qu.:19.53 1st Qu.:1.000 1st Qu.:2.000
Median :165.0 Median :21.60 Median :2.000 Median :2.000
Mean :165.5 Mean :22.39 Mean :1.738 Mean :2.415
3rd Qu.:171.0 3rd Qu.:24.30 3rd Qu.:2.000 3rd Qu.:3.000
Max. :185.0 Max. :47.86 Max. :2.000 Max. :4.000
TFEQ2r TFEQ3r TFEQ4r TFEQ5r
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
Median :2.000 Median :2.000 Median :2.000 Median :2.000
Mean :2.228 Mean :2.372 Mean :2.258 Mean :2.378
3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
TFEQ6r TFEQ7r TFEQ8r TFEQ9r
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000
Median :2.000 Median :2.000 Median :2.000 Median :2.000
Mean :2.215 Mean :2.468 Mean :2.089 Mean :1.994
3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
TFEQ10r TFEQ11r TFEQ12r TFEQ13r
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000
Median :2.000 Median :2.000 Median :2.000 Median :2.000
Mean :2.203 Mean :2.274 Mean :1.914 Mean :2.031
3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:2.000
Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
TFEQ14 TFEQ15 TFEQ16 TFEQ17
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
Median :2.000 Median :2.000 Median :3.000 Median :2.000
Mean :2.258 Mean :2.292 Mean :2.637 Mean :2.012
3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.000
Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
TFEQ18c IPAQ0 IPAQ1 IPAQ2 IPAQ3
Min. :1.000 Min. :1.000 Min. :0.000 Min. : 0 Min. :0.000
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:0.000 1st Qu.: 0 1st Qu.:0.000
Median :2.000 Median :3.000 Median :1.000 Median : 15 Median :2.000
Mean :2.135 Mean :2.409 Mean :1.563 Mean : 35 Mean :1.991
3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.: 60 3rd Qu.:3.000
Max. :4.000 Max. :3.000 Max. :7.000 Max. :300 Max. :7.000
IPAQ4 IPAQ5 IPAQ6 IPAQ7
Min. : 0.00 Min. :0.000 Min. : 0.00 Min. : 0.00
1st Qu.: 0.00 1st Qu.:4.000 1st Qu.: 20.00 1st Qu.: 6.00
Median : 24.00 Median :6.000 Median : 30.00 Median : 8.00
Mean : 34.78 Mean :5.348 Mean : 61.74 Mean : 19.85
3rd Qu.: 50.00 3rd Qu.:7.000 3rd Qu.: 60.00 3rd Qu.: 12.00
Max. :300.00 Max. :7.000 Max. :2046.00 Max. :360.00
IPAQ7c IPAQtotalMET IPAQexerciselevel Attitude1a
Min. : 0.000 Min. : 0 Min. :1.000 Min. :2.000
1st Qu.: 5.000 1st Qu.: 560 1st Qu.:1.000 1st Qu.:4.000
Median : 8.000 Median : 1386 Median :2.000 Median :5.000
Mean : 8.138 Mean : 2008 Mean :2.022 Mean :5.117
3rd Qu.:10.000 3rd Qu.: 2613 3rd Qu.:3.000 3rd Qu.:6.000
Max. :24.000 Max. :17598 Max. :3.000 Max. :7.000
Attitude1b Attitude1c Attitude1d Attitude1e Attitude1f
Min. :3.000 Min. :1.0 Min. :3.000 Min. :2.000 Min. :1.000
1st Qu.:6.000 1st Qu.:6.0 1st Qu.:5.000 1st Qu.:6.000 1st Qu.:4.000
Median :7.000 Median :7.0 Median :6.000 Median :7.000 Median :5.000
Mean :6.354 Mean :6.4 Mean :6.083 Mean :6.298 Mean :4.818
3rd Qu.:7.000 3rd Qu.:7.0 3rd Qu.:7.000 3rd Qu.:7.000 3rd Qu.:6.000
Max. :7.000 Max. :7.0 Max. :7.000 Max. :7.000 Max. :7.000
Attitude1g Attitude1h Attitude2a Attitude2b
Min. :1.000 Min. :3.000 Min. :2.000 Min. :3.000
1st Qu.:4.000 1st Qu.:6.000 1st Qu.:5.000 1st Qu.:6.000
Median :5.000 Median :7.000 Median :6.000 Median :7.000
Mean :4.935 Mean :6.274 Mean :5.471 Mean :6.289
3rd Qu.:6.000 3rd Qu.:7.000 3rd Qu.:7.000 3rd Qu.:7.000
Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000
Attitude2c Attitude2d Attitude2e Attitude2f Attitude2g
Min. :3.000 Min. :3.00 Min. :4.000 Min. :1.000 Min. :1.000
1st Qu.:6.000 1st Qu.:5.00 1st Qu.:6.000 1st Qu.:4.000 1st Qu.:5.000
Median :7.000 Median :6.00 Median :7.000 Median :5.000 Median :6.000
Mean :6.363 Mean :6.12 Mean :6.292 Mean :5.298 Mean :5.557
3rd Qu.:7.000 3rd Qu.:7.00 3rd Qu.:7.000 3rd Qu.:7.000 3rd Qu.:7.000
Max. :7.000 Max. :7.00 Max. :7.000 Max. :7.000 Max. :7.000
Attitude2h Subjectivenorm1 Subjectivenorm2 Subjectivenorm3
Min. :3.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:6.000 1st Qu.:3.000 1st Qu.:4.000 1st Qu.:2.000
Median :7.000 Median :5.000 Median :5.000 Median :4.000
Mean :6.302 Mean :4.477 Mean :4.603 Mean :3.751
3rd Qu.:7.000 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:5.000
Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000
Subjectivenorm4 Subjectivenorm5 Subjectivenorm6 PBC1
Min. :1.000 Min. :1.0 Min. :1.000 Min. :1.000
1st Qu.:2.000 1st Qu.:2.0 1st Qu.:3.000 1st Qu.:4.000
Median :3.000 Median :4.0 Median :4.000 Median :5.000
Mean :3.477 Mean :3.8 Mean :4.234 Mean :4.868
3rd Qu.:5.000 3rd Qu.:5.0 3rd Qu.:6.000 3rd Qu.:6.000
Max. :7.000 Max. :7.0 Max. :7.000 Max. :7.000
PBC2 PBC3 PBC4 PBC5
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:5.000 1st Qu.:3.000 1st Qu.:4.000 1st Qu.:4.000
Median :6.000 Median :4.000 Median :5.000 Median :5.000
Mean :5.825 Mean :3.945 Mean :4.686 Mean :4.935
3rd Qu.:7.000 3rd Qu.:5.000 3rd Qu.:6.000 3rd Qu.:6.000
Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000
PBC6 PBC7 PBC8 PBC9
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
Median :5.000 Median :5.000 Median :4.000 Median :4.000
Mean :4.582 Mean :4.655 Mean :4.188 Mean :4.385
3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:5.000 3rd Qu.:6.000
Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000
PBC10 Behavioralintention1 Behavioralintention2 Behavioralintention3
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:3.000 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:4.000
Median :5.000 Median :5.000 Median :5.000 Median :5.000
Mean :4.606 Mean :4.495 Mean :4.714 Mean :4.726
3rd Qu.:6.000 3rd Qu.:5.000 3rd Qu.:6.000 3rd Qu.:6.000
Max. :7.000 Max. :7.000 Max. :7.000 Max. :7.000
Behavioralintention4 Behavioralintention5 Behavioralintention6 WBIS1
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:3.000 1st Qu.:4.000 1st Qu.:4.000 1st Qu.:3.000
Median :5.000 Median :5.000 Median :5.000 Median :4.000
Mean :4.631 Mean :4.757 Mean :4.809 Mean :3.443
3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:6.000 3rd Qu.:4.000
Max. :7.000 Max. :7.000 Max. :7.000 Max. :5.000
WBIS2 WBIS3 WBIS4 WBIS5
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
Median :3.000 Median :3.000 Median :4.000 Median :3.000
Mean :3.009 Mean :3.163 Mean :3.372 Mean :2.858
3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
WBIS6 WBIS7 WBIS8 WBIS9
Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000
Median :3.000 Median :2.000 Median :2.000 Median :3.000
Mean :2.982 Mean :1.895 Mean :1.997 Mean :3.262
3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:4.000
Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
WBIS10 WBIS11 WSSQ1 WSSQ2
Min. :1.000 Min. :1.000 Min. :0.000 Min. :0.000
1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:1.000
Median :2.000 Median :2.000 Median :2.000 Median :3.000
Mean :2.182 Mean :2.169 Mean :1.803 Mean :2.557
3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:4.000
Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
WSSQ3 WSSQ4 WSSQ5 WSSQ6
Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
1st Qu.:1.000 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:1.000
Median :2.000 Median :1.000 Median :2.000 Median :3.000
Mean :2.212 Mean :1.498 Mean :2.068 Mean :2.437
3rd Qu.:4.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:4.000
Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
WSSQ7 WSSQ8 WSSQ9 WSSQ10
Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.000
Median :3.000 Median :1.000 Median :1.000 Median :2.000
Mean :2.628 Mean :1.658 Mean :1.542 Mean :1.914
3rd Qu.:4.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:3.000
Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
WSSQ11 WSSQ12 Weight_group WBIS1_r WBIS9_r
Min. :0.000 Min. :0.000 Min. :1.00 Min. :1.000 Min. :1.000
1st Qu.:0.000 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:2.000 1st Qu.:2.000
Median :1.000 Median :1.000 Median :1.00 Median :2.000 Median :3.000
Mean :1.529 Mean :1.535 Mean :1.32 Mean :2.557 Mean :2.738
3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:2.00 3rd Qu.:3.000 3rd Qu.:4.000
Max. :5.000 Max. :5.000 Max. :2.00 Max. :5.000 Max. :5.000
WBIS_Total_Score WSSQ_Q1to6_Total WSSQ_Q7to12_Total WSSQ_Total_Score
Min. :11.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
1st Qu.:22.00 1st Qu.: 7.00 1st Qu.: 6.00 1st Qu.:12.00
Median :30.00 Median :14.00 Median :12.00 Median :25.00
Mean :28.92 Mean :12.58 Mean :10.81 Mean :23.38
3rd Qu.:36.00 3rd Qu.:18.00 3rd Qu.:16.00 3rd Qu.:33.00
Max. :55.00 Max. :28.00 Max. :28.00 Max. :53.00
TFEQ_Total Attitude_Eat Attitude_PA SubNorm_Eat
Min. :12.0 Min. : 47.92 Min. : 41.67 Min. : 0.00
1st Qu.:22.0 1st Qu.: 70.83 1st Qu.: 72.92 1st Qu.: 38.89
Median :26.0 Median : 81.25 Median : 83.33 Median : 55.56
Mean :26.7 Mean : 79.75 Mean : 82.69 Mean : 54.62
3rd Qu.:31.0 3rd Qu.: 89.58 3rd Qu.: 95.83 3rd Qu.: 72.22
Max. :45.0 Max. :100.00 Max. :100.00 Max. :100.00
SubNorm_PA PBC_Eat PBC_PA Int_Eat
Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
1st Qu.: 27.78 1st Qu.: 58.33 1st Qu.: 37.50 1st Qu.: 50.00
Median : 50.00 Median : 66.67 Median : 58.33 Median : 66.67
Mean : 47.28 Mean : 67.97 Mean : 59.28 Mean : 60.75
3rd Qu.: 66.67 3rd Qu.: 79.17 3rd Qu.: 83.33 3rd Qu.: 77.78
Max. :100.00 Max. :100.00 Max. :100.00 Max. :100.00
Int_PA IPAQtotalMET2
Min. : 0.00 Min. : 0.00
1st Qu.: 50.00 1st Qu.: 5.60
Median : 66.67 Median : 13.86
Mean : 62.21 Mean : 20.08
3rd Qu.: 83.33 3rd Qu.: 26.13
Max. :100.00 Max. :175.98
#運用package lavaan
library(lavaan)
#CFA語法
#先依照變項建構因子，真實資料可能會先做EFA，決定變項屬於哪個因子
#這邊假設TFEQ1~TFEQ6屬於Factor1、TFEQ7~TFEQ12屬於Factor2、TFEQ13~TFEQ18屬於Factor3
#factor1=~(來自於)變項1+變項2+...
#存成TFEQ.model
TFEQ.model <-
'
factor1 =~ TFEQ1r+TFEQ2r+TFEQ3r+TFEQ4r+TFEQ5r+TFEQ6r
factor2 =~ TFEQ7r+TFEQ8r+TFEQ9r+TFEQ10r+TFEQ11r+TFEQ12r
factor3 =~ TFEQ13r+TFEQ14+TFEQ15+TFEQ16+TFEQ17+TFEQ18c
'
#用cfa做TFEQ.model的適配度檢定，data來自於dta
fit<-cfa(TFEQ.model, data=dta)
#fit.measures=T，常見的適配度資料
#standardized=T，係數標準化。
#經標準化後，factor loading:0-1，兩個變項的相關性是標準化係數
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 41 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 39
Number of observations 325
Model Test User Model:
Test statistic 916.449
Degrees of freedom 132
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2161.280
Degrees of freedom 153
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.609
Tucker-Lewis Index (TLI) 0.547
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6559.276
Loglikelihood unrestricted model (H1) -6101.052
Akaike (AIC) 13196.553
Bayesian (BIC) 13344.122
Sample-size adjusted Bayesian (BIC) 13220.417
Root Mean Square Error of Approximation:
RMSEA 0.135
90 Percent confidence interval - lower 0.127
90 Percent confidence interval - upper 0.144
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.133
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
TFEQ1r 1.000 0.493 0.587
TFEQ2r 0.131 0.105 1.242 0.214 0.064 0.076
TFEQ3r 1.170 0.134 8.722 0.000 0.576 0.633
TFEQ4r 1.294 0.135 9.551 0.000 0.637 0.729
TFEQ5r 1.063 0.121 8.807 0.000 0.524 0.642
TFEQ6r 1.142 0.132 8.678 0.000 0.563 0.628
factor2 =~
TFEQ7r 1.000 0.486 0.627
TFEQ8r 1.446 0.134 10.799 0.000 0.702 0.756
TFEQ9r 1.472 0.131 11.271 0.000 0.715 0.809
TFEQ10r 1.138 0.127 8.980 0.000 0.553 0.593
TFEQ11r 0.048 0.103 0.463 0.643 0.023 0.028
TFEQ12r 0.003 0.096 0.030 0.976 0.001 0.002
factor3 =~
TFEQ13r 1.000 0.680 0.791
TFEQ14 0.646 0.073 8.837 0.000 0.439 0.583
TFEQ15 -0.287 0.071 -4.046 0.000 -0.195 -0.255
TFEQ16 -0.307 0.077 -4.014 0.000 -0.209 -0.253
TFEQ17 0.311 0.067 4.674 0.000 0.211 0.296
TFEQ18c -0.167 0.062 -2.681 0.007 -0.114 -0.168
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 ~~
factor2 0.200 0.029 6.874 0.000 0.834 0.834
factor3 0.224 0.034 6.649 0.000 0.670 0.670
factor2 ~~
factor3 0.263 0.035 7.603 0.000 0.798 0.798
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.TFEQ1r 0.462 0.040 11.414 0.000 0.462 0.656
.TFEQ2r 0.719 0.056 12.733 0.000 0.719 0.994
.TFEQ3r 0.498 0.045 11.048 0.000 0.498 0.600
.TFEQ4r 0.358 0.036 9.825 0.000 0.358 0.468
.TFEQ5r 0.392 0.036 10.963 0.000 0.392 0.588
.TFEQ6r 0.486 0.044 11.090 0.000 0.486 0.606
.TFEQ7r 0.364 0.032 11.436 0.000 0.364 0.606
.TFEQ8r 0.369 0.037 9.987 0.000 0.369 0.428
.TFEQ9r 0.270 0.031 8.794 0.000 0.270 0.346
.TFEQ10r 0.564 0.048 11.656 0.000 0.564 0.648
.TFEQ11r 0.709 0.056 12.746 0.000 0.709 0.999
.TFEQ12r 0.614 0.048 12.748 0.000 0.614 1.000
.TFEQ13r 0.276 0.044 6.222 0.000 0.276 0.374
.TFEQ14 0.374 0.035 10.827 0.000 0.374 0.660
.TFEQ15 0.544 0.044 12.502 0.000 0.544 0.935
.TFEQ16 0.637 0.051 12.506 0.000 0.637 0.936
.TFEQ17 0.466 0.038 12.409 0.000 0.466 0.913
.TFEQ18c 0.443 0.035 12.645 0.000 0.443 0.972
factor1 0.243 0.045 5.338 0.000 1.000 1.000
factor2 0.236 0.040 5.907 0.000 1.000 1.000
factor3 0.462 0.066 6.982 0.000 1.000 1.000CFA結果判讀
Step1:先看卡方值和P值 Test statistic：916.449(卡方值)，Degrees of freedom：132，P-value (Chi-square)：0.000(顯著)
實際上希望CFA卡方值不顯著，但因為大樣本通常都容易顯著，所以也沒關係:D
Step2:看適配度，cfa default為最大概似法(ML)
Comparative Fit Index (CFI):0.609，並沒有>0.9→模型不好
Tucker-Lewis Index (TLI): 0.547，並沒有>0.9→模型不好
RMSEA:0.135，並沒有<0.08→模型不好
SRMR:0.133，並沒有<0.08→模型不好
Step3:看factor相關
knitr::include_graphics("cfa factor loading.png")
factor1和factor2、factor3有相關
factor2和factor3有相關
若模型成立，factor1、factor2、factor3之間會有雙向箭頭
Step4:思考模型為什麼不好
看factor中，各變項的factor loading，Std.all要>0.5
knitr::include_graphics("cfa factor loading.png")
factor1:TFEQ2r factor loading=0.076 (沒有>0.5，建議刪除此項)
factor2:TFEQ11r:0.028和TFEQ12r:0.002建議刪除
factor3:TFEQ15、TFEQ16、TFEQ18c，都是負值，檢查是否為反向題資料要倒轉，否則刪除。TFEQ17:0.296建議刪除
CFA實作
強迫factor間不相關
library(lavaan)
TFEQ.model <-
'
factor1 =~ TFEQ1r+TFEQ2r+TFEQ3r+ TFEQ4r+ TFEQ5r+TFEQ6r
factor2 =~ TFEQ7r+TFEQ8r+TFEQ9r+ TFEQ10r+ TFEQ11r+TFEQ12r
factor3 =~ TFEQ13r+TFEQ14+TFEQ15+ TFEQ16+ TFEQ17+TFEQ18c
#告訴lavaan,factor1, factor2相關性=0(強迫設為不相關的意思)
factor1~~0*factor2
#告訴lavaan,factor1, factor3相關性=0(強迫設為不相關的意思)
factor1~~0*factor3
#告訴lavaan,factor2, factor3相關性=0(強迫設為不相關的意思)
factor2~~0*factor3
'
fit<-cfa(TFEQ.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 37 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 325
Model Test User Model:
Test statistic 1247.197
Degrees of freedom 135
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2161.280
Degrees of freedom 153
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.446
Tucker-Lewis Index (TLI) 0.372
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -6724.650
Loglikelihood unrestricted model (H1) -6101.052
Akaike (AIC) 13521.300
Bayesian (BIC) 13657.518
Sample-size adjusted Bayesian (BIC) 13543.329
Root Mean Square Error of Approximation:
RMSEA 0.159
90 Percent confidence interval - lower 0.151
90 Percent confidence interval - upper 0.167
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.227
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
TFEQ1r 1.000 0.447 0.532
TFEQ2r 0.227 0.120 1.881 0.060 0.101 0.119
TFEQ3r 1.373 0.173 7.922 0.000 0.613 0.673
TFEQ4r 1.411 0.173 8.164 0.000 0.630 0.721
TFEQ5r 1.136 0.149 7.606 0.000 0.508 0.622
TFEQ6r 1.325 0.169 7.853 0.000 0.592 0.661
factor2 =~
TFEQ7r 1.000 0.431 0.556
TFEQ8r 1.677 0.175 9.566 0.000 0.722 0.778
TFEQ9r 1.823 0.191 9.549 0.000 0.785 0.888
TFEQ10r 1.096 0.150 7.298 0.000 0.472 0.506
TFEQ11r 0.062 0.117 0.527 0.598 0.027 0.032
TFEQ12r 0.049 0.109 0.450 0.652 0.021 0.027
factor3 =~
TFEQ13r 1.000 0.660 0.769
TFEQ14 0.672 0.123 5.476 0.000 0.444 0.589
TFEQ15 -0.324 0.085 -3.794 0.000 -0.214 -0.281
TFEQ16 -0.351 0.092 -3.797 0.000 -0.232 -0.281
TFEQ17 0.260 0.078 3.340 0.001 0.172 0.240
TFEQ18c -0.251 0.074 -3.404 0.001 -0.166 -0.246
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 ~~
factor2 0.000 0.000 0.000
factor3 0.000 0.000 0.000
factor2 ~~
factor3 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.TFEQ1r 0.505 0.044 11.372 0.000 0.505 0.717
.TFEQ2r 0.713 0.056 12.698 0.000 0.713 0.986
.TFEQ3r 0.455 0.046 9.817 0.000 0.455 0.547
.TFEQ4r 0.367 0.041 8.905 0.000 0.367 0.480
.TFEQ5r 0.408 0.039 10.527 0.000 0.408 0.613
.TFEQ6r 0.452 0.045 10.005 0.000 0.452 0.563
.TFEQ7r 0.414 0.035 11.693 0.000 0.414 0.690
.TFEQ8r 0.341 0.043 7.989 0.000 0.341 0.395
.TFEQ9r 0.165 0.041 4.040 0.000 0.165 0.211
.TFEQ10r 0.647 0.054 11.958 0.000 0.647 0.744
.TFEQ11r 0.709 0.056 12.745 0.000 0.709 0.999
.TFEQ12r 0.614 0.048 12.746 0.000 0.614 0.999
.TFEQ13r 0.302 0.077 3.901 0.000 0.302 0.409
.TFEQ14 0.370 0.045 8.257 0.000 0.370 0.653
.TFEQ15 0.536 0.044 12.234 0.000 0.536 0.921
.TFEQ16 0.627 0.051 12.233 0.000 0.627 0.921
.TFEQ17 0.481 0.039 12.386 0.000 0.481 0.942
.TFEQ18c 0.428 0.035 12.368 0.000 0.428 0.940
factor1 0.200 0.043 4.593 0.000 1.000 1.000
factor2 0.186 0.037 5.039 0.000 1.000 1.000
factor3 0.436 0.091 4.812 0.000 1.000 1.000結果判讀
強迫factor間設為不相關模型應該會更糟，因為破壞了原來的結構
knitr::include_graphics("0_covariance.png")
果不其然CFA:0.446、TLI:0.372，比前面的模型更糟糕
CFA再試一次
這次選WSSQ，WSSQ1WSSQ6設為factor1、WSSQ7WSSQ12設為factor2
WSSQ.model <-
'
factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6
factor2 =~ WSSQ7+WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
'
fit<-cfa(WSSQ.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 36 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 25
Number of observations 325
Model Test User Model:
Test statistic 273.552
Degrees of freedom 53
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2668.151
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.915
Tucker-Lewis Index (TLI) 0.894
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5683.696
Loglikelihood unrestricted model (H1) -5546.920
Akaike (AIC) 11417.391
Bayesian (BIC) 11511.987
Sample-size adjusted Bayesian (BIC) 11432.689
Root Mean Square Error of Approximation:
RMSEA 0.113
90 Percent confidence interval - lower 0.100
90 Percent confidence interval - upper 0.127
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.056
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.992 0.664
WSSQ2 1.336 0.102 13.035 0.000 1.326 0.828
WSSQ3 1.281 0.095 13.467 0.000 1.271 0.863
WSSQ4 1.085 0.089 12.225 0.000 1.077 0.767
WSSQ5 0.942 0.090 10.427 0.000 0.935 0.638
WSSQ6 1.132 0.094 12.093 0.000 1.123 0.757
factor2 =~
WSSQ7 1.000 0.853 0.587
WSSQ8 1.212 0.109 11.112 0.000 1.034 0.816
WSSQ9 1.131 0.104 10.872 0.000 0.964 0.788
WSSQ10 1.444 0.134 10.810 0.000 1.231 0.781
WSSQ11 1.281 0.114 11.196 0.000 1.092 0.827
WSSQ12 1.224 0.109 11.245 0.000 1.044 0.833
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 ~~
factor2 0.738 0.099 7.459 0.000 0.873 0.873
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.247 0.105 11.875 0.000 1.247 0.559
.WSSQ2 0.803 0.078 10.294 0.000 0.803 0.314
.WSSQ3 0.552 0.058 9.460 0.000 0.552 0.255
.WSSQ4 0.814 0.073 11.161 0.000 0.814 0.412
.WSSQ5 1.270 0.106 11.988 0.000 1.270 0.593
.WSSQ6 0.941 0.084 11.256 0.000 0.941 0.427
.WSSQ7 1.384 0.113 12.203 0.000 1.384 0.656
.WSSQ8 0.535 0.050 10.654 0.000 0.535 0.334
.WSSQ9 0.568 0.051 11.034 0.000 0.568 0.379
.WSSQ10 0.970 0.087 11.114 0.000 0.970 0.390
.WSSQ11 0.552 0.053 10.483 0.000 0.552 0.317
.WSSQ12 0.482 0.046 10.373 0.000 0.482 0.307
factor1 0.985 0.150 6.558 0.000 1.000 1.000
factor2 0.727 0.129 5.624 0.000 1.000 1.000結果判讀
Comparative Fit Index (CFI) 0.915(>0.9，好!)
Tucker-Lewis Index (TLI) 0.894(快要>0.9，有機會調整)
RMSEA 0.113(快要<0.08，有機會調整)
SRMR 0.056(<0.08，好!)
調整模型
運用指令modindices，表示: Modification Indices for Models
modindices(fit) #請幫我檢查如何幫我把fit適配度變好 lhs op rhs mi epc sepc.lv sepc.all sepc.nox
28 factor1 =~ WSSQ7 60.931 1.452 1.441 0.992 0.992
29 factor1 =~ WSSQ8 0.423 0.085 0.085 0.067 0.067
30 factor1 =~ WSSQ9 0.753 -0.113 -0.113 -0.092 -0.092
31 factor1 =~ WSSQ10 1.358 0.198 0.196 0.124 0.124
32 factor1 =~ WSSQ11 8.368 -0.391 -0.388 -0.294 -0.294
33 factor1 =~ WSSQ12 5.734 -0.305 -0.303 -0.242 -0.242
34 factor2 =~ WSSQ1 0.087 0.062 0.053 0.035 0.035
35 factor2 =~ WSSQ2 14.230 -0.737 -0.629 -0.393 -0.393
36 factor2 =~ WSSQ3 0.295 0.096 0.081 0.055 0.055
37 factor2 =~ WSSQ4 2.819 0.304 0.260 0.185 0.185
38 factor2 =~ WSSQ5 2.598 0.340 0.290 0.198 0.198
39 factor2 =~ WSSQ6 0.297 0.105 0.090 0.061 0.061
40 WSSQ1 ~~ WSSQ2 7.669 0.182 0.182 0.182 0.182
41 WSSQ1 ~~ WSSQ3 3.472 -0.107 -0.107 -0.129 -0.129
42 WSSQ1 ~~ WSSQ4 4.622 0.135 0.135 0.134 0.134
43 WSSQ1 ~~ WSSQ5 9.820 -0.236 -0.236 -0.187 -0.187
44 WSSQ1 ~~ WSSQ6 1.223 -0.074 -0.074 -0.069 -0.069
45 WSSQ1 ~~ WSSQ7 2.957 -0.132 -0.132 -0.101 -0.101
46 WSSQ1 ~~ WSSQ8 0.919 -0.049 -0.049 -0.060 -0.060
47 WSSQ1 ~~ WSSQ9 3.068 0.090 0.090 0.107 0.107
48 WSSQ1 ~~ WSSQ10 0.710 -0.057 -0.057 -0.052 -0.052
49 WSSQ1 ~~ WSSQ11 0.056 0.012 0.012 0.015 0.015
50 WSSQ1 ~~ WSSQ12 1.177 0.053 0.053 0.068 0.068
51 WSSQ2 ~~ WSSQ3 28.094 0.290 0.290 0.435 0.435
52 WSSQ2 ~~ WSSQ4 6.344 -0.142 -0.142 -0.176 -0.176
53 WSSQ2 ~~ WSSQ5 12.556 -0.233 -0.233 -0.231 -0.231
54 WSSQ2 ~~ WSSQ6 0.762 0.053 0.053 0.060 0.060
55 WSSQ2 ~~ WSSQ7 6.696 0.170 0.170 0.162 0.162
56 WSSQ2 ~~ WSSQ8 2.227 -0.065 -0.065 -0.100 -0.100
57 WSSQ2 ~~ WSSQ9 10.368 -0.143 -0.143 -0.212 -0.212
58 WSSQ2 ~~ WSSQ10 6.422 0.146 0.146 0.166 0.166
59 WSSQ2 ~~ WSSQ11 0.338 -0.026 -0.026 -0.039 -0.039
60 WSSQ2 ~~ WSSQ12 6.512 -0.108 -0.108 -0.173 -0.173
61 WSSQ3 ~~ WSSQ4 4.089 -0.101 -0.101 -0.151 -0.151
62 WSSQ3 ~~ WSSQ5 0.217 -0.027 -0.027 -0.032 -0.032
63 WSSQ3 ~~ WSSQ6 7.732 -0.148 -0.148 -0.205 -0.205
64 WSSQ3 ~~ WSSQ7 18.031 0.241 0.241 0.275 0.275
65 WSSQ3 ~~ WSSQ8 0.913 0.036 0.036 0.066 0.066
66 WSSQ3 ~~ WSSQ9 0.923 0.037 0.037 0.066 0.066
67 WSSQ3 ~~ WSSQ10 1.656 -0.064 -0.064 -0.088 -0.088
68 WSSQ3 ~~ WSSQ11 1.680 -0.050 -0.050 -0.091 -0.091
69 WSSQ3 ~~ WSSQ12 1.146 -0.039 -0.039 -0.076 -0.076
70 WSSQ4 ~~ WSSQ5 4.307 0.131 0.131 0.129 0.129
71 WSSQ4 ~~ WSSQ6 0.094 0.017 0.017 0.020 0.020
72 WSSQ4 ~~ WSSQ7 4.562 -0.136 -0.136 -0.129 -0.129
73 WSSQ4 ~~ WSSQ8 0.548 0.031 0.031 0.048 0.048
74 WSSQ4 ~~ WSSQ9 1.527 0.053 0.053 0.078 0.078
75 WSSQ4 ~~ WSSQ10 0.623 -0.044 -0.044 -0.050 -0.050
76 WSSQ4 ~~ WSSQ11 3.712 0.084 0.084 0.125 0.125
77 WSSQ4 ~~ WSSQ12 0.011 -0.004 -0.004 -0.007 -0.007
78 WSSQ5 ~~ WSSQ6 10.805 0.222 0.222 0.203 0.203
79 WSSQ5 ~~ WSSQ7 6.452 0.196 0.196 0.148 0.148
80 WSSQ5 ~~ WSSQ8 5.538 0.120 0.120 0.146 0.146
81 WSSQ5 ~~ WSSQ9 0.005 -0.004 -0.004 -0.004 -0.004
82 WSSQ5 ~~ WSSQ10 3.214 -0.121 -0.121 -0.109 -0.109
83 WSSQ5 ~~ WSSQ11 0.599 -0.041 -0.041 -0.048 -0.048
84 WSSQ5 ~~ WSSQ12 0.326 0.028 0.028 0.036 0.036
85 WSSQ6 ~~ WSSQ7 12.328 0.240 0.240 0.211 0.211
86 WSSQ6 ~~ WSSQ8 0.135 -0.017 -0.017 -0.024 -0.024
87 WSSQ6 ~~ WSSQ9 1.237 -0.051 -0.051 -0.070 -0.070
88 WSSQ6 ~~ WSSQ10 8.982 0.180 0.180 0.188 0.188
89 WSSQ6 ~~ WSSQ11 8.235 -0.133 -0.133 -0.185 -0.185
90 WSSQ6 ~~ WSSQ12 0.101 0.014 0.014 0.021 0.021
91 WSSQ7 ~~ WSSQ8 1.413 0.064 0.064 0.075 0.075
92 WSSQ7 ~~ WSSQ9 0.002 -0.003 -0.003 -0.003 -0.003
93 WSSQ7 ~~ WSSQ10 0.438 -0.047 -0.047 -0.041 -0.041
94 WSSQ7 ~~ WSSQ11 27.676 -0.292 -0.292 -0.334 -0.334
95 WSSQ7 ~~ WSSQ12 9.531 -0.161 -0.161 -0.197 -0.197
96 WSSQ8 ~~ WSSQ9 6.309 0.095 0.095 0.172 0.172
97 WSSQ8 ~~ WSSQ10 23.333 -0.237 -0.237 -0.329 -0.329
98 WSSQ8 ~~ WSSQ11 1.406 0.046 0.046 0.085 0.085
99 WSSQ8 ~~ WSSQ12 0.217 -0.017 -0.017 -0.034 -0.034
100 WSSQ9 ~~ WSSQ10 4.453 -0.104 -0.104 -0.140 -0.140
101 WSSQ9 ~~ WSSQ11 0.083 -0.011 -0.011 -0.020 -0.020
102 WSSQ9 ~~ WSSQ12 0.378 0.023 0.023 0.043 0.043
103 WSSQ10 ~~ WSSQ11 11.556 0.172 0.172 0.235 0.235
104 WSSQ10 ~~ WSSQ12 5.655 0.113 0.113 0.166 0.166
105 WSSQ11 ~~ WSSQ12 3.688 0.073 0.073 0.141 0.141knitr::include_graphics("mi1.png")
mi越大多做這件事，就會進步越多(mi做了卡方值下降多少)，通常mi值>3.84，就會降卡方值(因為卡方值>3.84就會顯著)
WSSQ7訂在factor1，卡方會下降60.931
WSSQ2~~WSSQ3做一個相關，卡方值會再下降28.094
優先處理大的→60.931
mi一次處理一條，然後再看一次modindices(fit)，一旦動了一個部分，其他數值都會變，modindices應該重做
WSSQ.model <-
' factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6+WSSQ7
factor2 =~ WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
'
fit<-cfa(WSSQ.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 32 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 25
Number of observations 325
Model Test User Model:
Test statistic 214.051
Degrees of freedom 53
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2668.151
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.938
Tucker-Lewis Index (TLI) 0.923
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5653.946
Loglikelihood unrestricted model (H1) -5546.920
Akaike (AIC) 11357.891
Bayesian (BIC) 11452.487
Sample-size adjusted Bayesian (BIC) 11373.189
Root Mean Square Error of Approximation:
RMSEA 0.097
90 Percent confidence interval - lower 0.083
90 Percent confidence interval - upper 0.110
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.043
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.977 0.654
WSSQ2 1.362 0.106 12.869 0.000 1.331 0.832
WSSQ3 1.312 0.098 13.331 0.000 1.283 0.871
WSSQ4 1.085 0.091 11.908 0.000 1.061 0.755
WSSQ5 0.964 0.093 10.398 0.000 0.942 0.643
WSSQ6 1.158 0.096 12.006 0.000 1.132 0.763
WSSQ7 1.016 0.093 10.951 0.000 0.993 0.683
factor2 =~
WSSQ8 1.000 1.030 0.813
WSSQ9 0.937 0.058 16.085 0.000 0.965 0.788
WSSQ10 1.199 0.075 15.943 0.000 1.235 0.783
WSSQ11 1.078 0.061 17.578 0.000 1.110 0.840
WSSQ12 1.025 0.058 17.627 0.000 1.055 0.842
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 ~~
factor2 0.847 0.100 8.475 0.000 0.841 0.841
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.277 0.107 11.964 0.000 1.277 0.572
.WSSQ2 0.789 0.076 10.365 0.000 0.789 0.308
.WSSQ3 0.522 0.056 9.405 0.000 0.522 0.241
.WSSQ4 0.848 0.075 11.350 0.000 0.848 0.430
.WSSQ5 1.256 0.105 12.008 0.000 1.256 0.586
.WSSQ6 0.921 0.082 11.282 0.000 0.921 0.418
.WSSQ7 1.125 0.095 11.829 0.000 1.125 0.533
.WSSQ8 0.543 0.051 10.606 0.000 0.543 0.338
.WSSQ9 0.567 0.052 10.953 0.000 0.567 0.378
.WSSQ10 0.960 0.087 11.013 0.000 0.960 0.386
.WSSQ11 0.513 0.051 10.110 0.000 0.513 0.294
.WSSQ12 0.458 0.045 10.074 0.000 0.458 0.291
factor1 0.955 0.148 6.444 0.000 1.000 1.000
factor2 1.061 0.122 8.715 0.000 1.000 1.000modindices(fit) #請幫我檢查如何幫我把fit適配度變好 lhs op rhs mi epc sepc.lv sepc.all sepc.nox
28 factor1 =~ WSSQ8 5.611 0.269 0.263 0.207 0.207
29 factor1 =~ WSSQ9 0.249 0.056 0.055 0.045 0.045
30 factor1 =~ WSSQ10 4.099 0.296 0.289 0.183 0.183
31 factor1 =~ WSSQ11 8.038 -0.326 -0.319 -0.241 -0.241
32 factor1 =~ WSSQ12 2.577 -0.175 -0.171 -0.136 -0.136
33 factor2 =~ WSSQ1 1.563 0.186 0.192 0.128 0.128
34 factor2 =~ WSSQ2 9.742 -0.412 -0.425 -0.265 -0.265
35 factor2 =~ WSSQ3 0.059 0.028 0.029 0.020 0.020
36 factor2 =~ WSSQ4 7.751 0.353 0.363 0.259 0.259
37 factor2 =~ WSSQ5 1.667 0.190 0.196 0.134 0.134
38 factor2 =~ WSSQ6 0.070 0.035 0.036 0.024 0.024
39 factor2 =~ WSSQ7 3.548 -0.266 -0.274 -0.188 -0.188
40 WSSQ1 ~~ WSSQ2 9.194 0.198 0.198 0.197 0.197
41 WSSQ1 ~~ WSSQ3 2.825 -0.095 -0.095 -0.116 -0.116
42 WSSQ1 ~~ WSSQ4 7.042 0.170 0.170 0.163 0.163
43 WSSQ1 ~~ WSSQ5 8.994 -0.225 -0.225 -0.178 -0.178
44 WSSQ1 ~~ WSSQ6 0.902 -0.064 -0.064 -0.059 -0.059
45 WSSQ1 ~~ WSSQ7 7.362 -0.195 -0.195 -0.163 -0.163
46 WSSQ1 ~~ WSSQ8 1.130 -0.055 -0.055 -0.066 -0.066
47 WSSQ1 ~~ WSSQ9 2.793 0.087 0.087 0.102 0.102
48 WSSQ1 ~~ WSSQ10 0.757 -0.059 -0.059 -0.053 -0.053
