How to set covariance equal to 1 between variables

[car...@ucn.cl]

Dear all,

I am new in lavaan. So, I wanted to ask for help.

I wanted to test that two variables (CA and SS) are distinct yet interrelated variables. So, I want to compare two models through a CFA. 

MODEL1 <- '

CA =~ CA1 + CA2 + CA3 

SS =~ SS1 + SS2 + SS3 +SS4 + SS5 

'

Whereas 

MODEL2 <- '

CA =~ CA1 + CA2 + CA3 

SS =~ SS1 + SS2 + SS3 +SS4 + SS5 

CA ~~ 1*SS '

With model 2, I am trying to set a covariation between the two variables that equaled one, representing one continuum (Lewis, 2002, p: 11 doi: https://www.jstor.org/stable/3069380?seq=1#metadata_info_tab_contents)

And then I wanted to compare the results of two CFA models through a Chi-squared test.

MODEL1.fit = cfa(MODELO1, data=DATAIND, std.lv = TRUE)

summary(MODEL1.fit, fit.measures=TRUE, standardized = TRUE, rsquare = TRUE)

MODEL2.fit = cfa(MODEL2, data=DATAIND, std.lv = TRUE)

summary(MODEL2.fit, fit.measures=TRUE, standardized = TRUE, rsquare = TRUE)

Anova (Model1, Model2)

Is that this approach correct?

In advance thank you very much for your help.

[Terrence Jorgensen]

Is that this approach correct?

Yes, but use lower-case anova(), or the lavTestLRT() function to access more arguments (usually only necessary with robust estimators).  The upper-case Anova() function in the car package is designed for other tasks.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Carolina Rojas Cordova]

Thank you very much Terrence!!!!.

Can I ask you additional questions, 

The model included four factors. Two factors (B = participative control and C = participative monitoring) represent emergent of project management and the other two (E = directive control and F = directive monitoring) represent planned style of project management. And I want to test that they are distinct yet interrelated. (As I mentioned in my previous mail). 

So according to (Lewis, 2002) to test this hypothesis, I have to test the following:

MODEL 1

- Each item was allowed to load only on the factor for which it was a proposed, and no correlations were permitted in the error structure.

 - Factors were allowed to covary within managerial activities (for example, participative (B) and directive control (E) were allowed to covary), because we proposed emergent and planned styles as offering interrelated approaches to each activity.

- Consistent with our conceptual framework, the two planned activities were allowed to covary, reflecting their tight coupling.

MODEL1 <- '

B =~ B1 + B2 + B3 

C =~ C1 + C2 + C3 +C4 + C5 

D =~ D1 + D2 + D3 

E =~ E1 + E2 + E3 +E4 

 B~~ E 

 C~~ F 

 B~~ C 

 E~~ F '

MODEL 2

Model 2 adds constraints to model 1. Specifically, we set the covariations between activities equal to one. These constraints signify that contrasting approaches comprise a single construct— for instance, that participative (B) and directive (E) control are two ends of the same continuum.

MODEL2 <- '

B =~ B1 + B2 + B3 

C =~ C1 + C2 + C3 +C4 + C5 

D =~ D1 + D2 + D3 

E =~ E1 + E2 + E3 +E4 

B ~~ 1*E 

C ~~ 1*F 

 B~~ C 

 E~~ F

'

and then we use the anova as you suggested.

I really appreciate your time, patience, and help!

Best,

Carolina 

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[Terrence Jorgensen]

B ~~ 1*E 

C ~~ 1*F 

 B~~ C 

 E~~ F

You additionally need to constrain correlations consistent with this hypothesis that B and E are the same variable, and that C and F are the same variable.  In other words, there is only 1 correlation between those 2 variables ({BE} with {CF}):

B~~ cor.label*C
B~~ cor.label*F

E~~ cor.label*F
E~~ cor.label*C

[Carolina Rojas Cordova]

thank you very much Terrence for your help!!!