# Structural Equation Modeling with ordinal dependent variable and categorical independent variable

I'd like to do a structural equation modeling for an ordinal dependent variable. Moreover, I have ordinal and categorical independent variables in the model.

The ordinal dependent variable is the frequency of visiting parks. The ordinal independent variables are demographic variables, including age, education level. The categorical independent variables are some demographic variables. Such as gender(female, male), marriage(single, married, widowed), occupation(student, employee, retire, and unemployed).

I've learned that Mplus could deal with categorical dependent variables? But how about the categorical independent variables?

What software and method could address such issue? Thanks!

• I don't have a full answer, but to confirm that Mplus handles interval and binary exogenous variables just fine. Nominal variables such as marriage and occupation can be accommodated by dummy coding. Ordinal is the tricky part. Apr 30, 2018 at 18:29

As Patrick Malone indicates, virtually every SEM software option is going to provide you with the capacity to analyze categorical predictors, assuming you have coded them appropriately (e.g., dummy-, effect-, or contrast-coded).

Mplus is definitely one of the more feature-rich SEM software options, but there are open-access alternatives that will do what you need. The lavaan() package (Rosseel, 2012) for R, for example, can definitely accommodate both the categorical predictors and the ordinal outcome that you have.

However, depending on how many levels there are in your outcome of frequency of visiting parks, it may not be necessary to use an ordinal estimator. Rhemtulla et al. (2012) have a nice simulation paper demonstrating that with 6-7 (and sometimes as few as 5) ordinal response categories, robust maximum likelihood estimators appear to perform just fine.

References

Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373.

Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36.

• Thanks so much! The lavaan() package seems to be useful. In addition, I want to include the demographic variables as control variables in the SEM. I've got age, gender, income level, education level, and marriage. They are all derived from survey and consists of categorical levels. If I convert them into dummy variables and include them as exogenous observed variables, the model seems to be too large(35 dummy variables are included). Is it reasonable to use CFA to fit a latent variable for all demographic variables? If not, how can I deal with too much dummy variables in SEM? May 3, 2018 at 1:29
• Again, some of these might not require categorical coding (e.g., age, education level) if you have a sufficient number of levels. It seems, however, like your follow up is a bit of a different question, but my intuition is that if you posted another question about data reduction techniques using categorically coded variables, that someone would be able to offer an insightful suggestion. I don't think you want a latent variable per se, because an overarching "demographic" latent variable seems theoretically questionable. But perhaps some sort of categorical principal component? May 6, 2018 at 19:14