10.Hafta Ev Çalışması

Doğrulayıcı Faktör Analizi (DFA)

10. HAFTANIN TEKRARI

lavaan

• =~ : “ölçülür” (faktör tanımlama). F1 =~ x1 + x2 + x3
• ~~ : kovaryans/varyans. F1 ~~ F2 (faktörler arası korelasyon)
• ~ : regresyon. Y ~ X

Uyum indeksleri

İndeks	Türü	İyi	Kabul
χ²	—	p > .05	—
RMSEA	Kötülük	< .05	< .08
CFI	İyilik	≥ .95	≥ .90
TLI	İyilik	≥ .95	≥ .90
SRMR	Kötülük	< .05	< .08

Kategorik veri

WLSMV

Maddeler 0/1 (ikili) ise normal ML kullanılamaz. Kategorik veri için:

• ordered = TRUE lavaan’da maddelerin sıralı olduğunu belirtir
• Otomatik olarak korelasyon matrisi hesaplanır
• Kestirim yöntemi WLSMV (Diagonally Weighted Least Squares) olur
• estimator = "WLSMV" manuel de ytazılabilir

İkinci dereceli DFA

Birinci dereceli faktörlerin altında yatan üst düzey bir faktör var mı? Söz gelimi doğal, bedensel, uzamsal zeka —> genel zeka. en az 3 birinci dereceli faktör olmalı (2 faktörlü yapılarda ikinci düzey kurulamaz)

İkili faktörlü (bi-factor) model

Her madde hem kendi spesifik faktörüne hem de genel bir faktöre yük verir. Genel faktör ve spesifik faktörler birbirinden bağımsız “ortogonal”. orthogonal = TRUE ile kurulur.

Modifikasyon

• modindices(fit) → MI değerleri. Yüksek MI = o parametre eklenirse ki-kare düşer.
• Artık kovaryanslar eklenebilir ama kuramsal gerekçe lazım
• Model karşılaştırmalar da anova(fit1, fit2) → ki-kare fark testi

SORU 2: MOTİVASYON ÖLÇEĞİ

17 madde, 0/1 puanlanmış. Dışsal (ext1-ext12) ve içsel (int1-int5) motivasyon.

mot <- readRDS("mot.Rds")
head(mot, 3)

##   ext1 ext2 ext3 ext4 ext5 ext6 ext7 ext8 ext9 ext10 ext11 ext12 int1 int2 int3
## 1    1    0    0    0    1    1    1    0    0     0     0     0    1    1    0
## 3    0    0    0    0    1    0    0    0    0     0     0     0    0    0    0
## 4    0    1    1    0    1    1    1    0    1     1     1     1    1    1    1
##   int4 int5
## 1    0    1
## 3    1    0
## 4    1    1

str(mot)

## 'data.frame':    852 obs. of  17 variables:
##  $ ext1 : num  1 0 0 1 0 1 1 1 1 0 ...
##  $ ext2 : num  0 0 1 0 NA 0 1 0 1 0 ...
##  $ ext3 : num  0 0 1 1 1 1 0 0 0 0 ...
##  $ ext4 : num  0 0 0 0 NA 0 0 0 1 0 ...
##  $ ext5 : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ ext6 : num  1 0 1 1 1 1 1 1 1 1 ...
##  $ ext7 : num  1 0 1 0 NA 0 0 1 0 1 ...
##  $ ext8 : num  0 0 0 1 NA 0 0 0 1 1 ...
##  $ ext9 : num  0 0 1 0 NA 0 0 0 0 0 ...
##  $ ext10: num  0 0 1 0 NA 1 0 0 1 0 ...
##  $ ext11: num  0 0 1 1 NA 0 0 0 0 0 ...
##  $ ext12: num  0 0 1 1 NA 1 1 0 1 1 ...
##  $ int1 : num  1 0 1 1 NA 1 1 1 1 0 ...
##  $ int2 : num  1 0 1 1 NA 1 1 1 1 1 ...
##  $ int3 : num  0 0 1 0 NA 0 1 0 0 1 ...
##  $ int4 : num  0 1 1 1 1 1 1 1 1 0 ...
##  $ int5 : num  1 0 1 0 NA 1 1 0 0 0 ...

