Model fit with and without correction for clustering

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Pasha

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Feb 27, 2020, 3:40:29 PM2/27/20
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Hello everyone!

I estimate a model with two latent factors (3 categorical indicators each), a control variable Gender and a manifest dependent variable.  Model converge with a good fit (chi-sq p-value = 0.11; CFI  0.99; RMSEA  0.02).

Since my sample is complex (students clustered in colleges), in the next model I introduce correction for clustering  (cluster = "ID_college")

Surprisingly,  outputs of both models are identical -- except  in the second one there is a line " Number of clusters [ID_college]     13"

Why the cluster correction didn't work?

Any help will be very much appreciated

Thank you!

Pasha 


First model - without cluster correction


pathmodel1202a <- '#measurement model

Monitoring =~ v22 + v23 + v24

Love =~ v5 + +v8 + v10

#regressions

v71 ~ Monitoring

v71 ~ Gender

Monitoring ~ Love

Monitoring ~ Gender

Love ~ Gender'

 

fit1202a <- sem(pathmodel1202a, data=datasem, ordered = c("v22", "v23", "v24", "v5", "v8", "v10", "v71"))

summary(fit1202a, fit.measures=T, rsquare = T)


lavaan 0.6-5 ended normally after 25 iterations
 
  Estimator                                       DWLS
  Optimization method                           NLMINB
  Number of free parameters                         41
                                                      
                                                  Used       Total
  Number of observations                          1452        1715
                                                                  
Model Test User Model:
                                              Standard      Robust
  Test Statistic                                14.936      24.283
  Degrees of freedom                                17          17
  P-value (Chi-square)                           0.600       0.112
  Scaling correction factor                                  0.682
  Shift parameter                                            2.373
    for the simple second-order correction 
 
Model Test Baseline Model:
 
  Test statistic                              6973.091    4885.216
  Degrees of freedom                                21          21
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.429
 
User Model versus Baseline Model:
 
  Comparative Fit Index (CFI)                    1.000       0.999
  Tucker-Lewis Index (TLI)                       1.000       0.998
                                                                  
  Robust Comparative Fit Index (CFI)                            NA
  Robust Tucker-Lewis Index (TLI)                               NA
 
Root Mean Square Error of Approximation:
 
  RMSEA                                          0.000       0.017
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.021       0.032
  P-value RMSEA <= 0.05                          1.000       1.000
                                                                  
  Robust RMSEA                                                  NA
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                        NA
 
Standardized Root Mean Square Residual:
 
  SRMR                                           0.023       0.023
 
Parameter Estimates:
 
  Information                                 Expected
  Information saturated (h1) model        Unstructured
  Standard errors                           Robust.sem
 
Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  Monitoring =~                                       
    v22               1.000                           
    v23               0.955    0.029   32.425    0.000
    v24               0.971    0.029   33.631    0.000
  Love =~                                             
    v5                1.000                           
    v8                0.970    0.035   27.954    0.000
    v10               0.861    0.032   26.971    0.000
 
Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  v71 ~                                               
    Monitoring       -0.364    0.039   -9.365    0.000
    Gender           -0.321    0.059   -5.450    0.000
  Monitoring ~                                        
    Love              0.332    0.032   10.535    0.000
    Gender           -0.171    0.047   -3.608    0.000
  Love ~                                              

    Gender           -0.137    0.061   -2.238    0.025


Second model -- Adding cluster argument:


fit1202a1 <- sem(pathmodel1202a, data=datasem, ordered = c("v22", "v23", "v24", "v5", "v8", "v10", "v71"), cluster = "ID_college")
summary(fit1202a1, fit.measures=T, rsquare = T)
lavaan 0.6-5 ended normally after 25 iterations
 
  Estimator                                       DWLS
  Optimization method                           NLMINB
  Number of free parameters                         41
                                                      
                                                  Used       Total
  Number of observations                          1452        1715
  Number of clusters [ID_college]                   13            
                                                                  
Model Test User Model:
                                              Standard      Robust
  Test Statistic                                14.936      24.283
  Degrees of freedom                                17          17
  P-value (Chi-square)                           0.600       0.112
  Scaling correction factor                                  0.682
  Shift parameter                                            2.373
    for the simple second-order correction 
 
Model Test Baseline Model:
 
  Test statistic                              6973.091    4885.216
  Degrees of freedom                                21          21
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.429
 
User Model versus Baseline Model:
 
  Comparative Fit Index (CFI)                    1.000       0.999
  Tucker-Lewis Index (TLI)                       1.000       0.998
                                                                  
  Robust Comparative Fit Index (CFI)                            NA
  Robust Tucker-Lewis Index (TLI)                               NA
 
Root Mean Square Error of Approximation:
 
  RMSEA                                          0.000       0.017
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.021       0.032
  P-value RMSEA <= 0.05                          1.000       1.000
                                                                  
  Robust RMSEA                                                  NA
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                        NA
 
Standardized Root Mean Square Residual:
 
  SRMR                                           0.023       0.023
 
Parameter Estimates:
 
  Information                                 Expected
  Information saturated (h1) model        Unstructured
  Standard errors                           Robust.sem
 
Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  Monitoring =~                                       
    v22               1.000                           
    v23               0.955    0.029   32.425    0.000
    v24               0.971    0.029   33.631    0.000
  Love =~                                             
    v5                1.000                           
    v8                0.970    0.035   27.954    0.000
    v10               0.861    0.032   26.971    0.000
 
Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  v71 ~                                               
    Monitoring       -0.364    0.039   -9.365    0.000
    Gender           -0.321    0.059   -5.450    0.000
  Monitoring ~                                        
    Love              0.332    0.032   10.535    0.000
    Gender           -0.171    0.047   -3.608    0.000
  Love ~                                              
    Gender           -0.137    0.061   -2.238    0.025


P.S. Also, I am not sure that my initial model syntax is correct, so I add the picture of
theoretical model I tried to specify here. 

12.PNG

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