[R-sig-ME] Is it ok to use lmer() for an ordered categorical (5 levels) response variable?

[Pierce, Steven]

Again, I never said the sum scores were the right choice. That was why I recommended a measurement methodology based on using confirmatory factor analysis in my first message. If such a CFA model is estimated via methods appropriate for binary indicator variables and the model fit is adequate, you can compute meaningful factor score estimates of the latent variable from the model results. Such factor score estimates have different properties than either the raw, item-level responses or the sum of the binary items. That should make the factor score estimates more appropriate for use in a mixed model than the sum scores would have been. I further pointed out that solving the entire problem within a structural equation model framework would be better than just saving out the factor score estimates and treating them as an observed variable. 

Neither you nor Harold have (a) made a principled argument about how using CFA and SEM would be flawed, or (b) suggested a better approach. Instead you've criticized a minor point where I acknowledged a similarity between how the scores Nicolas had described were constructed and a commonly-used but flawed approach to measurement in the social sciences. I only mentioned that similarity as a bridge to suggesting the CFA approach that more statistically rigorous social scientists have developed for translating binary item-level data into decent measures of theoretical constructs. 

If you have specific suggestions for better methodology, I'd like to hear them. 

Steven J. Pierce, Ph.D.
Acting Director; Associate Director
Center for Statistical Training & Consulting (CSTAT)
Michigan State University

-----Original Message-----
From: Stuart Luppescu <lupp using uchicago.edu> 
Sent: Wednesday, March 6, 2019 9:03 PM
To: r-sig-mixed-models using r-project.org
Subject: Re: [R-sig-ME] Is it ok to use lmer() for an ordered categorical (5 levels) response variable?

On Wed, 2019-03-06 at 16:49 +0000, Pierce, Steven wrote:
> Many researchers refer to a survey instrument as a scale, refer to
> the sum of the items from such an instrument as a scale score, then
> go on to use such scores in their research. That's the sense in which
> I am using the term scale score. It's obviously a looser, more
> informal usage than you prefer but that doesn’t mean I'm wrong. It's
> an empirical fact that lots of people use the term the way I did. 

I'm with Harold Doran on this one (not for the first time by any
means). Just because a lot of people do it doesn't have anything to do
whether it's a good method or not. When I was in graduate school a long
time ago we learned that the numerical codes associated with the
response categories for survey data are category labels, nominal data,
not numeric data. And as such it is not appropriate to do arithmetic
(such as calculating sums and means) on them.
-- 
Stuart Luppescu
Chief Psychometrician (ret.)
UChicago Consortium on School Research
https://urldefense.proofpoint.com/v2/url?u=http-3A__consortium.uchicago.edu&d=DwIGaQ&c=nE__W8dFE-shTxStwXtp0A&r=91SB6keVyEb7FtX7ZipxyQ&m=wu_gseOOQ6GxLdRbKFj3lZ-oY6-ir99D2ZwFW9FqwNY&s=u_SaGEXn3sueWiFNbjnsoCpPAOGD9xbBkgxy5uw9GFY&e=

lupp using uchicago.edu