Dear Rita,

   To the extent that your variable is ordinal it doesn't fit inside a lmm. That it appears to be "normal" on a histogram is not too helpful - this is conflating the apparent categories with an unobserved underlying dimension. The fact that it is described as multinomial instead of normal is less of a problem provided you have a good number of categories. There is no technical answer for how many categories as this varies from reviewer to reviewer ... but it is worth considering the state of literature in your field as you pass through 7 or more categories. That is not to suggest that it is in any way correct, just that is an occasionally accepted practice to proceed (as with pretending that likert scales are normal and continuous variates as well...)

   Returning the the question of ordinal data, this is very much a reason not to pursue a straight lmm. Sadly you will need to work with other software. If you do not have the funds (or even if you do) then investing some time with R is probably worthwhile. It may or may not be useful for you to consider the SABRE modelling package which can work with R or Stata and is very good for generalized mixed models of many types. R will certainly require a little bit of time to learn and R with SABRE even more. 

Good luck

Bonjour Rita,

Bruce is right !

Maybe you can read  the beginning of this paper to have a look of what can be expected with generalised linear mixed effects models.

https://www.researchgate.net/publication/264243006_Multivariate_Analysis_of_Longitudinal_Ordinal_Data_With_Mixed_Effects_Models_With_Application_to_Clinical_Outcomes_in_Osteoarthritis

Sabre is a well known R package, Maybe it could be a little bit difficult to begin with.

There is another R package totally devoted to the analysis of multinomial mixed effects models

https://hlplab.wordpress.com/2009/05/07/multinomial-random-effects-models-in-r/

Maybe it could be useful for you.

Good luck

Article Multivariate Analysis of Longitudinal Ordinal Data With Mixe...

Hi Rita,

I personally would also do the anylsis in R (which give you the greatest flexibility and is more user firendly than generalized linear mixed models in SPSS; see my second point), but I acknowledge that R has a very steep learning curve. In addition to the previous response, I have two questions/suggestions:

1) you say that the variable "shows a normal distribution by looking at it, but the K-S test is significant and it has categories". The K-S test is way too progressive and rejects the null-hypothesis too often if sample size is high (and "high" does not have to be 10000, I have seen false significant K-S test also with a sample size as little as 80). So if your only concern is based on a significant K-S test and your sample is large, then I would say you have no problem with the violation of the normality assumption. The question is: are there enogh categories and is there reason that the variable is distributed normally in the population? If your distribution looks normal, you have a "sufficient" number of cateogories (but see Bruce's comment that there is no clear cut number that would count as sufficient), you have theoretical reasons that the variable should be distributed normal, and your sample size is "large" (again, a very unspecific condition), you could, imho, very well ignore the significant K-S test and proceed with a linear mixed efects model.

2) If you decide that your variable should be treated as multinomially distributed, you can switch to generalized liner mixed effects models in SPSS. For an introduction into these models in SPSS see Heck et al. (2012): http://www.amazon.de/Multilevel-Modeling-Categorical-Quantitative-Methodology/dp/1848729561

Do I understad correctly that you tried this, but it didn't work? Note that you have to change the variable type of your dependent variable to ordnial for this anylsis.

Hope  that was of any help for you

Thank you for your useful answers! I attach the distribution of one of my

ordinal variables.  What is your opinion, could I use it as a normally distributed variable? Considering Andrea's second point, I have an old version of SPSS, but I will try with a newer one.

My understanding is that SPSS will estimate multinomial mixed models - see Chapter 6 of

Ronald H. Heck, Scott Thomas, Lynn Naomi Tabata (2012) Multilevel Modeling of Categorical Outcomes Using IBM SPSS

the blurb

This is the first workbook that introduces the multilevel approach to modeling with categorical outcomes using IBM SPSS Version 20. Readers learn how to develop, estimate, and interpret multilevel models with categorical outcomes. The authors walk readers through data management, diagnostic tools, model conceptualization, and model specification issues related to single-level and multilevel models with categorical outcomes. Screen shots clearly demonstrate techniques and navigation of the program. Modeling syntax is provided in the appendix.  Examples of various types of categorical outcomes demonstrate how to set up each model and interpret the output. Extended examples illustrate the logic of model development, interpretation of output, the context of the research questions, and the steps around which the analyses are structured. Readers can replicate examples in each chapter by using the corresponding data and syntax files available at www.psypress.com/9781848729568.

The book opens with a review of multilevel with categorical outcomes, followed by a chapter on IBM SPSS data management techniques to facilitate working with multilevel and longitudinal data sets. Chapters 3 and 4 detail the basics of the single-level and multilevel generalized linear model for various types of categorical outcomes. These chapters review underlying concepts to assist with trouble-shooting common programming and modeling problems. Next population-average and unit-specific longitudinal models for investigating individual or organizational developmental processes are developed. Chapter 6 focuses on single- and multilevel models using multinomial and ordinal data followed by a chapter on models for count data. The book concludes with additional trouble shooting techniques and tips for expanding on the modeling techniques introduced.

Dear Rita,

   I feel slightly silly. When you say that your software cannot calculate this model - what do you mean? That you do not know how to do so, or that there is a technical problem?

Dear Bruce,

I have meant that there was a problem with this error message: There are no valid records. I don't understand what the problem could be, I can calculate with linear mixed model with the same variables.

Dear Rita,

   Well sorry about the above posts.  I haven't used SPSS for years, but there are plenty of resources on the net for this. Ordinarily this message means that you have made a typing error / point and click error when defining your terms. 

Although this will not help with your specific SPSS problem (I am not a SPSS user) this material at the Centre for Multilevel Modelling provides a lot of background material on the ordered and un-ordered multinomial mixed model 

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#discrete

including a complete tutorial with an online course

These are the current modules that are freely available

Modules

Using quantitative data in research (watch video introduction)

Introduction to quantitative data analysis (watch video introduction)

Multiple regression

Multilevel structures and classifications (watch video introduction)

Introduction to multilevel modelling

Regression models for binary responses

Multilevel models for binary responses

Multilevel modelling in practice: Research questions, data preparation and analysis

Single-level and multilevel models for ordinal responses

Single-level and multilevel models for nominal responses

Three-level multilevel models

Cross-classified multilevel models

Multiple membership multilevel models

Missing Data

Multilevel Modelling of Repeated Measures Data

see http://www.bristol.ac.uk/cmm/learning/online-course/