multilevel model with dependent ordinal value(Likert scale) and longitudinal data

[SangWon Choi]

Hello everyone,

i am handling the data with Likert scale(Survey data) and i have to use multilevel model with the data.

In case of the multilevel model with dependent ordinal value(Likert scale), i know that i have to use -meologit-

And in case of the multilevel model with the longitudinal data , i know that i have to use growth model

But in case that i have to use the multilevel model with dependent ordinal value(Likert scale) and longitudinal data,
which model and code do i have to use? is there any link function in -mixed-??

I think it is inappropriate just to use growth model because Likert scale isn't continous value.

Thank you in advance.

[Joseph Coveney]

which model and code do i have to use? is there any link function in -mixed-??

-mixed- doesn't have any option for a link function, but If you have a Likert scale, then you'd sum (or average) the individual ordered-categorical questionnaire items at each observation time point and you could look into using -mixed- on their sumscores. On the other hand, if you have only a single ordered-category outcome variable with relatively few categories, especially if you observe floor and ceiling effects, then you probably won't want to try fitting a linear mixed model to your data.

You could look into using -meologit- (or -meoprobit-), as you already have discerned. If you're that interested in emulating a latent growth model, then you could include a random slope. I think that the command's help file illustrates a use case having a random intercept and slope, but if not, then you can see one in action below. (Begin at the "Begin here" comment; the first part is just to create a toy dataset for illustration. I'm assuming that you don't have a complex survey,)

.ÿ
.ÿversionÿ17.0

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.ÿclearÿ*

.ÿ
.ÿseedem
setÿseedÿ820843297

.ÿ
.ÿquietlyÿdrawnormÿinterceptÿslope,ÿdoubleÿcorr(1ÿ-0.25ÿ\ÿ-0.25ÿ1)ÿn(3000)

.ÿgenerateÿintÿpidÿ=ÿ_n

.ÿgenerateÿbyteÿtrtÿ=ÿmod(_n,ÿ2)

.ÿ
.ÿquietlyÿexpandÿ3

.ÿbysortÿpid:ÿgenerateÿbyteÿtimÿ=ÿ_n

.ÿ
.ÿsummarizeÿtim,ÿmeanonly

.ÿgenerateÿdoubleÿxbuÿ=ÿinterceptÿ+ÿ(timÿ-ÿr(mean))ÿ*ÿslopeÿ/ÿr(mean)

.ÿ
.ÿlocalÿcutsÿ`=invnormal(0.25)'ÿ0ÿ`=invnormal(0.75)'

.ÿgrologitÿxbu,ÿgenerate(out)ÿcuts(`cuts')ÿprobit

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿsummarizeÿtim,ÿmeanonly

.ÿgenerateÿdoubleÿctiÿ=ÿtimÿ-ÿr(mean)

.ÿmeoprobitÿoutÿi.trt##c.ctiÿ||ÿpid:ÿcti,ÿcovariance(unstructured)ÿnolog

Mixed-effectsÿoprobitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ9,000
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿ3,000

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Logÿlikelihoodÿ=ÿ-11531.327ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.8986
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ÿÿÿÿÿÿÿÿÿÿÿctiÿ|ÿÿ-.0109173ÿÿÿ.0241896ÿÿÿÿ-0.45ÿÿÿ0.652ÿÿÿÿ-.0583281ÿÿÿÿ.0364935
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ÿÿÿÿÿÿÿÿÿ/cut1ÿ|ÿÿ-.6491915ÿÿÿ.0343569ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-.7165299ÿÿÿ-.5818532
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---------------+----------------------------------------------------------------
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ÿÿÿÿÿÿÿvar(cti)|ÿÿÿ.1480947ÿÿÿÿ.034318ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0940352ÿÿÿÿ.2332322
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pidÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿcov(cti,_cons)|ÿÿ-.1118914ÿÿÿ.0309773ÿÿÿÿ-3.61ÿÿÿ0.000ÿÿÿÿ-.1726058ÿÿÿ-.0511769
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LRÿtestÿvs.ÿoprobitÿmodel:ÿchi2(3)ÿ=ÿ1137.03ÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

Note:ÿLRÿtestÿisÿconservativeÿandÿprovidedÿonlyÿforÿreference.

.ÿ
.ÿexit

endÿofÿdo-file


.

You could also try generalizing the latent growth model case included among the examples for -sem- to an ordered-categorical outcome variable with -gsem-, but setting it up, including all of the constraints, would be involved.

[SangWon Choi]

Thank you for your reply Mr. Joseph Coveney


It would be better for me to explain more about my data and hypothesis.

here are 2 questions.

1.
I have a survey data 2008~2018 which include respondents' age, district, how they think about social safety(dependent variable, ordinal one 1~5) ---> these are level 1 data

And in the case of level 2, I have a population decrease rate of the district, crime rate of each district.

If I hypothesize like below, What command I should use and how???

"The more population decrease rate of the district, the more people feel safe"

In my opinion,
If It is okay to handle my dependent variable as a continuous variable because it is can be seen as a number, i think i just can use mixed.

But it is not,then maybe i have to treat them as order logit data.


2.
I've learned that if I want to use a growth model, there would be a time-variant independent variable in level-1.

But what I want to see is level 1 dependent variable's change according to other level1's and level 2's change yearly.

is it okay to use the growth model in this case also??

in other word, it would be a kind of panel with hierarchy data

Thank you very much in advance.

[Joseph Coveney]

If I hypothesize like below, What command I should use and how???

"The more population decrease rate of the district, the more people feel safe"

Are you following each person over 10 years? How do you manage respondents' moving out (or in, or between districts)? Or is the question posed to a different (perhaps overlapping) group of respondents more or less randomly polled each year from within each district?

Anyway, you might be better off looking at what others in your field of inquiry have done in similar observational studies to yours. If it were me, I'd probably just plot change in population, change in crime rate and change in average response (or average change in response if you're tracking each person over time) for each district in a SPLOM separately for each year, and then combine the SPLOMs to see if the pattern of association, if any, between the three phenomena holds up over the nine years of follow-up. Naïve, I know, but that's how I'd approach your research question, at least initially.