ALT model with mixed variables

[Sara]

Hello,

I am trying to estimate an Autoregressive Latent Trajectory (ALT) model in lavaan.
My data include:

• one continuous variable,

• one categorical variable with 5 ordered categories,

• one binary variable (0/1).

I first tried to treat the binary as ordered,  keeping the remianing variables as continuous. I attempted to estimate the model using both estimator="DWLS" and estimator="WLSMV", but the model does not run (I get estimation errors).

So, I specified all variables as continuous and used estimator="ML". In this case the model runs and converges.

 Is it acceptable to proceed with ML treating the ordinal/binary variables as continuous in this context, or does this create serious problems for the validity of the ALT estimates?
Thank you very much in advance for your help

[Terrence Jorgensen]

I attempted to estimate the model using both estimator="DWLS" and estimator="WLSMV"

If you declared any variables as ordered=, this is superfluous because lavaan sets the estimator by default.  The option estimator="WLSMV" is a shortcut for 3 arguments:

• estimator = "DWLS"
• se = "robust.sem"
• test = "scaled.shifted" 

Again, this is the default behavior whenever any endogenous ordered= variables are modeled.

So, I specified all variables as continuous and used estimator="ML". In this case the model runs and converges.

This can yield similar standardized solutions for 5-category data, but MLM (or MLR, if you need missing = "FIML") is recommended because discrete data can only approximate normality, so SEs and tests should be corrected.

 Is it acceptable to proceed with ML treating the ordinal/binary variables as continuous in this context

Not for binary data.

If you haven't already read this, it is highly informative about how you identify your latent growth parameters for categorical data:

https://doi.org/10.1017/psy.2024.23

Terrence D. Jorgensen    (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen