Generate Cross-Loadings

[sandeep]

Hello Folks,

I am using Lavaan to do CFA. I am facing problems with getting cross loading for factors- this is required for running discriminant validity tests. Essentially, when I run 

My issue is that I would like to get values where the current values are 0.00. 

Model after performing EFA: 

model1<-'lav_f1=~f11+f12+f14

lav_f2=~f21+f22+f23

lav_f3=~f22+f23+f21

...

.

.

lav_f6=~f61+f62

fit1<- cfa(model1, data= my_data, missing = "ML", std.lv=T)

lavTech(fit1, what="std")$lambda

I get an output like this:

Partial Output:

          [,1]      [,2]      [,3]      [,4]      [,5]      [,6]

 [1,] 0.9048272 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000

 [2,] 0.8887490 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000

 [3,] 0.8725165 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000

 [4,] 0.0000000 0.8745323 0.0000000 0.0000000 0.0000000 0.0000000

 [5,] 0.0000000 0.9263597 0.0000000 0.0000000 0.0000000 0.0000000

 [6,] 0.0000000 0.9428641 0.0000000 0.0000000 0.0000000 0.0000000

 [7,] 0.0000000 0.0000000 0.8963720 0.0000000 0.0000000 0.0000000

 [8,] 0.0000000 0.0000000 0.6624981 0.0000000 0.0000000 0.0000000

 [9,] 0.0000000 0.0000000 0.8820272 0.0000000 0.0000000 0.0000000

[10,] 0.0000000 0.0000000 0.0000000 0.8726296 0.0000000 0.0000000

[11,] 0.0000000 0.0000000 0.0000000 0.7293126 0.0000000 0.0000000

[12,] 0.0000000 0.0000000 0.0000000 0.8406514 0.0000000 0.0000000

[13,] 0.0000000 0.0000000 0.0000000 0.0000000 0.8589600 0.0000000

[14,] 0.0000000 0.0000000 0.0000000 0.0000000 0.9441202 0.0000000

[15,] 0.0000000 0.0000000 0.0000000 0.0000000 0.9326328 0.0000000

[16,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.9470186

[17,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.9297788

Any help is really appreciated. I don't want to use any commercial applications to solve this problem.

Thank You.

[Edward Rigdon]

Sandeep--

     In the CFA model that you ran, cross-loadings are all constrained to 0. Only the loadings specified as free parameters are estimated. You can find information on what cross-loadings might have been, if they had been free parameters, via the modification indices. However, there are no hidden cross-loadings in your model. You can see he impact of this and other model constraints by looking at the fit indices.

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[sandeep]

Thank You. Sorry for my ignorance, I have two doubts here:

1) I did read Lavaan documentation, but was still not clear. Can you please suggest how could I add a free parameter? Is adding all line items to group.partial going to make them free? 

2) Once I do step 1, which of these columns would I need to check? 

         lhs op rhs      mi    epc sepc.lv sepc.all sepc.nox

66  lav_sec =~ SL2   1.586 -0.081  -0.081   -0.046   -0.046

Thank You so much once again in advance.

[sandeep]

I prefixed each line item with NA* in the model to make them free. However, two issues remain.

1)  lavTech(fit1, what="std")$lambda still returns 0 values.

2) Which column value in Modification Index should I look at? and should I look at lav_f2=~ f13: This means: factor_two =~ Factor_1_line_Item_3 as an example of a cross loading?

Thank You :)

[Edward Rigdon]

If you want a loading to be a free parameter, you need to mention it in your model syntax. However, you cannot make every loading free for every common factor--such a model would not be statistically identified, without special restrictions. EFA approaches impose such restrictions by default, hiding the restrictions from the casual user. Here, the user has the freedom to free or constrain, but cannot escape statistical limitations.

The expected parameter change (epc) statistic shows the (unstandardized) estimated value that the parameter would take on if it were free AND if every other parameter retained its current value. Of course, if you relax a constraint, it is possible that other parameter values will change as well.

[Edward Rigdon]

You'll have to share your actual syntax and output, if you want advice about interpretation.

[sandeep]

Thank You.

#Model

model1<-'lav_ce=~C1+C2+E3+C4

lav_L=~L2+L3+L1

lav_a=~A3+A1

lav_b=~B1+B2+B3

lav_i=~I1+I2

'

#Fit

fit<- cfa(model1, data= my_data, missing = "ML", std.lv=T)

#Loadings.

lavInspect(fit1, what="std")$lambda

    lav_ce lav_l lav_a lav_b lav_i

C1  0.848  0.000  0.000  0.000  0.000

E2  0.905  0.000  0.000  0.000  0.000

E3  0.917  0.000  0.000  0.000  0.000

C4  0.830  0.000  0.000  0.000  0.000

L2  0.000  0.894  0.000  0.000  0.000

L3  0.000  0.661  0.000  0.000  0.000

L1  0.000  0.885  0.000  0.000  0.000

A3  0.000  0.000  0.718  0.000  0.000

A1  0.000  0.000  0.882  0.000  0.000

B1  0.000  0.000  0.000  0.859  0.000

B2  0.000  0.000  0.000  0.945  0.000

B3  0.000  0.000  0.000  0.932  0.000

I1  0.000  0.000  0.000  0.000  0.947

I2  0.000  0.000  0.000  0.000  0.930

Please let me know if I need to add more information. I did not want to add a lot of unnecessary information.