49 WSSQ1 ~~ WSSQ11 0.173 0.021 0.021 0.026 0.026
50 WSSQ1 ~~ WSSQ12 1.333 0.056 0.056 0.073 0.073
51 WSSQ2 ~~ WSSQ3 20.594 0.237 0.237 0.370 0.370
52 WSSQ2 ~~ WSSQ4 4.063 -0.113 -0.113 -0.138 -0.138
53 WSSQ2 ~~ WSSQ5 15.149 -0.251 -0.251 -0.252 -0.252
54 WSSQ2 ~~ WSSQ6 0.174 0.024 0.024 0.029 0.029
55 WSSQ2 ~~ WSSQ7 0.047 -0.013 -0.013 -0.014 -0.014
56 WSSQ2 ~~ WSSQ8 1.715 -0.057 -0.057 -0.087 -0.087
57 WSSQ2 ~~ WSSQ9 8.741 -0.130 -0.130 -0.194 -0.194
58 WSSQ2 ~~ WSSQ10 8.291 0.164 0.164 0.188 0.188
59 WSSQ2 ~~ WSSQ11 0.075 0.012 0.012 0.019 0.019
60 WSSQ2 ~~ WSSQ12 4.086 -0.083 -0.083 -0.138 -0.138
61 WSSQ3 ~~ WSSQ4 2.953 -0.084 -0.084 -0.126 -0.126
62 WSSQ3 ~~ WSSQ5 1.099 -0.058 -0.058 -0.072 -0.072
63 WSSQ3 ~~ WSSQ6 13.942 -0.191 -0.191 -0.276 -0.276
64 WSSQ3 ~~ WSSQ7 6.001 0.131 0.131 0.171 0.171
65 WSSQ3 ~~ WSSQ8 1.198 0.041 0.041 0.076 0.076
66 WSSQ3 ~~ WSSQ9 1.566 0.047 0.047 0.086 0.086
67 WSSQ3 ~~ WSSQ10 1.115 -0.051 -0.051 -0.072 -0.072
68 WSSQ3 ~~ WSSQ11 0.212 -0.017 -0.017 -0.033 -0.033
69 WSSQ3 ~~ WSSQ12 0.249 -0.017 -0.017 -0.036 -0.036
70 WSSQ4 ~~ WSSQ5 4.644 0.136 0.136 0.132 0.132
71 WSSQ4 ~~ WSSQ6 0.252 0.028 0.028 0.032 0.032
72 WSSQ4 ~~ WSSQ7 9.672 -0.188 -0.188 -0.193 -0.193
73 WSSQ4 ~~ WSSQ8 0.279 0.023 0.023 0.034 0.034
74 WSSQ4 ~~ WSSQ9 1.226 0.048 0.048 0.070 0.070
75 WSSQ4 ~~ WSSQ10 0.699 -0.047 -0.047 -0.052 -0.052
76 WSSQ4 ~~ WSSQ11 4.717 0.093 0.093 0.142 0.142
77 WSSQ4 ~~ WSSQ12 0.005 -0.003 -0.003 -0.005 -0.005
78 WSSQ5 ~~ WSSQ6 9.125 0.200 0.200 0.186 0.186
79 WSSQ5 ~~ WSSQ7 4.951 0.158 0.158 0.133 0.133
80 WSSQ5 ~~ WSSQ8 5.876 0.124 0.124 0.150 0.150
81 WSSQ5 ~~ WSSQ9 0.003 0.003 0.003 0.004 0.004
82 WSSQ5 ~~ WSSQ10 2.823 -0.113 -0.113 -0.103 -0.103
83 WSSQ5 ~~ WSSQ11 0.170 -0.021 -0.021 -0.026 -0.026
84 WSSQ5 ~~ WSSQ12 0.777 0.042 0.042 0.056 0.056
85 WSSQ6 ~~ WSSQ7 6.458 0.161 0.161 0.158 0.158
86 WSSQ6 ~~ WSSQ8 0.044 -0.010 -0.010 -0.013 -0.013
87 WSSQ6 ~~ WSSQ9 0.794 -0.041 -0.041 -0.056 -0.056
88 WSSQ6 ~~ WSSQ10 10.855 0.195 0.195 0.207 0.207
89 WSSQ6 ~~ WSSQ11 5.676 -0.107 -0.107 -0.156 -0.156
90 WSSQ6 ~~ WSSQ12 0.672 0.035 0.035 0.054 0.054
91 WSSQ7 ~~ WSSQ8 4.509 0.104 0.104 0.133 0.133
92 WSSQ7 ~~ WSSQ9 1.542 0.061 0.061 0.076 0.076
93 WSSQ7 ~~ WSSQ10 0.017 -0.008 -0.008 -0.008 -0.008
94 WSSQ7 ~~ WSSQ11 12.614 -0.172 -0.172 -0.227 -0.227
95 WSSQ7 ~~ WSSQ12 1.682 -0.060 -0.060 -0.083 -0.083
96 WSSQ8 ~~ WSSQ9 7.031 0.102 0.102 0.184 0.184
97 WSSQ8 ~~ WSSQ10 23.634 -0.242 -0.242 -0.336 -0.336
98 WSSQ8 ~~ WSSQ11 0.371 0.024 0.024 0.045 0.045
99 WSSQ8 ~~ WSSQ12 0.768 -0.033 -0.033 -0.066 -0.066
100 WSSQ9 ~~ WSSQ10 5.182 -0.113 -0.113 -0.153 -0.153
101 WSSQ9 ~~ WSSQ11 1.171 -0.042 -0.042 -0.078 -0.078
102 WSSQ9 ~~ WSSQ12 0.015 0.004 0.004 0.009 0.009
103 WSSQ10 ~~ WSSQ11 7.908 0.142 0.142 0.202 0.202
104 WSSQ10 ~~ WSSQ12 3.592 0.090 0.090 0.136 0.136
105 WSSQ11 ~~ WSSQ12 0.280 0.020 0.020 0.042 0.042WSSQ.model <-
' factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6+WSSQ7
factor2 =~ WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
WSSQ8 ~~ WSSQ10
'
fit<-cfa(WSSQ.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 31 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 26
Number of observations 325
Model Test User Model:
Test statistic 186.881
Degrees of freedom 52
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2668.151
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.948
Tucker-Lewis Index (TLI) 0.934
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5640.360
Loglikelihood unrestricted model (H1) -5546.920
Akaike (AIC) 11332.721
Bayesian (BIC) 11431.100
Sample-size adjusted Bayesian (BIC) 11348.630
Root Mean Square Error of Approximation:
RMSEA 0.089
90 Percent confidence interval - lower 0.076
90 Percent confidence interval - upper 0.103
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.041
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.974 0.652
WSSQ2 1.367 0.107 12.832 0.000 1.332 0.832
WSSQ3 1.315 0.099 13.272 0.000 1.281 0.870
WSSQ4 1.087 0.092 11.860 0.000 1.059 0.754
WSSQ5 0.967 0.093 10.379 0.000 0.942 0.644
WSSQ6 1.165 0.097 11.995 0.000 1.135 0.765
WSSQ7 1.021 0.093 10.942 0.000 0.995 0.685
factor2 =~
WSSQ8 1.000 1.063 0.839
WSSQ9 0.895 0.055 16.386 0.000 0.952 0.778
WSSQ10 1.205 0.081 14.926 0.000 1.281 0.813
WSSQ11 1.038 0.057 18.221 0.000 1.103 0.835
WSSQ12 0.980 0.054 18.061 0.000 1.041 0.831
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ8 ~~
.WSSQ10 -0.247 0.046 -5.419 0.000 -0.247 -0.391
factor1 ~~
factor2 0.872 0.102 8.569 0.000 0.842 0.842
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.283 0.107 11.980 0.000 1.283 0.575
.WSSQ2 0.786 0.076 10.378 0.000 0.786 0.307
.WSSQ3 0.526 0.056 9.466 0.000 0.526 0.243
.WSSQ4 0.851 0.075 11.372 0.000 0.851 0.431
.WSSQ5 1.255 0.104 12.014 0.000 1.255 0.586
.WSSQ6 0.915 0.081 11.278 0.000 0.915 0.415
.WSSQ7 1.121 0.095 11.831 0.000 1.121 0.531
.WSSQ8 0.473 0.049 9.700 0.000 0.473 0.295
.WSSQ9 0.592 0.052 11.388 0.000 0.592 0.395
.WSSQ10 0.843 0.083 10.159 0.000 0.843 0.339
.WSSQ11 0.527 0.050 10.638 0.000 0.527 0.302
.WSSQ12 0.487 0.045 10.723 0.000 0.487 0.310
factor1 0.949 0.148 6.420 0.000 1.000 1.000
factor2 1.130 0.124 9.093 0.000 1.000 1.000modindices(fit) lhs op rhs mi epc sepc.lv sepc.all sepc.nox
29 factor1 =~ WSSQ8 2.694 0.197 0.192 0.151 0.151
30 factor1 =~ WSSQ9 0.830 0.101 0.098 0.080 0.080
31 factor1 =~ WSSQ10 1.696 0.201 0.196 0.124 0.124
32 factor1 =~ WSSQ11 6.028 -0.273 -0.266 -0.201 -0.201
33 factor1 =~ WSSQ12 0.810 -0.095 -0.093 -0.074 -0.074
34 factor2 =~ WSSQ1 0.726 0.120 0.128 0.086 0.086
35 factor2 =~ WSSQ2 8.388 -0.363 -0.386 -0.241 -0.241
36 factor2 =~ WSSQ3 0.007 0.009 0.010 0.007 0.007
37 factor2 =~ WSSQ4 6.432 0.305 0.324 0.231 0.231
38 factor2 =~ WSSQ5 1.582 0.175 0.186 0.127 0.127
39 factor2 =~ WSSQ6 0.331 0.072 0.077 0.052 0.052
40 factor2 =~ WSSQ7 2.636 -0.217 -0.230 -0.159 -0.159
41 WSSQ1 ~~ WSSQ2 9.550 0.201 0.201 0.201 0.201
42 WSSQ1 ~~ WSSQ3 2.309 -0.086 -0.086 -0.104 -0.104
43 WSSQ1 ~~ WSSQ4 7.426 0.175 0.175 0.167 0.167
44 WSSQ1 ~~ WSSQ5 8.700 -0.222 -0.222 -0.175 -0.175
45 WSSQ1 ~~ WSSQ6 0.880 -0.063 -0.063 -0.058 -0.058
46 WSSQ1 ~~ WSSQ7 7.236 -0.193 -0.193 -0.161 -0.161
47 WSSQ1 ~~ WSSQ8 2.646 -0.081 -0.081 -0.104 -0.104
48 WSSQ1 ~~ WSSQ9 3.734 0.101 0.101 0.116 0.116
49 WSSQ1 ~~ WSSQ10 2.218 -0.097 -0.097 -0.094 -0.094
50 WSSQ1 ~~ WSSQ11 0.579 0.039 0.039 0.047 0.047
51 WSSQ1 ~~ WSSQ12 2.203 0.072 0.072 0.091 0.091
52 WSSQ2 ~~ WSSQ3 20.422 0.235 0.235 0.366 0.366
53 WSSQ2 ~~ WSSQ4 3.952 -0.111 -0.111 -0.135 -0.135
54 WSSQ2 ~~ WSSQ5 15.385 -0.252 -0.252 -0.254 -0.254
55 WSSQ2 ~~ WSSQ6 0.083 0.017 0.017 0.020 0.020
56 WSSQ2 ~~ WSSQ7 0.089 -0.018 -0.018 -0.020 -0.020
57 WSSQ2 ~~ WSSQ8 0.859 -0.039 -0.039 -0.064 -0.064
58 WSSQ2 ~~ WSSQ9 8.198 -0.125 -0.125 -0.184 -0.184
59 WSSQ2 ~~ WSSQ10 5.757 0.132 0.132 0.162 0.162
60 WSSQ2 ~~ WSSQ11 0.027 0.007 0.007 0.011 0.011
61 WSSQ2 ~~ WSSQ12 3.754 -0.079 -0.079 -0.128 -0.128
62 WSSQ3 ~~ WSSQ4 2.516 -0.077 -0.077 -0.116 -0.116
63 WSSQ3 ~~ WSSQ5 1.035 -0.057 -0.057 -0.070 -0.070
64 WSSQ3 ~~ WSSQ6 14.412 -0.194 -0.194 -0.279 -0.279
65 WSSQ3 ~~ WSSQ7 5.761 0.128 0.128 0.167 0.167
66 WSSQ3 ~~ WSSQ8 0.179 0.015 0.015 0.031 0.031
67 WSSQ3 ~~ WSSQ9 2.113 0.054 0.054 0.097 0.097
68 WSSQ3 ~~ WSSQ10 1.717 -0.062 -0.062 -0.093 -0.093
69 WSSQ3 ~~ WSSQ11 0.049 -0.008 -0.008 -0.015 -0.015
70 WSSQ3 ~~ WSSQ12 0.024 -0.005 -0.005 -0.011 -0.011
71 WSSQ4 ~~ WSSQ5 4.695 0.137 0.137 0.133 0.133
72 WSSQ4 ~~ WSSQ6 0.217 0.026 0.026 0.030 0.030
73 WSSQ4 ~~ WSSQ7 9.736 -0.189 -0.189 -0.193 -0.193
74 WSSQ4 ~~ WSSQ8 0.000 0.001 0.001 0.001 0.001
75 WSSQ4 ~~ WSSQ9 1.678 0.057 0.057 0.080 0.080
76 WSSQ4 ~~ WSSQ10 1.179 -0.059 -0.059 -0.070 -0.070
77 WSSQ4 ~~ WSSQ11 5.276 0.097 0.097 0.146 0.146
78 WSSQ4 ~~ WSSQ12 0.045 0.009 0.009 0.013 0.013
79 WSSQ5 ~~ WSSQ6 8.842 0.196 0.196 0.183 0.183
