MIMIC using MLR/FIML with ordinal endogenous variable

[Gregor]

Hey guys,

I have the following model consisting of four latent factors f1-f4 (each with 5 manifest continuous indicators item1-item20) and one manifest endogenous ordinal variable var1 (expression 0 to 4); model see attachment. My goal is to investigate how the latent factors f1-f4 explain the variable var1.

I have specified the model as follows:

mod1 <-'

f1 =~ item1 + item2 + item3 + item4 + item5

f2 =~ item6 + item7 + item8 + item9 + item10

f3 =~ item11 + item12 + item13 + item14 + item15

f4 =~ item16 + item17 + item18 + item19 + item20

var1 ~ f1 + f2 + f3 + f4

'

fit.mod1 <- sem(model = mod1, data = data, estimator = "MLR", missing = "FIML", std.lv = TRUE)

It is important for me to use MLR/FIML as estimator. I am aware that lava an can only calculate something like this with the WLSMV estimator if I specify var1 as ordered. However, for feasibility reasons, I assume a continuous distribution of var1 and reason with Rhemtulla et al. (2012) that the MLR estimator for this is robust to violation when I want to interpret the regressions.

I am now asking myself the following questions:

1) Is this a MIMIC model, or can I only speak of MIMIC when I have more manifest endogenous variables that I am testing for correlation?

2) Have I specified the model correctly like this?

3) Does anyone know literature/have a tip for me on how I can consider var1 as an ordinal scaled variable after all and check that with lava an using MLR/FIML?

Thank a lot for help,

Gregor

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. https://doi.org/10.1037/a0029315

[Terrence Jorgensen]

I wouldn't call this MIMIC because you only have reflective indicators.  There is no exogenous predictor of any factor.

You can use estimator = "PML" with some options for missing= (see ?lavOptions).  This paper has some example syntax:

https://doi.org/10.1111/bmsp.12243

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen