Creating a composite mediator using formative approch in lavaan

[ahmad]

Hi,

I have a couple of questions regarding creating a composite factor using a formative approach in lavaan.

1. Is there a confirmatory factor analysis (CFA) for a composite approach using a formative approach, similar to a reflective approach?
2. Is the following CFA model with binary indicators using a formative approach correctly specified? 
Model <- '
  risk <~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8

risk ~~ 1*risk

'
cfa(Model, data, ordered = TRUE)
3. Can I use this model as is in a structural model as a mediator when I have latent independent variables (IVs) and dependent variables (DVs)?
Best wishes,
Ahmad

[Jeremy Miles]

On Tue, 13 May 2025 at 12:45, ahmad <valik...@gmail.com> wrote:

Hi,

I have a couple of questions regarding creating a composite factor using a formative approach in lavaan.

1. Is there a confirmatory factor analysis (CFA) for a composite approach using a formative approach, similar to a reflective approach?

I'm not exactly sure what you mean. Not really - composite measurement models are generally saturated (that is, they have zero degrees of freedom) so there's nothing to test.

 

2. Is the following CFA model with binary indicators using a formative approach correctly specified? 
Model <- '
  risk <~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8

risk ~~ 1*risk

'

That model is not identified. You have fewer than zero degrees of freedom.  

You need some exogenous variables to identify the model.

Here's a full example :

library(dplyr)

library(lavaan)

set.seed(420)

n <- 1000

d <- data.frame(

x1 = rnorm(n),

x2 = rnorm(n),

x3 = rnorm(n),

x4 = rnorm(n),

x5 = rnorm(n),

x6 = rnorm(n)

) %>%

dplyr::mutate(

risk = x1 + x2 + x3 + rnorm(n),

y1 = rnorm(n),

y2 = rnorm(n)

) %>% dplyr::select(-risk)

Model <- '

risk <~ x1 + x2 + x3 + x4 + x5 + x6

risk ~~ 0 * risk

risk =~ y1 + y2

y1 ~~ 0 * y2

y1 ~~ 1 * y1

y2 ~~ 1 * y2

'

fit <- lavaan::lavaan(Model, data = d)

print(summary(fit))

 

cfa(Model, data, ordered = TRUE)
3. Can I use this model as is in a structural model as a mediator when I have latent independent variables (IVs) and dependent variables (DVs)?
Best wishes,

Not really. 

Your model looks like (I didn't draw all of the X variables):

There isn't really any distinction between the IV(s) and the x variables. With a single DV this is saturated and is the same as a regression model (if you add the correlations between Xs and IV, and you'd need a really good reason not to*). 

With a second DV you gain some more degrees of freedom, but there's no mediation going on - you have a multivariate regression with restrictions (or a MIMIC model). 

Hope that helps,

Jeremy

* And I can't think of a reason good enough.