80 WSSQ5 ~~ WSSQ7 4.810 0.155 0.155 0.131 0.131
81 WSSQ5 ~~ WSSQ8 3.760 0.096 0.096 0.124 0.124
82 WSSQ5 ~~ WSSQ9 0.015 0.006 0.006 0.007 0.007
83 WSSQ5 ~~ WSSQ10 1.755 -0.085 -0.085 -0.083 -0.083
84 WSSQ5 ~~ WSSQ11 0.134 -0.018 -0.018 -0.023 -0.023
85 WSSQ5 ~~ WSSQ12 0.817 0.044 0.044 0.056 0.056
86 WSSQ6 ~~ WSSQ7 6.015 0.155 0.155 0.153 0.153
87 WSSQ6 ~~ WSSQ8 0.236 0.021 0.021 0.032 0.032
88 WSSQ6 ~~ WSSQ9 1.017 -0.046 -0.046 -0.062 -0.062
89 WSSQ6 ~~ WSSQ10 10.654 0.186 0.186 0.211 0.211
90 WSSQ6 ~~ WSSQ11 6.510 -0.113 -0.113 -0.162 -0.162
91 WSSQ6 ~~ WSSQ12 0.338 0.025 0.025 0.037 0.037
92 WSSQ7 ~~ WSSQ8 4.396 0.099 0.099 0.135 0.135
93 WSSQ7 ~~ WSSQ9 1.175 0.053 0.053 0.066 0.066
94 WSSQ7 ~~ WSSQ10 0.090 0.018 0.018 0.019 0.019
95 WSSQ7 ~~ WSSQ11 12.947 -0.172 -0.172 -0.224 -0.224
96 WSSQ7 ~~ WSSQ12 1.854 -0.062 -0.062 -0.084 -0.084
97 WSSQ8 ~~ WSSQ9 0.840 0.037 0.037 0.070 0.070
98 WSSQ8 ~~ WSSQ11 0.101 -0.013 -0.013 -0.027 -0.027
99 WSSQ8 ~~ WSSQ12 4.370 -0.084 -0.084 -0.175 -0.175
100 WSSQ9 ~~ WSSQ10 10.260 -0.167 -0.167 -0.236 -0.236
101 WSSQ9 ~~ WSSQ11 0.029 -0.006 -0.006 -0.012 -0.012
102 WSSQ9 ~~ WSSQ12 1.488 0.044 0.044 0.082 0.082
103 WSSQ10 ~~ WSSQ11 2.277 0.082 0.082 0.123 0.123
104 WSSQ10 ~~ WSSQ12 0.020 0.007 0.007 0.011 0.011
105 WSSQ11 ~~ WSSQ12 2.241 0.055 0.055 0.109 0.109WSSQ.model <-
' factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6+WSSQ7
factor2 =~ WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
WSSQ8 ~~ WSSQ10
WSSQ2~~WSSQ3
'
#每做一次mi(modification index，自由度就會-1
#mi值>3.84，通常會降卡方值
fit<-cfa(WSSQ.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 32 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 27
Number of observations 325
Model Test User Model:
Test statistic 167.785
Degrees of freedom 51
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2668.151
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.955
Tucker-Lewis Index (TLI) 0.942
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5630.813
Loglikelihood unrestricted model (H1) -5546.920
Akaike (AIC) 11315.625
Bayesian (BIC) 11417.788
Sample-size adjusted Bayesian (BIC) 11332.147
Root Mean Square Error of Approximation:
RMSEA 0.084
90 Percent confidence interval - lower 0.070
90 Percent confidence interval - upper 0.098
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.038
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.972 0.650
WSSQ2 1.313 0.108 12.182 0.000 1.276 0.797
WSSQ3 1.275 0.100 12.723 0.000 1.238 0.841
WSSQ4 1.109 0.093 11.884 0.000 1.078 0.767
WSSQ5 0.995 0.095 10.501 0.000 0.967 0.661
WSSQ6 1.186 0.099 11.993 0.000 1.152 0.776
WSSQ7 1.020 0.095 10.790 0.000 0.991 0.682
factor2 =~
WSSQ8 1.000 1.064 0.840
WSSQ9 0.896 0.054 16.434 0.000 0.953 0.779
WSSQ10 1.203 0.081 14.925 0.000 1.280 0.812
WSSQ11 1.036 0.057 18.223 0.000 1.102 0.835
WSSQ12 0.980 0.054 18.106 0.000 1.042 0.831
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ8 ~~
.WSSQ10 -0.246 0.045 -5.402 0.000 -0.246 -0.389
.WSSQ2 ~~
.WSSQ3 0.238 0.061 3.922 0.000 0.238 0.309
factor1 ~~
factor2 0.884 0.103 8.573 0.000 0.855 0.855
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.288 0.109 11.861 0.000 1.288 0.577
.WSSQ2 0.934 0.091 10.283 0.000 0.934 0.365
.WSSQ3 0.634 0.066 9.548 0.000 0.634 0.292
.WSSQ4 0.811 0.074 10.999 0.000 0.811 0.411
.WSSQ5 1.208 0.102 11.811 0.000 1.208 0.564
.WSSQ6 0.876 0.080 10.894 0.000 0.876 0.398
.WSSQ7 1.128 0.097 11.693 0.000 1.128 0.535
.WSSQ8 0.472 0.049 9.709 0.000 0.472 0.294
.WSSQ9 0.590 0.052 11.384 0.000 0.590 0.394
.WSSQ10 0.848 0.083 10.192 0.000 0.848 0.341
.WSSQ11 0.529 0.050 10.660 0.000 0.529 0.303
.WSSQ12 0.486 0.045 10.722 0.000 0.486 0.309
factor1 0.944 0.148 6.360 0.000 1.000 1.000
factor2 1.131 0.124 9.104 0.000 1.000 1.000modindices(fit) lhs op rhs mi epc sepc.lv sepc.all sepc.nox
30 factor1 =~ WSSQ8 2.881 0.221 0.215 0.170 0.170
31 factor1 =~ WSSQ9 1.133 0.128 0.124 0.101 0.101
32 factor1 =~ WSSQ10 1.322 0.194 0.188 0.119 0.119
33 factor1 =~ WSSQ11 6.954 -0.319 -0.310 -0.235 -0.235
34 factor1 =~ WSSQ12 0.603 -0.090 -0.087 -0.069 -0.069
35 factor2 =~ WSSQ1 0.358 0.093 0.099 0.066 0.066
36 factor2 =~ WSSQ2 3.331 -0.240 -0.255 -0.160 -0.160
37 factor2 =~ WSSQ3 2.789 0.192 0.204 0.139 0.139
38 factor2 =~ WSSQ4 2.588 0.214 0.228 0.162 0.162
39 factor2 =~ WSSQ5 0.082 0.043 0.046 0.031 0.031
40 factor2 =~ WSSQ6 0.354 -0.083 -0.088 -0.060 -0.060
41 factor2 =~ WSSQ7 4.325 -0.307 -0.326 -0.224 -0.224
42 WSSQ1 ~~ WSSQ2 15.961 0.255 0.255 0.232 0.232
43 WSSQ1 ~~ WSSQ3 2.306 -0.083 -0.083 -0.092 -0.092
44 WSSQ1 ~~ WSSQ4 6.596 0.166 0.166 0.162 0.162
45 WSSQ1 ~~ WSSQ5 11.465 -0.255 -0.255 -0.204 -0.204
46 WSSQ1 ~~ WSSQ6 1.551 -0.084 -0.084 -0.079 -0.079
47 WSSQ1 ~~ WSSQ7 6.796 -0.191 -0.191 -0.158 -0.158
48 WSSQ1 ~~ WSSQ8 2.887 -0.085 -0.085 -0.110 -0.110
49 WSSQ1 ~~ WSSQ9 3.432 0.098 0.098 0.112 0.112
50 WSSQ1 ~~ WSSQ10 2.151 -0.097 -0.097 -0.093 -0.093
51 WSSQ1 ~~ WSSQ11 0.519 0.037 0.037 0.045 0.045
52 WSSQ1 ~~ WSSQ12 1.840 0.067 0.067 0.084 0.084
53 WSSQ2 ~~ WSSQ4 0.539 -0.040 -0.040 -0.045 -0.045
54 WSSQ2 ~~ WSSQ5 9.147 -0.187 -0.187 -0.176 -0.176
55 WSSQ2 ~~ WSSQ6 4.362 0.118 0.118 0.130 0.130
56 WSSQ2 ~~ WSSQ7 0.000 0.000 0.000 0.000 0.000
57 WSSQ2 ~~ WSSQ8 0.439 -0.027 -0.027 -0.041 -0.041
58 WSSQ2 ~~ WSSQ9 8.465 -0.124 -0.124 -0.168 -0.168
59 WSSQ2 ~~ WSSQ10 8.291 0.155 0.155 0.174 0.174
60 WSSQ2 ~~ WSSQ11 0.108 0.014 0.014 0.019 0.019
61 WSSQ2 ~~ WSSQ12 2.801 -0.067 -0.067 -0.099 -0.099
62 WSSQ3 ~~ WSSQ4 0.170 -0.019 -0.019 -0.027 -0.027
63 WSSQ3 ~~ WSSQ5 0.130 0.019 0.019 0.022 0.022
64 WSSQ3 ~~ WSSQ6 9.271 -0.149 -0.149 -0.200 -0.200
65 WSSQ3 ~~ WSSQ7 9.280 0.158 0.158 0.187 0.187
66 WSSQ3 ~~ WSSQ8 0.828 0.032 0.032 0.058 0.058
67 WSSQ3 ~~ WSSQ9 4.740 0.079 0.079 0.130 0.130
68 WSSQ3 ~~ WSSQ10 2.245 -0.069 -0.069 -0.094 -0.094
69 WSSQ3 ~~ WSSQ11 0.020 -0.005 -0.005 -0.009 -0.009
70 WSSQ3 ~~ WSSQ12 0.165 0.014 0.014 0.025 0.025
71 WSSQ4 ~~ WSSQ5 2.041 0.090 0.090 0.091 0.091
72 WSSQ4 ~~ WSSQ6 0.258 -0.029 -0.029 -0.034 -0.034
73 WSSQ4 ~~ WSSQ7 12.913 -0.220 -0.220 -0.230 -0.230
74 WSSQ4 ~~ WSSQ8 0.092 -0.013 -0.013 -0.020 -0.020
75 WSSQ4 ~~ WSSQ9 1.241 0.048 0.048 0.070 0.070
76 WSSQ4 ~~ WSSQ10 1.694 -0.071 -0.071 -0.086 -0.086
77 WSSQ4 ~~ WSSQ11 4.968 0.094 0.094 0.144 0.144
78 WSSQ4 ~~ WSSQ12 0.007 -0.003 -0.003 -0.005 -0.005
79 WSSQ5 ~~ WSSQ6 5.358 0.152 0.152 0.148 0.148
80 WSSQ5 ~~ WSSQ7 3.674 0.136 0.136 0.117 0.117
81 WSSQ5 ~~ WSSQ8 2.839 0.082 0.082 0.109 0.109
82 WSSQ5 ~~ WSSQ9 0.007 -0.004 -0.004 -0.005 -0.005
83 WSSQ5 ~~ WSSQ10 2.456 -0.100 -0.100 -0.099 -0.099
84 WSSQ5 ~~ WSSQ11 0.281 -0.026 -0.026 -0.033 -0.033
85 WSSQ5 ~~ WSSQ12 0.443 0.032 0.032 0.041 0.041
86 WSSQ6 ~~ WSSQ7 5.366 0.148 0.148 0.149 0.149
87 WSSQ6 ~~ WSSQ8 0.024 0.007 0.007 0.010 0.010
88 WSSQ6 ~~ WSSQ9 1.672 -0.058 -0.058 -0.081 -0.081
89 WSSQ6 ~~ WSSQ10 10.223 0.182 0.182 0.211 0.211
90 WSSQ6 ~~ WSSQ11 7.912 -0.124 -0.124 -0.182 -0.182
91 WSSQ6 ~~ WSSQ12 0.082 0.012 0.012 0.018 0.018
92 WSSQ7 ~~ WSSQ8 3.959 0.094 0.094 0.129 0.129
93 WSSQ7 ~~ WSSQ9 0.947 0.048 0.048 0.059 0.059
94 WSSQ7 ~~ WSSQ10 0.078 0.017 0.017 0.018 0.018
95 WSSQ7 ~~ WSSQ11 13.465 -0.177 -0.177 -0.230 -0.230
96 WSSQ7 ~~ WSSQ12 2.369 -0.071 -0.071 -0.096 -0.096
97 WSSQ8 ~~ WSSQ9 0.699 0.034 0.034 0.064 0.064
98 WSSQ8 ~~ WSSQ11 0.055 -0.010 -0.010 -0.020 -0.020
99 WSSQ8 ~~ WSSQ12 4.686 -0.087 -0.087 -0.181 -0.181
100 WSSQ9 ~~ WSSQ10 10.349 -0.167 -0.167 -0.236 -0.236
101 WSSQ9 ~~ WSSQ11 0.032 -0.007 -0.007 -0.012 -0.012
102 WSSQ9 ~~ WSSQ12 1.325 0.042 0.042 0.078 0.078
103 WSSQ10 ~~ WSSQ11 2.720 0.089 0.089 0.133 0.133
104 WSSQ10 ~~ WSSQ12 0.023 0.008 0.008 0.012 0.012
105 WSSQ11 ~~ WSSQ12 2.279 0.055 0.055 0.109 0.109WSSQ.model <-
' factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6+WSSQ7
factor2 =~ WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
WSSQ8 ~~ WSSQ10
