Very large parameters that are non-significant ?

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Hannah C

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Nov 7, 2018, 1:22:29 PM11/7/18
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Hi 

I have a model with two latent factors (Var 1 and Var 2 below), loading onto four variables each. When I include a third variable (TestVar) that loads onto both of the latent variables, the loading onto Var 1 is .22 and significant, whereas to Var 2 is .79 but non-significant (highlighted below in yellow). How can this be? 

In addition, the association between the two latent factors (Var 1 and Var 2) was initially .76 and significant, but when I include the TestVar variable, this association changes to .91 and also becomes non-significant (highlighted below in green) - again, how can this be so bit yet not significant?

Does anybody know how I should interpret this? 

Thanks a lot in advance!

Hannah



Model2 <- 'Var1 =~ x1 + x2 + y1 +y2                     
+                Var2 =~ x3 + x4 + y3 + y4
+                x1 ~~ x2
+                y1 ~~ y2
+                x3 ~~ x4
+                y3 ~~ y4
+                Var1 ~ TestVar
+                Var2 ~ TestVar
+              '
>              
> fitModel2 <- sem(Model2, data=newdata, std.lv=TRUE)
> summary(fitModel2, standardized=TRUE, fit.measures=TRUE)
lavaan 0.6-3 ended normally after 76 iterations

  Optimization method                           NLMINB
  Number of free parameters                         23

  Number of observations                           318

  Estimator                                         ML
  Model Fit Test Statistic                      18.508
  Degrees of freedom                                21
  P-value (Chi-square)                           0.617

Comparative Fit Index (CFI)                    1.000
Akaike (AIC)                                9917.021
RMSEA                                          0.000

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  Var1 =~                                                             
    x1             1.336    0.257    5.198    0.000    1.371    0.658
    x2             1.430    0.264    5.418    0.000    1.468    0.704
    y1             0.901    0.197    4.576    0.000    0.925    0.391
    y2             1.062    0.202    5.255    0.000    1.090    0.483
  Var2 =~                                                            
    x3             0.281    0.213    1.319    0.187    0.454    0.268
    x4             0.322    0.242    1.329    0.184    0.520    0.292
    y3             0.145    0.117    1.241    0.215    0.234    0.166
    y4             0.170    0.131    1.302    0.193    0.275    0.219

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  Var1 ~                                                              
    TestVar               0.018    0.006    3.016    0.003    0.017    0.224
  Var2 ~                                                             
    TestVar              0.098    0.074    1.331    0.183    0.061    0.786

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .x1 ~~                                                              
   .x2             0.449    0.652    0.688    0.491    0.449    0.193
 .y1 ~~                                                              
   .y2             2.274    0.423    5.377    0.000    2.274    0.528
 .x3 ~~                                                              
   .x4             0.554    0.206    2.698    0.007    0.554    0.200
 .y3 ~~                                                              
   .y4             0.071    0.102    0.695    0.487    0.071    0.042 
.Var1 ~~                                                             
   .Var2           0.910    0.673    1.352    0.176    0.910    0.910

Edward Rigdon

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Nov 7, 2018, 1:55:47 PM11/7/18
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Hannah--
The second factor is only weakly identified. None of the loadings on this factor are statistically significant, nor is its correlaton with the other factor or TestVar significant. The free residual covariances further weaken identification, and thus expand standard errors relating to that factor. The regression coefficient predicting the first factor is 3 times its standard error, while the regression coefficient predicting the second factor is little more than 1 times its standard error.
Is TestVar dichotomous? The variance of a dichotomous variable can never be equal to 1, so standardized estimates for dichotomous variables are a statistical fantasy. Does it make sense to think of TestVar having a variance of 1?

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Hannah C

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Nov 12, 2018, 9:56:55 AM11/12/18
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Hi Ed

Thanks a lot for your reply - that makes good sense about the second factor. And TestVar is a continuous variable (scores on a cognitive reasoning test)

Hannah
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