Very large parameters that are non-significant ?

[Hannah C]

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]

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?

--
You received this message because you are subscribed to the Google Groups "lavaan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+un...@googlegroups.com.
To post to this group, send email to lav...@googlegroups.com.
Visit this group at https://groups.google.com/group/lavaan.
For more options, visit https://groups.google.com/d/optout.

[Hannah C]

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