WSSQ2~~WSSQ3+WSSQ1
'
fit<-cfa(WSSQ.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 28
Number of observations 325
Model Test User Model:
Test statistic 152.028
Degrees of freedom 50
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2668.151
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.961
Tucker-Lewis Index (TLI) 0.948
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5622.934
Loglikelihood unrestricted model (H1) -5546.920
Akaike (AIC) 11301.868
Bayesian (BIC) 11407.815
Sample-size adjusted Bayesian (BIC) 11319.001
Root Mean Square Error of Approximation:
RMSEA 0.079
90 Percent confidence interval - lower 0.065
90 Percent confidence interval - upper 0.094
P-value RMSEA <= 0.05 0.001
Standardized Root Mean Square Residual:
SRMR 0.037
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.947 0.634
WSSQ2 1.320 0.101 13.009 0.000 1.250 0.782
WSSQ3 1.307 0.106 12.276 0.000 1.238 0.841
WSSQ4 1.138 0.099 11.502 0.000 1.078 0.767
WSSQ5 1.033 0.100 10.326 0.000 0.978 0.668
WSSQ6 1.217 0.105 11.604 0.000 1.153 0.777
WSSQ7 1.051 0.100 10.534 0.000 0.995 0.685
factor2 =~
WSSQ8 1.000 1.065 0.841
WSSQ9 0.895 0.054 16.468 0.000 0.953 0.779
WSSQ10 1.201 0.080 14.925 0.000 1.278 0.811
WSSQ11 1.035 0.057 18.237 0.000 1.102 0.834
WSSQ12 0.979 0.054 18.133 0.000 1.042 0.831
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ8 ~~
.WSSQ10 -0.246 0.045 -5.404 0.000 -0.246 -0.389
.WSSQ2 ~~
.WSSQ3 0.266 0.060 4.460 0.000 0.266 0.335
.WSSQ1 ~~
.WSSQ2 0.253 0.068 3.736 0.000 0.253 0.219
factor1 ~~
factor2 0.865 0.102 8.446 0.000 0.858 0.858
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.335 0.112 11.876 0.000 1.335 0.598
.WSSQ2 0.995 0.094 10.570 0.000 0.995 0.389
.WSSQ3 0.635 0.066 9.563 0.000 0.635 0.293
.WSSQ4 0.811 0.074 10.935 0.000 0.811 0.411
.WSSQ5 1.187 0.101 11.736 0.000 1.187 0.554
.WSSQ6 0.875 0.081 10.823 0.000 0.875 0.397
.WSSQ7 1.121 0.096 11.637 0.000 1.121 0.531
.WSSQ8 0.470 0.048 9.695 0.000 0.470 0.293
.WSSQ9 0.589 0.052 11.381 0.000 0.589 0.393
.WSSQ10 0.851 0.083 10.205 0.000 0.851 0.342
.WSSQ11 0.531 0.050 10.670 0.000 0.531 0.304
.WSSQ12 0.486 0.045 10.724 0.000 0.486 0.309
factor1 0.897 0.146 6.136 0.000 1.000 1.000
factor2 1.133 0.124 9.118 0.000 1.000 1.000為什麼要加這些進去? 必須回答
SEM或CFA有很多估計法
沒有跟lavaan說，一定用最大概似估計法 可以改估計法Estimators DWLS:用在非continues的score上，表現會比較好(像)
WSSQ.model <-
' factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6
factor2 =~ WSSQ7+WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
'
#DWLS的缺點是，sample size小的時候不好用
#會幫忙把scale切成不同階段，需要更多的樣本數
fit<-cfa(WSSQ.model, data=dta, estimator="DWLS")
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 36 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 25
Number of observations 325
Model Test User Model:
Test statistic 65.750
Degrees of freedom 53
P-value (Chi-square) 0.112
Model Test Baseline Model:
Test statistic 6823.391
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.998
Tucker-Lewis Index (TLI) 0.998
Root Mean Square Error of Approximation:
RMSEA 0.027
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.047
P-value RMSEA <= 0.05 0.975
Standardized Root Mean Square Residual:
SRMR 0.051
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Unstructured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.985 0.658
WSSQ2 1.302 0.060 21.662 0.000 1.283 0.801
WSSQ3 1.291 0.058 22.166 0.000 1.272 0.863
WSSQ4 1.110 0.052 21.219 0.000 1.094 0.777
WSSQ5 0.973 0.050 19.520 0.000 0.958 0.654
WSSQ6 1.155 0.055 21.111 0.000 1.138 0.766
factor2 =~
WSSQ7 1.000 0.943 0.648
WSSQ8 1.091 0.052 20.887 0.000 1.029 0.812
WSSQ9 1.006 0.048 20.901 0.000 0.949 0.774
WSSQ10 1.303 0.062 20.996 0.000 1.229 0.779
WSSQ11 1.111 0.053 20.913 0.000 1.048 0.793
WSSQ12 1.077 0.051 20.987 0.000 1.016 0.809
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 ~~
factor2 0.836 0.043 19.529 0.000 0.900 0.900
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.268 0.138 9.215 0.000 1.268 0.567
.WSSQ2 0.923 0.162 5.693 0.000 0.923 0.359
.WSSQ3 0.556 0.142 3.912 0.000 0.556 0.256
.WSSQ4 0.783 0.151 5.197 0.000 0.783 0.396
.WSSQ5 1.231 0.133 9.285 0.000 1.231 0.573
.WSSQ6 0.915 0.142 6.434 0.000 0.915 0.414
.WSSQ7 1.227 0.138 8.902 0.000 1.227 0.580
.WSSQ8 0.549 0.123 4.464 0.000 0.549 0.341
.WSSQ9 0.602 0.115 5.254 0.000 0.602 0.401
.WSSQ10 0.982 0.152 6.458 0.000 0.982 0.394
.WSSQ11 0.651 0.135 4.837 0.000 0.651 0.372
.WSSQ12 0.544 0.115 4.736 0.000 0.544 0.345
factor1 0.971 0.068 14.303 0.000 1.000 1.000
factor2 0.890 0.065 13.715 0.000 1.000 1.000TLI(NNFI)，有可能會超過1
stucture part (SEM)
WSSQ.model <-
' factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6
factor2 =~ WSSQ7+WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
factor3=~PBC6+PBC7+PBC8+PBC9+PBC10
factor3~factor1+factor2
factor1~factor2
'
fit<-sem(WSSQ.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 46 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 37
Number of observations 325
Model Test User Model:
Test statistic 385.900
Degrees of freedom 116
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 4159.722
Degrees of freedom 136
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.933
Tucker-Lewis Index (TLI) 0.921
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -8174.601
Loglikelihood unrestricted model (H1) -7981.651
Akaike (AIC) 16423.201
Bayesian (BIC) 16563.203
Sample-size adjusted Bayesian (BIC) 16445.842
Root Mean Square Error of Approximation:
RMSEA 0.085
90 Percent confidence interval - lower 0.075
90 Percent confidence interval - upper 0.094
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.058
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.991 0.664
WSSQ2 1.336 0.103 13.012 0.000 1.324 0.828
WSSQ3 1.281 0.095 13.444 0.000 1.270 0.863
WSSQ4 1.086 0.089 12.213 0.000 1.077 0.767
WSSQ5 0.942 0.090 10.417 0.000 0.934 0.638
WSSQ6 1.137 0.094 12.116 0.000 1.127 0.759
factor2 =~
WSSQ7 1.000 0.851 0.586
WSSQ8 1.215 0.110 11.088 0.000 1.034 0.816
WSSQ9 1.134 0.104 10.851 0.000 0.965 0.788
WSSQ10 1.445 0.134 10.779 0.000 1.229 0.780
WSSQ11 1.284 0.115 11.177 0.000 1.093 0.827
WSSQ12 1.228 0.109 11.224 0.000 1.045 0.833
factor3 =~
PBC6 1.000 1.597 0.916
PBC7 0.911 0.037 24.897 0.000 1.455 0.878
PBC8 -0.231 0.058 -4.009 0.000 -0.369 -0.223
PBC9 1.031 0.034 30.253 0.000 1.646 0.942
PBC10 1.014 0.036 27.893 0.000 1.619 0.916
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor3 ~
factor1 -0.301 0.250 -1.206 0.228 -0.187 -0.187
factor2 0.349 0.291 1.200 0.230 0.186 0.186
factor1 ~
factor2 1.017 0.111 9.156 0.000 0.873 0.873
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.249 0.105 11.878 0.000 1.249 0.560
.WSSQ2 0.806 0.078 10.310 0.000 0.806 0.315
.WSSQ3 0.555 0.058 9.482 0.000 0.555 0.256
.WSSQ4 0.814 0.073 11.162 0.000 0.814 0.412
.WSSQ5 1.270 0.106 11.989 0.000 1.270 0.593
.WSSQ6 0.933 0.083 11.233 0.000 0.933 0.423
.WSSQ7 1.387 0.114 12.207 0.000 1.387 0.657
.WSSQ8 0.535 0.050 10.656 0.000 0.535 0.334
.WSSQ9 0.567 0.051 11.035 0.000 0.567 0.379
.WSSQ10 0.974 0.087 11.128 0.000 0.974 0.392
.WSSQ11 0.551 0.053 10.476 0.000 0.551 0.316
.WSSQ12 0.481 0.046 10.369 0.000 0.481 0.306
.PBC6 0.488 0.051 9.496 0.000 0.488 0.161
.PBC7 0.627 0.059 10.691 0.000 0.627 0.228
.PBC8 2.601 0.205 12.717 0.000 2.601 0.950
.PBC9 0.345 0.044 7.860 0.000 0.345 0.113
.PBC10 0.504 0.053 9.509 0.000 0.504 0.161
.factor1 0.234 0.044 5.327 0.000 0.238 0.238
factor2 0.724 0.129 5.611 0.000 1.000 1.000
.factor3 2.526 0.237 10.666 0.000 0.991 0.991WSSQ.model <-
' factor1 =~ WSSQ1+WSSQ2+WSSQ3+ WSSQ4+ WSSQ5+WSSQ6
factor2 =~ WSSQ7+WSSQ8+WSSQ9+ WSSQ10+ WSSQ11+WSSQ12
factor3=~PBC6+PBC7+PBC8+PBC9+PBC10
#regression 想控制某些變項
factor3~Age+Gender+factor1+factor2
factor1~Age+Gender+factor2
'
#如果Gender已經是類別變項>2，就要dummy
#有些SEM的圖，不會在model上劃Age或Gender出來(比較美觀)，因為只是要control的variables
fit<-sem(WSSQ.model, data=dta, estimator="DWLS")
