An issue with you data is that is is made up of summing answers to sets of questions. There are specific mixed models to deal with this type of problem that come under the label of Item Response Theory (altough it is not a theory but a model). In a mixed model you would see each question as nesting in each individual and the answers could be binary or ordinal. It is then possible to to have a three -level model with occasions nested with response nested with inidividuals to study change in the underlying trait your are trying to measure.  An easy to implement (but for some a rather restrictive) version of this model is called the Rasch model. Have a look at

Item Analysis by the Hierarchical Generalized Linear Model

http://onlinelibrary.wiley.com/doi/10.1111/j.1745-3984.2001.tb01117.x/abstract

and

http://www.ssicentral.com/hlm/techdocs/SM03.pdf

and

https://www.researchgate.net/publication/237544153_A_REPEATED_MEASURES_MULTILEVEL_RASCH_MODEL_WITH_APPLICATION_TO_SELF-REPORTED_CRIMINAL_BEHAVIOR

and

http://apm.sagepub.com/content/30/2/100.refs

The first one makes the essential link between IRT  and mixed models

Sorry for complicating things!

Article A REPEATED MEASURES, MULTILEVEL RASCH MODEL WITH APPLICATION...

GLIMMIX Procedure is recommended by SAS to deal with data basically violating three major classical assumptions of OLS for example autocorrelation, heteroskedasticity, normality. So, you can try to see if it improves the results.

But I think non normality is very difficult to correct from the model, unless you can take care of the reason why your data is not normally distributed which might be outliers or missing data.

Thanks for your response. The data is not normal because it ranges between 0 and 8 although the majority of answers are towards the lower bound (0,2). 

Proc mixed uses maximum likelihood not OLS so missing data isn't a problem here. As far as I can see any way. So my only concerns are that the variances and covariances can be modelled by one of the covariance structures in proc mixed (which they can!) and that the data is normally distributed. But it is positively skewed.

I'll see if I can make any improvements using GLIMMIX, thanks!

Hi Emily,

I am glad to help you. I think social studies like survey are very often not normally distributed, because people's opinion varies greatly. So, your best choice would be statistical tools (not regression) without need of normality, for example Mann-Whitney test, Kruskal-Wallis test, One-sample sign test, Levene's test and so on. In my opinion, linear parametric regression or even nonlinear cannot really predict people's behavior, which is illogical due to their limited rationality and opportunism bounded by information asymmetry unless you have a mind reader tapped into their brain to get some concrete data like certain brain waves related to behavioral changes (at least inconclusive for now).

I am referring to this website which will help you tremendously:

http://www.isixsigma.com/tools-templates/normality/dealing-non-normal-data-strategies-and-tools/ 

I am also quoting SAS exact words, "GLIMMIX can address data not necessarily normally distributed". So you can see the tone is not quite strong, because data without normal distribution often means results are biased in regression analysis, which is difficult to adjust as I stated within the model but possible outside in the sample itself.

Since majority of your answers are toward (0, 2), can you test with and without higher outliers if you really want to run regression?

No there are no outliers. Data is just clustered toward 0. So majorioty at 0, next highest at 1, etc.. Also since we are talking about survey response, they are discrete variables, throwing away higher values would be throwing away the most important data. I had a look at GLIMMIX. It looks promising, just trying to figure out how to use it for repeated measures. 

For repeated measure, please refer to this post:

http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_sect018.htm

https://communities.sas.com/message/145049

That's why I do not recommend parametric regression analysis on any kind of social or medical or life-science studies particularly survey or drug-trial. If you really want to run regression, you have to consider both mathematical efficiency and practical meaningfulness. It's the same logic if you should consider p-value larger than 0.05 insignificant for coefficient estimates or hypothesis tests. Please read the post directly above your last post and check out other alternative statistical tests on the website for non-normally distributed data. You can compare them with your regression analysis to get a more comprehensive picture of the data.

I 100% agree with Paul on his recommendation of CTA analysis. Thank you for providing so many invaluable references. In my research, linear model often does not work very well due to violations of classical assumptions (normality, autocorrelation, heteroskedasticity). Therefore, I am always seeking for more dynamic and stochastic non-linear models. In my opinion, residuals play the key role in modeling and you have to use the appropriate approaches for different types of data such as cross-sectional, panel, time series. For example, GARCH and VAR work significantly better than ARMA to catch volatile behavior. I think any kind of model should serve the purpose of research objectives and its unique context rather than the opposite.

You could also consider an ordered logistic regression or a count model. If most of the responses are near zero modeling the outcome as discrete seems like a good thing to try.

An issue with you data is that is is made up of summing answers to sets of questions. There are specific mixed models to deal with this type of problem that come under the label of Item Response Theory (altough it is not a theory but a model). In a mixed model you would see each question as nesting in each individual and the answers could be binary or ordinal. It is then possible to to have a three -level model with occasions nested with response nested with inidividuals to study change in the underlying trait your are trying to measure.  An easy to implement (but for some a rather restrictive) version of this model is called the Rasch model. Have a look at

Item Analysis by the Hierarchical Generalized Linear Model

http://onlinelibrary.wiley.com/doi/10.1111/j.1745-3984.2001.tb01117.x/abstract

and

http://www.ssicentral.com/hlm/techdocs/SM03.pdf

and

https://www.researchgate.net/publication/237544153_A_REPEATED_MEASURES_MULTILEVEL_RASCH_MODEL_WITH_APPLICATION_TO_SELF-REPORTED_CRIMINAL_BEHAVIOR

and

http://apm.sagepub.com/content/30/2/100.refs

The first one makes the essential link between IRT  and mixed models

Sorry for complicating things!

Article A REPEATED MEASURES, MULTILEVEL RASCH MODEL WITH APPLICATION...

Along with non-normality unequal variance may also be an issue for your data. If you prefer to go with "Proc Mixed", power transformatioin may be useful. You may sought an appropriate power transformation through checking residuals. It will be trail and error type approach. Finally, you will need to bring your all necessary estimates back to original scale.