Modeling manifest covariates

[Niels]

Hi lavaan-users!

I have two questions. Let me use a modified version of the lavaan-example (http://lavaan.ugent.be/tutorial/sem.html) for demonstration.
In this case, ind60 is a second-order-factor. Also, i added a manifest variable "age" as preditor.

model <- '
  # measurement model with ind60 beeing a second-order-factor.
    Firstorder1 =~ x1 + x2 + x3 
    Firstorder2 =~ x4 + x5 + x6
    Firstorder3 =~ x7 + x8 + x9  
    Firstorder4 =~ x10 + x11 + x12
    ind60 =~ Firstorder1 + Firstorder2 + Firstorder3 + Firstorder4
    dem60 =~ y1 + y2 + y3 + y4
    dem65 =~ y5 + y6 + y7 + y8

 # regressions
    ind60 ~                 age    
    dem60 ~ ind60         + age
    dem65 ~ ind60 + dem60 + age'

1.) If i want to add a manifest variable ("age") as a covariate in my SEM, should i just use it as predictor for the endogenous latent variables (dem60, dem65), or also for the other predictor variable (ind60)?  My guess would be, to add a path to every latent variable, predictor or not (ind60, dem60, dem65 in the example). This would also be in line with my theory.
2.) My structural equation model involves a second-order-factor as predictor. Inspecting the residual-matrix i found out, that the relationship of age and the indicators of one first-order-factor is higher than in the estimated model. That is a source of model-misfit i got after adding "age". How do i model a covariance between the manifest variable "age" and the Factor "Firstorder1"? Or if this isn´t possible: How do i estimate covariances of age and x1-x3?

Thank you for any advice!

[Terrence Jorgensen]

1.) If i want to add a manifest variable ("age") as a covariate in my SEM, should i just use it as predictor for the endogenous latent variables (dem60, dem65), or also for the other predictor variable (ind60)?  My guess would be, to add a path to every latent variable, predictor or not (ind60, dem60, dem65 in the example). This would also be in line with my theory.

If that is your theory, then that should be your model.  Excluding the effect of age on ind60 probably would not change age's estimated effects on dem60 or dem65 -- either way, they would be the effects of age holding ind60  constant.

2.) My structural equation model involves a second-order-factor as predictor. Inspecting the residual-matrix i found out, that the relationship of age and the indicators of one first-order-factor is higher than in the estimated model. That is a source of model-misfit i got after adding "age". How do i model a covariance between the manifest variable "age" and the Factor "Firstorder1"? Or if this isn´t possible: How do i estimate covariances of age and x1-x3?

How about regressing Firstorder1 on age (like you would in a MIMIC model that tests DIF/invariance across levels of age).

Terry

[Niels]

Hi Terrence,

thank you for your answer.
You´re right, it makes sense to use age as a predictor for the Firstorder-latent (because i also used it as predictor for the second-order-factor) and my model fit went back to the good fit it had before i added the covariate.
Niels

[Jessica Fritz]

Hi everyone,

I placed my question over to this chat because I felt that it would fit much better here.

I tried to inlcude a covariate in my mediation model. Thus I want to correct the whole model (all mediation pathes: a,b and c) with the same covariate. I thought that I simply could add the covariate as 'second predictor' to the model, because I thought that this would be the same as running three regressions instead of 1 SEM, includign the covariate respectively in each regression.

In contrast to Niels model I do not include a prediction of  Xvar from the covariate, because this would not make sense given that mediation implies a causal timeline and my covariate was timewise assessed after assessing Xvar. But the model still includes a correlation between Xvar and the covariate (by default). So I think that the relationship between Xvar and the covariate is still taken into account in my model.

QUESTION: But I am wondering whether my model is too simple and whether I need to incorporate the covariate into the calculation of the indirect and the total effect, as well?

So far I used the following script:

Model <-'Yvar ~ c*Xvar
Mvar ~ a*Xvar
Yvar ~ b*Mvar
Yvar ~ covariate
Mvar ~ covariate
ab := a*b
total := c + (a*b)'

Thank you for your help,

Jes