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 70 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 44
Number of observations 325
Model Test User Model:
Test statistic 188.368
Degrees of freedom 146
P-value (Chi-square) 0.010
Model Test Baseline Model:
Test statistic 8479.225
Degrees of freedom 170
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.995
Tucker-Lewis Index (TLI) 0.994
Root Mean Square Error of Approximation:
RMSEA 0.030
90 Percent confidence interval - lower 0.015
90 Percent confidence interval - upper 0.042
P-value RMSEA <= 0.05 0.999
Standardized Root Mean Square Residual:
SRMR 0.056
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Unstructured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor1 =~
WSSQ1 1.000 0.986 0.659
WSSQ2 1.299 0.060 21.680 0.000 1.281 0.799
WSSQ3 1.289 0.058 22.190 0.000 1.271 0.862
WSSQ4 1.109 0.052 21.246 0.000 1.094 0.777
WSSQ5 0.971 0.050 19.531 0.000 0.957 0.653
WSSQ6 1.158 0.055 21.159 0.000 1.142 0.768
factor2 =~
WSSQ7 1.000 0.943 0.648
WSSQ8 1.091 0.052 20.886 0.000 1.029 0.812
WSSQ9 1.006 0.048 20.900 0.000 0.949 0.774
WSSQ10 1.303 0.062 20.994 0.000 1.229 0.779
WSSQ11 1.112 0.053 20.912 0.000 1.049 0.793
WSSQ12 1.077 0.051 20.986 0.000 1.016 0.809
factor3 =~
PBC6 1.000 1.606 0.920
PBC7 0.904 0.057 15.756 0.000 1.452 0.875
PBC8 -0.222 0.039 -5.728 0.000 -0.357 -0.216
PBC9 1.031 0.066 15.673 0.000 1.656 0.946
PBC10 1.005 0.064 15.624 0.000 1.615 0.912
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
factor3 ~
Age 0.003 0.023 0.129 0.897 0.002 0.005
Gender -1.095 0.117 -9.399 0.000 -0.682 -0.333
factor1 -0.220 0.223 -0.985 0.325 -0.135 -0.135
factor2 0.209 0.228 0.918 0.359 0.123 0.123
factor1 ~
Age 0.029 0.012 2.425 0.015 0.029 0.086
Gender 0.087 0.065 1.329 0.184 0.088 0.043
factor2 0.941 0.053 17.917 0.000 0.900 0.900
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Age ~~
Gender -0.301 0.081 -3.722 0.000 -0.301 -0.209
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.WSSQ1 1.267 0.138 9.202 0.000 1.267 0.566
.WSSQ2 0.928 0.162 5.729 0.000 0.928 0.361
.WSSQ3 0.559 0.142 3.936 0.000 0.559 0.257
.WSSQ4 0.783 0.151 5.197 0.000 0.783 0.396
.WSSQ5 1.234 0.133 9.309 0.000 1.234 0.574
.WSSQ6 0.907 0.142 6.372 0.000 0.907 0.410
.WSSQ7 1.227 0.138 8.904 0.000 1.227 0.580
.WSSQ8 0.549 0.123 4.464 0.000 0.549 0.341
.WSSQ9 0.602 0.115 5.254 0.000 0.602 0.401
.WSSQ10 0.982 0.152 6.459 0.000 0.982 0.394
.WSSQ11 0.650 0.135 4.836 0.000 0.650 0.372
.WSSQ12 0.544 0.115 4.734 0.000 0.544 0.345
.PBC6 0.468 0.273 1.712 0.087 0.468 0.154
.PBC7 0.643 0.248 2.598 0.009 0.643 0.234
.PBC8 2.618 0.176 14.887 0.000 2.618 0.954
.PBC9 0.322 0.281 1.144 0.253 0.322 0.105
.PBC10 0.528 0.279 1.894 0.058 0.528 0.168
.factor1 0.177 0.043 4.152 0.000 0.182 0.182
factor2 0.890 0.065 13.713 0.000 1.000 1.000
.factor3 2.277 0.198 11.494 0.000 0.883 0.883
Age 8.698 0.856 10.163 0.000 8.698 1.000
Gender 0.238 0.006 39.165 0.000 0.238 1.000SEM結果解釋
看卡方值 Test statistic 188.368 Degrees of freedom 146 P-value (Chi-square) 0.010
看適配度 Comparative Fit Index (CFI) 0.995 Tucker-Lewis Index (TLI) 0.994 RMSEA(只有這個有分布，能夠算進賴區間) 0.030 90 Percent confidence interval - lower 0.015 90 Percent confidence interval - upper 0.042 P-value RMSEA <= 0.05 0.999 SRMR 0.056
看模型 =~表示測量模型 factor3: PBC-0.261 負的要看一下資料是不是反向題，或者考慮刪除
factor3 ~
Age 0.003 0.023 0.129 0.897 0.002 0.005 Gender -1.095 0.117 -9.399 0.000 -0.682 -0.333 Age部會影響到factor3 Gender顯著，表示在factor3是有影響的
factor1 ~
Age 0.029 0.012 2.425 0.015 0.029 0.086
Gender 0.087 0.065 1.329 0.184 0.088 0.043
factor2 0.941 0.053 17.917 0.000 0.900 0.900age越高→factor1越高，factor2越高→factor1越高
Variances:看std.all有沒有違反規定(1.不可>1；2.不可為負值)
covariances Age~Gender (觀察到的才會做相關)
遵循節約原則(模型越簡單越好) 甚麼時候只考慮做簡單模型(structure part)，可能複雜模型(measurement part)結果不好的時… # 單純發展量表→做CFA 想知道變項兼因果關係→做SEM(可用資料做出方向性)
Simple.model <-
'
att =~Attitude_PA
sn =~ SubNorm_PA
PBC=~PBC_PA
int=~Int_PA
PA=~IPAQtotalMET2
#regression 想控制某些變項
int~att+sn+PBC
PA~PBC+int
'
fit<-sem(Simple.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 156 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 13
Number of observations 325
Model Test User Model:
Test statistic 4.046
Degrees of freedom 2
P-value (Chi-square) 0.132
Model Test Baseline Model:
Test statistic 382.161
Degrees of freedom 10
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.995
Tucker-Lewis Index (TLI) 0.973
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -7173.500
Loglikelihood unrestricted model (H1) -7171.478
Akaike (AIC) 14373.001
Bayesian (BIC) 14422.191
Sample-size adjusted Bayesian (BIC) 14380.956
Root Mean Square Error of Approximation:
RMSEA 0.056
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.136
P-value RMSEA <= 0.05 0.344
Standardized Root Mean Square Residual:
SRMR 0.025
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
att =~
Attitude_PA 1.000 13.919 1.000
sn =~
SubNorm_PA 1.000 26.133 1.000
PBC =~
PBC_PA 1.000 26.955 1.000
int =~
Int_PA 1.000 27.243 1.000
PA =~
IPAQtotalMET2 1.000 21.411 1.000
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
int ~
att 0.295 0.086 3.423 0.001 0.151 0.151
sn 0.210 0.041 5.143 0.000 0.201 0.201
PBC 0.574 0.045 12.732 0.000 0.568 0.568
PA ~
PBC 0.219 0.058 3.805 0.000 0.276 0.276
int 0.027 0.057 0.479 0.632 0.035 0.035
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
att ~~
sn 48.258 20.354 2.371 0.018 0.133 0.133
PBC 185.865 23.225 8.003 0.000 0.495 0.495
sn ~~
PBC 142.892 39.869 3.584 0.000 0.203 0.203
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Attitude_PA 0.000 0.000 0.000
.SubNorm_PA 0.000 0.000 0.000
.PBC_PA 0.000 0.000 0.000
.Int_PA 0.000 0.000 0.000
.IPAQtotalMET2 0.000 0.000 0.000
att 193.740 15.198 12.748 0.000 1.000 1.000
sn 682.926 53.573 12.748 0.000 1.000 1.000
PBC 726.557 56.996 12.748 0.000 1.000 1.000
.int 352.779 27.674 12.748 0.000 0.475 0.475
.PA 417.054 32.716 12.748 0.000 0.910 0.910#不建議用DWLS，因為裡面是總分，改回default是ML(最大概似法)#老師的寫法
Simple.model <-
'
IPAQtotalMET2~Int_PA+PBC_PA
Int_PA~Attitude_PA+SubNorm_PA+PBC_PA
'
fit<-sem(Simple.model, data=dta)
summary(fit,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 17 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 7
Number of observations 325
Model Test User Model:
Test statistic 4.046
Degrees of freedom 2
P-value (Chi-square) 0.132
Model Test Baseline Model:
Test statistic 276.522
Degrees of freedom 7
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.992
Tucker-Lewis Index (TLI) 0.973
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -2855.907
Loglikelihood unrestricted model (H1) -2853.884
Akaike (AIC) 5725.813
Bayesian (BIC) 5752.300
Sample-size adjusted Bayesian (BIC) 5730.097
Root Mean Square Error of Approximation:
RMSEA 0.056
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.136
P-value RMSEA <= 0.05 0.344
Standardized Root Mean Square Residual:
SRMR 0.025
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IPAQtotalMET2 ~
Int_PA 0.027 0.057 0.479 0.632 0.027 0.035
PBC_PA 0.219 0.058 3.805 0.000 0.219 0.276
Int_PA ~
Attitude_PA 0.295 0.086 3.423 0.001 0.295 0.151
SubNorm_PA 0.210 0.041 5.143 0.000 0.210 0.201
PBC_PA 0.574 0.045 12.732 0.000 0.574 0.568
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.IPAQtotalMET2 417.054 32.716 12.748 0.000 417.054 0.910
.Int_PA 352.779 27.674 12.748 0.000 352.779 0.475Simple.model <-
'
att =~Attitude_PA
sn =~ SubNorm_PA
PBC=~PBC_PA
int=~Int_PA
PA=~IPAQtotalMET2
#regression 想控制某些變項
int~att+sn+PBC+WBIS_Total_Score
PA~PBC+int
'
fit1<-sem(Simple.model, data=dta)
summary(fit1,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 158 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 14
Number of observations 325
Model Test User Model:
Test statistic 48.652
Degrees of freedom 6
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 430.750
Degrees of freedom 15
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.897