Temel nbasit Model

Kategorik veri → ordered = TRUE → tetrakorik korelasyon + WLSMV.

model_mot <- '
  dissel =~ ext1 + ext2 + ext3 + ext4 + ext5 + ext6 + ext7 + ext8 + ext9 + ext10 + ext11 + ext12
  icsel  =~ int1 + int2 + int3 + int4 + int5
'

fit_mot <- cfa(model_mot, data = mot, ordered = TRUE)
summary(fit_mot, fit.measures = TRUE, standardized = TRUE)

## lavaan 0.6-20 ended normally after 42 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        35
## 
##                                                   Used       Total
##   Number of observations                           794         852
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               492.422     464.935
##   Degrees of freedom                               118         118
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.136
##   Shift parameter                                           31.654
##     simple second-order correction                                
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4421.778    3011.080
##   Degrees of freedom                               136         136
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.491
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.913       0.879
##   Tucker-Lewis Index (TLI)                       0.899       0.861
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.063       0.061
##   90 Percent confidence interval - lower         0.058       0.055
##   90 Percent confidence interval - upper         0.069       0.067
##   P-value H_0: RMSEA <= 0.050                    0.000       0.001
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
##   P-value H_0: Robust RMSEA <= 0.050                            NA
##   P-value H_0: Robust RMSEA >= 0.080                            NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.119       0.119
## 
## Parameter Estimates:
## 
##   Parameterization                               Delta
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   dissel =~                                                             
##     ext1              1.000                               0.391    0.391
##     ext2              1.018    0.173    5.881    0.000    0.398    0.398
##     ext3              0.529    0.148    3.562    0.000    0.207    0.207
##     ext4              1.494    0.263    5.684    0.000    0.585    0.585
##     ext5              0.181    0.175    1.034    0.301    0.071    0.071
##     ext6              0.419    0.173    2.425    0.015    0.164    0.164
##     ext7              1.422    0.208    6.846    0.000    0.557    0.557
##     ext8              2.045    0.274    7.470    0.000    0.801    0.801
##     ext9              1.893    0.273    6.930    0.000    0.741    0.741
##     ext10             1.577    0.229    6.899    0.000    0.617    0.617
##     ext11             2.030    0.276    7.363    0.000    0.794    0.794
##     ext12             1.835    0.250    7.330    0.000    0.718    0.718
##   icsel =~                                                              
##     int1              1.000                               0.821    0.821
##     int2              0.924    0.066   14.092    0.000    0.758    0.758
##     int3              0.997    0.050   19.793    0.000    0.818    0.818
##     int4              0.906    0.057   15.980    0.000    0.744    0.744
##     int5              1.100    0.050   21.863    0.000    0.903    0.903
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   dissel ~~                                                             
##     icsel             0.047    0.017    2.744    0.006    0.148    0.148
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     ext1|t1           0.041    0.045    0.922    0.356    0.041    0.041
##     ext2|t1           0.584    0.047   12.327    0.000    0.584    0.584
##     ext3|t1           0.493    0.047   10.591    0.000    0.493    0.493
##     ext4|t1           1.541    0.070   21.954    0.000    1.541    1.541
##     ext5|t1          -1.128    0.056  -19.964    0.000   -1.128   -1.128
##     ext6|t1          -1.059    0.055  -19.296    0.000   -1.059   -1.059
##     ext7|t1           0.242    0.045    5.386    0.000    0.242    0.242
##     ext8|t1           1.042    0.055   19.122    0.000    1.042    1.042
##     ext9|t1           1.481    0.068   21.880    0.000    1.481    1.481
##     ext10|t1          0.622    0.048   13.016    0.000    0.622    0.622
##     ext11|t1          1.048    0.055   19.180    0.000    1.048    1.048
##     ext12|t1          0.013    0.045    0.284    0.777    0.013    0.013
##     int1|t1          -0.657    0.048  -13.632    0.000   -0.657   -0.657
##     int2|t1          -1.242    0.060  -20.865    0.000   -1.242   -1.242
##     int3|t1           0.194    0.045    4.324    0.000    0.194    0.194
##     int4|t1          -0.873    0.051  -17.028    0.000   -0.873   -0.873
##     int5|t1          -0.272    0.045   -6.022    0.000   -0.272   -0.272
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .ext1              0.847                               0.847    0.847
##    .ext2              0.841                               0.841    0.841
##    .ext3              0.957                               0.957    0.957
##    .ext4              0.658                               0.658    0.658
##    .ext5              0.995                               0.995    0.995
##    .ext6              0.973                               0.973    0.973
##    .ext7              0.690                               0.690    0.690
##    .ext8              0.359                               0.359    0.359
##    .ext9              0.451                               0.451    0.451
##    .ext10             0.619                               0.619    0.619
##    .ext11             0.369                               0.369    0.369
##    .ext12             0.484                               0.484    0.484
##    .int1              0.327                               0.327    0.327
##    .int2              0.425                               0.425    0.425
##    .int3              0.331                               0.331    0.331
##    .int4              0.447                               0.447    0.447
##    .int5              0.185                               0.185    0.185
##     dissel            0.153    0.038    3.984    0.000    1.000    1.000
##     icsel             0.673    0.051   13.305    0.000    1.000    1.000

fitMeasures(fit_mot, c("chisq.scaled","df.scaled","pvalue.scaled",
                        "cfi.scaled","tli.scaled","rmsea.scaled","srmr"))

##  chisq.scaled     df.scaled pvalue.scaled    cfi.scaled    tli.scaled 
##       464.935       118.000         0.000         0.879         0.861 
##  rmsea.scaled          srmr 
##         0.061         0.119

Modifikasyon

mi_mot <- modindices(fit_mot, sort = TRUE)
head(mi_mot, 15)

##       lhs op   rhs     mi    epc sepc.lv sepc.all sepc.nox
## 166  ext5 ~~  ext6 134.88  0.636   0.636    0.646    0.646
## 98  icsel =~  ext3  46.67  0.298   0.244    0.244    0.244
## 209  ext9 ~~ ext11  43.77  0.470   0.470    1.151    1.151
## 202  ext8 ~~ ext12  29.62  0.353   0.353    0.846    0.846
## 103 icsel =~  ext8  26.61 -0.288  -0.237   -0.237   -0.237
## 156  ext4 ~~  ext8  22.32  0.366   0.366    0.752    0.752
## 102 icsel =~  ext7  17.63  0.187   0.154    0.154    0.154
## 152  ext3 ~~  int5  14.51  0.219   0.219    0.519    0.519
## 210  ext9 ~~ ext12  11.93 -0.319  -0.319   -0.682   -0.682
## 150  ext3 ~~  int3  11.89  0.196   0.196    0.348    0.348
## 104 icsel =~  ext9  11.79  0.233   0.191    0.191    0.191
## 108  ext1 ~~  ext2  10.02  0.185   0.185    0.220    0.220
## 154  ext4 ~~  ext6   9.08 -0.308  -0.308   -0.385   -0.385
## 199  ext8 ~~  ext9   9.07 -0.293  -0.293   -0.729   -0.729
## 201  ext8 ~~ ext11   8.81 -0.240  -0.240   -0.659   -0.659

#en yüksek MI değerlerine bakarak artık kovaryanslar eklenir

model_mot2 <- '
  dissel =~ ext1 + ext2 + ext3 + ext4 + ext5 + ext6 + ext7 + ext8 + ext9 + ext10 + ext11 + ext12
  icsel  =~ int1 + int2 + int3 + int4 + int5
  
