multilevel model. Dependent variable is not truly interval

noetsi

Fortran must die
#1
I want to run multilevel regression. My dependent variable is a four point likert scale variable (as are predictors in most cases). Can you run multilevel models with a DV that is not classically interval (of course some argue likert scale is effectively interval, but for the moment I am not going there).

It would help if you can not readily do multilevel modeling with a 4 point DV to know what can analyze this. I am testing the result of area on satisfaction.
 

hlsmith

Not a robit
#3
For MLMs I really like the "Multilevel Models: Applications Using SAS book by Wang et al. It covers MLM multinomial models on page 147. I always find it hard to believe, but over the years I still have not conducted a multinomial logistic reg model. I know SAS also has a MLM book they print, which may have been updated in the recent years. I would imagine that book should cover the topic as well.
 

noetsi

Fortran must die
#4
thanks hlsmith. If your data is ordered will it create problems using multinomial (I believe not from my knowledge of logistic regression, but I have been wrong before).

I will look for both books. If I run this and send the results with my comments would you tell me if I interpreted it correctly :p
 

hlsmith

Not a robit
#5
I can try to help the best I can. The ordering shouldn't be a big issue as long as you select the right reference group - I think.
 

noetsi

Fortran must die
#6
I was wondering today how serious a problem it would create if I treated a 4 point likert variable as interval and used interval multilevel. Probably one of those questions no one agrees on.
 

noetsi

Fortran must die
#7
Ok I have a different question. OLS regression is very common including among academicians. But MLM modeling argues essentially that if something can be nested inside something else then they will generate errors. That is the chance of getting a type 1 or type 2 error is much greater. My question is how you know when this is a problem or not. They do linear regression in my area (vocational rehabilitation) yet virtually all data is going to be nested (customers inside units inside areas).

How do you know if the linear method is valid in this case, as compared to having to use multilevel models. I am not sure statistical test are valid period in honesty because I usually have at least 60 percent of the data and often 100 percent.

To make things more confusing to me what I am interested in is the nesting inside areas. There are only 7 of these. Based on this comment I am not sure it is even valid to analyze this few groups with multilevel data.

"Guidelines for sample-size requirements and their implications for model complexity, the regression coefficients, variance components, and their standard errors are given in various studies and texts. For example, models with fewer than 20–25 groups may not provide accurate estimates of the regression coefficients and their standard errors, or of the variance components and their standard errors."

https://ies.ed.gov/ncee/edlabs/regions/northeast/pdf/REL_2015046.pdf

I do have a lower level called units, but no one cares about units and there are issues because some units overlap each other while being administrative separate.
 
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noetsi

Fortran must die
#8
This is the type of comment that drives me crazy. It is in the context of multilevel models. To me it suggest that, ignoring issues of standard errors, you can hardly use OLS for issues that involving variables nested inside others.

"Traditionally, researchers tended to use model results at one level to draw statistical inference at another level [individual to group]. This has proven incorrect. The results from the two single level models frequently differ either in magnitude or in sign. The relationships found at the group level are not reliable predictors for relationships at the individual level. "

Individual variables are variables that operate at the individual level, group variables operate at a higher level like a school. So my question would be, ignoring wrong SE which can be dealt with by robust SE, can you run OLS with variables where some variables are nested inside others like person in school. I know this is done a lot - formally it violates independence. But does it seriously bias the results?

And if it does does this mean all OLS with a variable that can be placed in a hierarchy is wrong? :p

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