# Very large parameters that are non-significant ?

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### Hannah C

Nov 7, 2018, 1:22:29 PM11/7/18
to lavaan
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?

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

Nov 7, 2018, 1:55:47 PM11/7/18
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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