  # MI değerlerine göre eklenecek artık kovaryanslar:
  # ext_? ~~ ext_?  (MI çıktısından en yüksek değerler)
'

fit_mot2 <- cfa(model_mot2, data = mot, ordered = TRUE)
summary(fit_mot2, fit.measures = TRUE, standardized = TRUE)

## lavaan 0.6-20 ended normally after 42 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        35
## 
##                                                   Used       Total
##   Number of observations                           794         852
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               492.422     464.935
##   Degrees of freedom                               118         118
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.136
##   Shift parameter                                           31.654
##     simple second-order correction                                
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4421.778    3011.080
##   Degrees of freedom                               136         136
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.491
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.913       0.879
##   Tucker-Lewis Index (TLI)                       0.899       0.861
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.063       0.061
##   90 Percent confidence interval - lower         0.058       0.055
##   90 Percent confidence interval - upper         0.069       0.067
##   P-value H_0: RMSEA <= 0.050                    0.000       0.001
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
##   P-value H_0: Robust RMSEA <= 0.050                            NA
##   P-value H_0: Robust RMSEA >= 0.080                            NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.119       0.119
## 
## Parameter Estimates:
## 
##   Parameterization                               Delta
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   dissel =~                                                             
##     ext1              1.000                               0.391    0.391
##     ext2              1.018    0.173    5.881    0.000    0.398    0.398
##     ext3              0.529    0.148    3.562    0.000    0.207    0.207
##     ext4              1.494    0.263    5.684    0.000    0.585    0.585
##     ext5              0.181    0.175    1.034    0.301    0.071    0.071
##     ext6              0.419    0.173    2.425    0.015    0.164    0.164
##     ext7              1.422    0.208    6.846    0.000    0.557    0.557
##     ext8              2.045    0.274    7.470    0.000    0.801    0.801
##     ext9              1.893    0.273    6.930    0.000    0.741    0.741
##     ext10             1.577    0.229    6.899    0.000    0.617    0.617
##     ext11             2.030    0.276    7.363    0.000    0.794    0.794
##     ext12             1.835    0.250    7.330    0.000    0.718    0.718
##   icsel =~                                                              
##     int1              1.000                               0.821    0.821
##     int2              0.924    0.066   14.092    0.000    0.758    0.758
##     int3              0.997    0.050   19.793    0.000    0.818    0.818
##     int4              0.906    0.057   15.980    0.000    0.744    0.744
##     int5              1.100    0.050   21.863    0.000    0.903    0.903
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   dissel ~~                                                             
##     icsel             0.047    0.017    2.744    0.006    0.148    0.148
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     ext1|t1           0.041    0.045    0.922    0.356    0.041    0.041
##     ext2|t1           0.584    0.047   12.327    0.000    0.584    0.584
##     ext3|t1           0.493    0.047   10.591    0.000    0.493    0.493
##     ext4|t1           1.541    0.070   21.954    0.000    1.541    1.541
##     ext5|t1          -1.128    0.056  -19.964    0.000   -1.128   -1.128
##     ext6|t1          -1.059    0.055  -19.296    0.000   -1.059   -1.059
##     ext7|t1           0.242    0.045    5.386    0.000    0.242    0.242
##     ext8|t1           1.042    0.055   19.122    0.000    1.042    1.042
##     ext9|t1           1.481    0.068   21.880    0.000    1.481    1.481
##     ext10|t1          0.622    0.048   13.016    0.000    0.622    0.622
##     ext11|t1          1.048    0.055   19.180    0.000    1.048    1.048
##     ext12|t1          0.013    0.045    0.284    0.777    0.013    0.013
##     int1|t1          -0.657    0.048  -13.632    0.000   -0.657   -0.657
##     int2|t1          -1.242    0.060  -20.865    0.000   -1.242   -1.242
##     int3|t1           0.194    0.045    4.324    0.000    0.194    0.194
##     int4|t1          -0.873    0.051  -17.028    0.000   -0.873   -0.873
##     int5|t1          -0.272    0.045   -6.022    0.000   -0.272   -0.272
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .ext1              0.847                               0.847    0.847
##    .ext2              0.841                               0.841    0.841
##    .ext3              0.957                               0.957    0.957
##    .ext4              0.658                               0.658    0.658
##    .ext5              0.995                               0.995    0.995
##    .ext6              0.973                               0.973    0.973
##    .ext7              0.690                               0.690    0.690
##    .ext8              0.359                               0.359    0.359
##    .ext9              0.451                               0.451    0.451
##    .ext10             0.619                               0.619    0.619
##    .ext11             0.369                               0.369    0.369
##    .ext12             0.484                               0.484    0.484
##    .int1              0.327                               0.327    0.327
##    .int2              0.425                               0.425    0.425
##    .int3              0.331                               0.331    0.331
##    .int4              0.447                               0.447    0.447
##    .int5              0.185                               0.185    0.185
##     dissel            0.153    0.038    3.984    0.000    1.000    1.000
##     icsel             0.673    0.051   13.305    0.000    1.000    1.000

Modelleri Karşılaştırma

anova(fit_mot, fit_mot2)

## 
## Chi-Squared Difference Test
## 
##           Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit_mot  118           492                                    
## fit_mot2 118           492          0     0       0

İki faktörlü yapılarda ikinci düzey DFA yapılamaz en az 3 birinci dereceli faktör gerekliydi

SORU 3: AİDİYET ÖLÇEĞİ

12 madde, 0/1 puanlanmış. Kurumsal (4), katılımsal (5), bireysel (4).

aid <- readRDS("aidiyet.Rds")
head(aid, 3)

##   kurumsal1 kurumsal2 kurumsal3 kurumsal4 bireysel1 bireysel2 bireysel3
## 1         1         0         0         0         1         0         1
## 3         0         0         0         0         0         0         1
## 4         0         1         1         0         1         1         1
##   bireysel4 katilimsal1 katilimsal2 katilimsal3 katilimsal4
## 1         0           1           1           0           0
## 3         0           0           0           0           1
## 4         1           1           1           1           1

str(aid)

## 'data.frame':    794 obs. of  12 variables:
##  $ kurumsal1  : num  1 0 0 1 1 1 1 1 0 0 ...
##  $ kurumsal2  : num  0 0 1 0 0 1 0 1 0 1 ...
##  $ kurumsal3  : num  0 0 1 1 1 0 0 0 0 0 ...
##  $ kurumsal4  : num  0 0 0 0 0 0 0 1 0 0 ...
##  $ bireysel1  : num  1 0 1 1 1 1 1 1 1 1 ...
##  $ bireysel2  : num  0 0 1 0 1 0 0 1 0 0 ...
##  $ bireysel3  : num  1 1 1 0 1 0 0 1 0 1 ...
##  $ bireysel4  : num  0 0 1 1 1 1 0 1 1 1 ...
##  $ katilimsal1: num  1 0 1 1 1 1 1 1 0 1 ...
##  $ katilimsal2: num  1 0 1 1 1 1 1 1 1 1 ...
##  $ katilimsal3: num  0 0 1 0 0 1 0 0 1 1 ...
##  $ katilimsal4: num  0 1 1 1 1 1 1 1 0 1 ...
##  - attr(*, "na.action")= 'omit' Named int [1:58] 5 14 28 54 59 77 81 95 99 107 ...
##   ..- attr(*, "names")= chr [1:58] "6" "22" "44" "101" ...