Tucker-Lewis Index (TLI) 0.744
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -7171.509
Loglikelihood unrestricted model (H1) -7147.183
Akaike (AIC) 14371.017
Bayesian (BIC) 14423.991
Sample-size adjusted Bayesian (BIC) 14379.584
Root Mean Square Error of Approximation:
RMSEA 0.148
90 Percent confidence interval - lower 0.111
90 Percent confidence interval - upper 0.188
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.081
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
att =~
Attitude_PA 1.000 13.919 1.000
sn =~
SubNorm_PA 1.000 26.133 1.000
PBC =~
PBC_PA 1.000 26.955 1.000
int =~
Int_PA 1.000 27.095 1.000
PA =~
IPAQtotalMET2 1.000 21.410 1.000
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
int ~
att 0.319 0.086 3.720 0.000 0.164 0.164
sn 0.183 0.040 4.514 0.000 0.176 0.176
PBC 0.569 0.045 12.708 0.000 0.566 0.566
WBIS_Total_Scr 0.230 0.108 2.125 0.034 0.008 0.081
PA ~
PBC 0.219 0.058 3.805 0.000 0.276 0.276
int 0.027 0.057 0.476 0.634 0.035 0.035
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
att ~~
sn 48.258 20.354 2.371 0.018 0.133 0.133
PBC 185.865 23.225 8.003 0.000 0.495 0.495
sn ~~
PBC 142.892 39.869 3.584 0.000 0.203 0.203
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Attitude_PA 0.000 0.000 0.000
.SubNorm_PA 0.000 0.000 0.000
.PBC_PA 0.000 0.000 0.000
.Int_PA 0.000 0.000 0.000
.IPAQtotalMET2 0.000 0.000 0.000
att 193.740 15.198 12.748 0.000 1.000 1.000
sn 682.926 53.573 12.748 0.000 1.000 1.000
PBC 726.557 56.996 12.748 0.000 1.000 1.000
.int 348.481 27.337 12.748 0.000 0.475 0.475
.PA 417.054 32.716 12.748 0.000 0.910 0.910#不建議用DWLS，因為裡面是總分，改回default是ML(最大概似法)Simple.model <-
'
att =~Attitude_PA
sn =~ SubNorm_PA
PBC=~PBC_PA
int=~Int_PA
PA=~IPAQtotalMET2
#regression 想控制某些變項
WBIS_Total_Score~att
int~att+sn+PBC+WBIS_Total_Score
PA~PBC+int
'
fit2<-sem(Simple.model, data=dta)
summary(fit2,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 169 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 16
Number of observations 325
Model Test User Model:
Test statistic 46.579
Degrees of freedom 5
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 430.750
Degrees of freedom 15
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.900
Tucker-Lewis Index (TLI) 0.700
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -8365.465
Loglikelihood unrestricted model (H1) -8342.175
Akaike (AIC) 16762.929
Bayesian (BIC) 16823.470
Sample-size adjusted Bayesian (BIC) 16772.720
Root Mean Square Error of Approximation:
RMSEA 0.160
90 Percent confidence interval - lower 0.120
90 Percent confidence interval - upper 0.203
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.083
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
att =~
Attitude_PA 1.000 13.919 1.000
sn =~
SubNorm_PA 1.000 26.133 1.000
PBC =~
PBC_PA 1.000 26.955 1.000
int =~
Int_PA 1.000 27.013 1.000
PA =~
IPAQtotalMET2 1.000 21.409 1.000
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
WBIS_Total_Score ~
att -0.055 0.038 -1.442 0.149 -0.763 -0.080
int ~
att 0.319 0.086 3.711 0.000 0.164 0.164
sn 0.183 0.040 4.514 0.000 0.177 0.177
PBC 0.569 0.045 12.708 0.000 0.568 0.568
WBIS_Total_Scr 0.230 0.109 2.119 0.034 0.009 0.081
PA ~
PBC 0.219 0.057 3.810 0.000 0.276 0.276
int 0.027 0.057 0.476 0.634 0.034 0.034
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
att ~~
sn 48.258 20.354 2.371 0.018 0.133 0.133
PBC 185.865 23.225 8.003 0.000 0.495 0.495
sn ~~
PBC 142.892 39.869 3.584 0.000 0.203 0.203
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Attitude_PA 0.000 0.000 0.000
.SubNorm_PA 0.000 0.000 0.000
.PBC_PA 0.000 0.000 0.000
.Int_PA 0.000 0.000 0.000
.IPAQtotalMET2 0.000 0.000 0.000
.WBIS_Total_Scr 90.880 7.129 12.748 0.000 90.880 0.994
att 193.740 15.198 12.748 0.000 1.000 1.000
sn 682.926 53.573 12.748 0.000 1.000 1.000
PBC 726.557 56.996 12.748 0.000 1.000 1.000
.int 348.481 27.337 12.748 0.000 0.478 0.478
.PA 417.054 32.716 12.748 0.000 0.910 0.910#老師的寫法
Simple.model <-
'
IPAQtotalMET2~Int_PA+PBC_PA
Int_PA~WBIS_Total_Score+Attitude_PA+SubNorm_PA+PBC_PA
'
fit1<-sem(Simple.model, data=dta)
summary(fit1,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 19 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 8
Number of observations 325
Model Test User Model:
Test statistic 9.767
Degrees of freedom 3
P-value (Chi-square) 0.021
Model Test Baseline Model:
Test statistic 286.227
Degrees of freedom 9
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.976
Tucker-Lewis Index (TLI) 0.927
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -2853.915
Loglikelihood unrestricted model (H1) -2849.031
Akaike (AIC) 5723.830
Bayesian (BIC) 5754.100
Sample-size adjusted Bayesian (BIC) 5728.725
Root Mean Square Error of Approximation:
RMSEA 0.083
90 Percent confidence interval - lower 0.029
90 Percent confidence interval - upper 0.144
P-value RMSEA <= 0.05 0.134
Standardized Root Mean Square Residual:
SRMR 0.039
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IPAQtotalMET2 ~
Int_PA 0.027 0.057 0.479 0.632 0.027 0.035
PBC_PA 0.219 0.058 3.805 0.000 0.219 0.276
Int_PA ~
WBIS_Total_Scr 0.230 0.115 2.002 0.045 0.230 0.081
Attitude_PA 0.319 0.087 3.685 0.000 0.319 0.163
SubNorm_PA 0.183 0.043 4.287 0.000 0.183 0.175
PBC_PA 0.569 0.045 12.692 0.000 0.569 0.563
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.IPAQtotalMET2 417.054 32.716 12.748 0.000 417.054 0.910
.Int_PA 348.481 27.337 12.748 0.000 348.481 0.470#老師的寫法
Simple.model <-
'
IPAQtotalMET2~Int_PA+PBC_PA
WBIS_Total_Score~Attitude_PA
Int_PA~WBIS_Total_Score+Attitude_PA+SubNorm_PA+PBC_PA
'
fit2<-sem(Simple.model, data=dta)
summary(fit2,fit.measures=T, standardized=T)lavaan 0.6-9 ended normally after 22 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 10
Number of observations 325
Model Test User Model:
Test statistic 46.579
Degrees of freedom 5
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 325.111
Degrees of freedom 12
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.867
Tucker-Lewis Index (TLI) 0.681
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -4047.871
Loglikelihood unrestricted model (H1) -4024.581
Akaike (AIC) 8115.742
Bayesian (BIC) 8153.580
Sample-size adjusted Bayesian (BIC) 8121.861
Root Mean Square Error of Approximation:
RMSEA 0.160
90 Percent confidence interval - lower 0.120
90 Percent confidence interval - upper 0.203
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.083
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IPAQtotalMET2 ~
Int_PA 0.027 0.057 0.476 0.634 0.027 0.034
PBC_PA 0.219 0.057 3.810 0.000 0.219 0.276
WBIS_Total_Score ~
Attitude_PA -0.055 0.038 -1.442 0.149 -0.055 -0.080
Int_PA ~
WBIS_Total_Scr 0.230 0.109 2.119 0.034 0.230 0.081
Attitude_PA 0.319 0.086 3.711 0.000 0.319 0.164
SubNorm_PA 0.183 0.040 4.514 0.000 0.183 0.177
PBC_PA 0.569 0.045 12.708 0.000 0.569 0.568
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.IPAQtotalMET2 417.054 32.716 12.748 0.000 417.054 0.910
.WBIS_Total_Scr 90.880 7.129 12.748 0.000 90.880 0.994
.Int_PA 348.481 27.337 12.748 0.000 348.481 0.478anova(fit1, fit2)Chi-Squared Difference Test
Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
fit1 3 5723.8 5754.1 9.767
fit2 5 8115.7 8153.6 46.579 36.812 2 1.015e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1這兩個模型有顯著差異 比較兩個模式的卡方值，p=1.015e-08 AIC, BIC越小越好
若兩個模型沒有顯著差異，就選結構簡單的模型
測量衡等性measurement invariance
依據不同的group做分群的分析 如何檢測group間的factor loading是否一致 group.equal=c(“loadings”, “intercepts”) 如何檢測group間的Intercepts是否一致 形成三個模型(稱之為nested model) (1)figural model (2)loading-constrained model (3)loading & intercept constrained model (1)→(2)模型是否顯著變差，變差表示，把group限制在equal是不合理的，在因素負荷量不一致 (2)→(3)有變差，表示factor在起始點是不一致的 皆不能宣稱，模型具有測量衡等性(表示，如果是男生和女生，應該各自畫一個model)
依據Chen F.F, 2007 △CFI(CFI後-CFI前)>-0,01 △PRSEA<0.015 △SRMR<0.03在loading/ △SRMR<0.01在intercept △TLI(Chen F.F沒有做這個) 都符合的話，表示有測量衡等性