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

[Sara]

Thank you very much for your detailed explanation and the reference.

I initially thought my model specification was correct, but since I keep running into the error "Model estimation FAILED! Returning starting values", I am starting to wonder if the problem could actually be due to model misspecification rather than just the estimator or data treatment.  Can this specification of the ALT model can be considered okay?

model <- '

   
   i_drug =~ 1*drug_2000 + 1*drug_2002 + 1*drug_2004 + 1*drug_2006 + 1*drug_2008 + 1*drug_2010
   s_drug =~ 0*drug_2000 + 1*drug_2002 + 2*drug_2004 + 3*drug_2006 + 4*drug_2008 + 5*drug_2010

   
   i_dep =~ 1*depression_2000 + 1*depression_2002 + 1*depression_2004 + 1*depression_2006 + 1*depression_2008 + 1*depression_2010
   s_dep =~ 0*depression_2000 + 1*depression_2002 + 2*depression_2004 + 3*depression_2006 + 4*depression_2008 + 5*depression_2010

   i_health =~ 1*health_2000 + 1*health_2002 + 1*health_2004 + 1*health_2006 + 1*health_2008 + 1*health_2010
   s_health =~ 0*health_2000 + 1*health_2002 + 2*health_2004 + 3*health_2006 + 4*health_2008 + 5*health_2010

   drug_2002 ~ drug_2000
   drug_2004 ~ drug_2002
   drug_2006 ~ drug_2004
   drug_2008 ~ drug_2006
   drug_2010 ~ drug_2008
 
   depression_2002 ~ depression_2000
   depression_2004 ~ depression_2002
   depression_2006 ~ depression_2004
   depression_2008 ~ depression_2006
   depression_2010 ~ depression_2008

   health_2002 ~ health_2000
   health_2004 ~ health_2002
   health_2006 ~ health_2004
   health_2008 ~ health_2006
   health_2010 ~ health_2008

  
  depression_2002 ~ drug_2000
  depression_2004 ~ drug_2002
  depression_2006 ~ drug_2004
  depression_2008 ~ drug_2006
  depression_2010 ~ drug_2008
 
   drug_2002 ~ depression_2000
   drug_2004 ~ depression_2002
   drug_2006 ~ depression_2004
   drug_2008 ~ depression_2006
   drug_2010 ~ depression_2008
 
   health_2002 ~ drug_2000
   health_2004 ~ drug_2002
   health_2006 ~ drug_2004
   health_2008 ~ drug_2006
   health_2010 ~ drug_2008

   drug_2002 ~ health_2000
   drug_2004 ~ health_2002
   drug_2006 ~ health_2004
   drug_2008 ~ health_2006
   drug_2010 ~ health_2008

   health_2002 ~ depression_2000
   health_2004 ~ depression_2002
   health_2006 ~ depression_2004
   health_2008 ~ depression_2006
   health_2010 ~ depression_2008
 
   depression_2002 ~ health_2000
   depression_2004 ~ health_2002
   depression_2006 ~ health_2004
   depression_2008 ~ health_2006
   depression_2010 ~ health_2008
 
  i_dep ~~ s_dep
  i_health ~~ s_health
  i_drug ~~ s_drug
 
 i_dep ~~ i_health
 i_dep ~~ i_drug
 i_drug ~~ i_health
 
 s_dep ~~ s_health
 s_dep ~~ s_drug
 s_drug ~~ s_health
 
 i_dep ~~ s_health
 i_drug ~~ s_health
 i_dep ~~ s_drug
 
 s_dep ~~ i_health
 s_drug ~~ i_health
 s_dep ~~ i_drug