Üç Faktörlü Model

model_aid <- '
  kurumsal   =~ kurumsal1 + kurumsal2 + kurumsal3 + kurumsal4
  katilimsal =~ katilimsal1 + katilimsal2 + katilimsal3 + katilimsal4
  bireysel   =~ bireysel1 + bireysel2 + bireysel3 + bireysel4
'

names(aid)

##  [1] "kurumsal1"   "kurumsal2"   "kurumsal3"   "kurumsal4"   "bireysel1"  
##  [6] "bireysel2"   "bireysel3"   "bireysel4"   "katilimsal1" "katilimsal2"
## [11] "katilimsal3" "katilimsal4"

fit_aid <- cfa(model_aid, data = aid, ordered = TRUE)
summary(fit_aid, fit.measures = TRUE, standardized = TRUE)

## lavaan 0.6-20 ended normally after 43 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        27
## 
##   Number of observations                           794
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               161.148     189.809
##   Degrees of freedom                                51          51
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.882
##   Shift parameter                                            7.113
##     simple second-order correction                                
## 
## Model Test Baseline Model:
## 
##   Test statistic                              2506.101    1939.031
##   Degrees of freedom                                66          66
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.303
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.955       0.926
##   Tucker-Lewis Index (TLI)                       0.942       0.904
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.816
##   Robust Tucker-Lewis Index (TLI)                            0.762
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.052       0.059
##   90 Percent confidence interval - lower         0.043       0.050
##   90 Percent confidence interval - upper         0.061       0.068
##   P-value H_0: RMSEA <= 0.050                    0.331       0.053
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.126
##   90 Percent confidence interval - lower                     0.101
##   90 Percent confidence interval - upper                     0.151
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.999
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.088       0.088
## 
## Parameter Estimates:
## 
##   Parameterization                               Delta
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   kurumsal =~                                                           
##     kurumsal1         1.000                               0.361    0.361
##     kurumsal2         0.655    0.248    2.636    0.008    0.237    0.237
##     kurumsal3         1.424    0.374    3.807    0.000    0.515    0.515
##     kurumsal4         0.627    0.381    1.647    0.100    0.227    0.227
##   katilimsal =~                                                         
##     katilimsal1       1.000                               0.833    0.833
##     katilimsal2       0.988    0.067   14.710    0.000    0.823    0.823
##     katilimsal3       0.870    0.068   12.758    0.000    0.725    0.725
##     katilimsal4       0.947    0.061   15.551    0.000    0.789    0.789
##   bireysel =~                                                           
##     bireysel1         1.000                               0.602    0.602
##     bireysel2         0.834    0.100    8.311    0.000    0.502    0.502
##     bireysel3         1.412    0.132   10.717    0.000    0.850    0.850
##     bireysel4         1.421    0.132   10.730    0.000    0.855    0.855
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   kurumsal ~~                                                           
##     katilimsal        0.145    0.038    3.780    0.000    0.480    0.480
##     bireysel          0.121    0.030    4.011    0.000    0.557    0.557
##   katilimsal ~~                                                         
##     bireysel          0.232    0.033    6.932    0.000    0.462    0.462
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     kurumsal1|t1      0.041    0.045    0.922    0.356    0.041    0.041
##     kurumsal2|t1      0.592    0.047   12.465    0.000    0.592    0.592
##     kurumsal3|t1      0.489    0.046   10.522    0.000    0.489    0.489
##     kurumsal4|t1      1.541    0.070   21.954    0.000    1.541    1.541
##     katilimsal1|t1   -0.665    0.048  -13.769    0.000   -0.665   -0.665
##     katilimsal2|t1   -1.256    0.060  -20.956    0.000   -1.256   -1.256
##     katilimsal3|t1    0.184    0.045    4.112    0.000    0.184    0.184
##     katilimsal4|t1   -0.868    0.051  -16.963    0.000   -0.868   -0.868
##     bireysel1|t1     -0.725    0.049  -14.785    0.000   -0.725   -0.725
##     bireysel2|t1      0.025    0.045    0.567    0.570    0.025    0.025
##     bireysel3|t1     -0.385    0.046   -8.419    0.000   -0.385   -0.385
##     bireysel4|t1     -0.493    0.047  -10.591    0.000   -0.493   -0.493
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .kurumsal1         0.869                               0.869    0.869
##    .kurumsal2         0.944                               0.944    0.944
##    .kurumsal3         0.735                               0.735    0.735
##    .kurumsal4         0.949                               0.949    0.949
##    .katilimsal1       0.306                               0.306    0.306
##    .katilimsal2       0.322                               0.322    0.322
##    .katilimsal3       0.475                               0.475    0.475
##    .katilimsal4       0.378                               0.378    0.378
##    .bireysel1         0.638                               0.638    0.638
##    .bireysel2         0.748                               0.748    0.748
##    .bireysel3         0.278                               0.278    0.278
##    .bireysel4         0.268                               0.268    0.268
##     kurumsal          0.131    0.052    2.519    0.012    1.000    1.000
##     katilimsal        0.694    0.058   11.960    0.000    1.000    1.000
##     bireysel          0.362    0.059    6.123    0.000    1.000    1.000

fitMeasures(fit_aid, c("chisq.scaled","df.scaled","pvalue.scaled",
                        "cfi.scaled","tli.scaled","rmsea.scaled","srmr"))

##  chisq.scaled     df.scaled pvalue.scaled    cfi.scaled    tli.scaled 
##       189.809        51.000         0.000         0.926         0.904 
##  rmsea.scaled          srmr 
##         0.059         0.088

İkinci Dereceli Üç Faktörlü Model

model_aid2 <- '
  kurumsal   =~ kurumsal1 + kurumsal2 + kurumsal3 + kurumsal4
  katilimsal =~ katilimsal1 + katilimsal2 + katilimsal3 + katilimsal4
  bireysel   =~ bireysel1 + bireysel2 + bireysel3 + bireysel4
  aidiyet =~ kurumsal + katilimsal + bireysel
'

fit_aid2 <- cfa(model_aid2, data = aid, ordered = TRUE)
summary(fit_aid2, fit.measures = TRUE, standardized = TRUE)

## lavaan 0.6-20 ended normally after 59 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        27
## 
##   Number of observations                           794
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                               161.148     189.809
##   Degrees of freedom                                51          51
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.882
##   Shift parameter                                            7.113
##     simple second-order correction                                
## 
## Model Test Baseline Model:
## 
##   Test statistic                              2506.101    1939.031
##   Degrees of freedom                                66          66
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.303
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.955       0.926
##   Tucker-Lewis Index (TLI)                       0.942       0.904
##                                                                   
##   Robust Comparative Fit Index (CFI)                         0.816
##   Robust Tucker-Lewis Index (TLI)                            0.762
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.052       0.059
##   90 Percent confidence interval - lower         0.043       0.050
##   90 Percent confidence interval - upper         0.061       0.068
##   P-value H_0: RMSEA <= 0.050                    0.331       0.053
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.126
##   90 Percent confidence interval - lower                     0.101
##   90 Percent confidence interval - upper                     0.151
##   P-value H_0: Robust RMSEA <= 0.050                         0.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.999
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.088       0.088
## 
## Parameter Estimates:
## 
##   Parameterization                               Delta
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   kurumsal =~                                                           
##     kurumsal1         1.000                               0.361    0.361
##     kurumsal2         0.655    0.248    2.636    0.008    0.237    0.237
##     kurumsal3         1.424    0.374    3.807    0.000    0.515    0.515
##     kurumsal4         0.627    0.381    1.647    0.100    0.227    0.227
##   katilimsal =~                                                         
##     katilimsal1       1.000                               0.833    0.833
##     katilimsal2       0.988    0.067   14.710    0.000    0.823    0.823
##     katilimsal3       0.870    0.068   12.758    0.000    0.725    0.725
##     katilimsal4       0.947    0.061   15.551    0.000    0.789    0.789
##   bireysel =~                                                           
##     bireysel1         1.000                               0.602    0.602
##     bireysel2         0.834    0.100    8.311    0.000    0.502    0.502
##     bireysel3         1.412    0.132   10.717    0.000    0.850    0.850
##     bireysel4         1.421    0.132   10.730    0.000    0.855    0.855
##   aidiyet =~                                                            
##     kurumsal          1.000                               0.761    0.761
##     katilimsal        1.910    0.493    3.872    0.000    0.631    0.631
##     bireysel          1.602    0.450    3.561    0.000    0.732    0.732
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     kurumsal1|t1      0.041    0.045    0.922    0.356    0.041    0.041
##     kurumsal2|t1      0.592    0.047   12.465    0.000    0.592    0.592
##     kurumsal3|t1      0.489    0.046   10.522    0.000    0.489    0.489
##     kurumsal4|t1      1.541    0.070   21.954    0.000    1.541    1.541
##     katilimsal1|t1   -0.665    0.048  -13.769    0.000   -0.665   -0.665
##     katilimsal2|t1   -1.256    0.060  -20.956    0.000   -1.256   -1.256
##     katilimsal3|t1    0.184    0.045    4.112    0.000    0.184    0.184
##     katilimsal4|t1   -0.868    0.051  -16.963    0.000   -0.868   -0.868
##     bireysel1|t1     -0.725    0.049  -14.785    0.000   -0.725   -0.725
##     bireysel2|t1      0.025    0.045    0.567    0.570    0.025    0.025
##     bireysel3|t1     -0.385    0.046   -8.419    0.000   -0.385   -0.385
##     bireysel4|t1     -0.493    0.047  -10.591    0.000   -0.493   -0.493
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .kurumsal1         0.869                               0.869    0.869
##    .kurumsal2         0.944                               0.944    0.944
##    .kurumsal3         0.735                               0.735    0.735
##    .kurumsal4         0.949                               0.949    0.949
##    .katilimsal1       0.306                               0.306    0.306
##    .katilimsal2       0.322                               0.322    0.322
##    .katilimsal3       0.475                               0.475    0.475
##    .katilimsal4       0.378                               0.378    0.378
##    .bireysel1         0.638                               0.638    0.638
##    .bireysel2         0.748                               0.748    0.748
##    .bireysel3         0.278                               0.278    0.278
##    .bireysel4         0.268                               0.268    0.268
##    .kurumsal          0.055    0.036    1.535    0.125    0.420    0.420
##    .katilimsal        0.418    0.072    5.797    0.000    0.602    0.602
##    .bireysel          0.168    0.051    3.312    0.001    0.464    0.464
##     aidiyet           0.076    0.035    2.180    0.029    1.000    1.000

fitMeasures(fit_aid2, c("chisq.scaled","df.scaled","pvalue.scaled",
                         "cfi.scaled","tli.scaled","rmsea.scaled","srmr"))

##  chisq.scaled     df.scaled pvalue.scaled    cfi.scaled    tli.scaled 
##       189.809        51.000         0.000         0.926         0.904 
##  rmsea.scaled          srmr 
##         0.059         0.088

Model Karşılaştırmaları

anova(fit_aid, fit_aid2)

## 
## Chi-Squared Difference Test
## 
##          Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit_aid  51           161                                    
## fit_aid2 51           161   1.09e-10     0       0

YANSITMA

Bu hafta DFA ile dört farklı model yapısını (birinci dereceli ilişkisiz, ikinci dereceli g faktörlü, iki ikinci dereceli faktörlü, ilişkili birinci dereceli) öğrendim. Castejon makalesindeki sonuçları tekrarlamak iyi başlayan sonu benim için hüsran bir denemeydi çünkü 1.soruyu yapamadım. Kategorik veri ile DFA yapmak benim için yeni bir deneyimdi. ordered = TRUE dediğinde lavaan otomatik olarak WLSMV kullanıyor bu kolaylık harika ama neden böyle yapıldığı karışık geldi.