I am examining the effect of daily work-family conflict on daily enacted incivility. None of my data is normally distributed.
1) Do your predictors and criterion need to be normally distributed when conducting multilevel modeling on daily data?
2) I am planning to standardize my predictor variables so that the data is normally distributed.
I am using maximum scores for enacted incivility as opposed to the mean for each person and as a result I don't think it makes sense to standardize those scores. Is it problematic then that the criterion variable (enacted incivility) will not be normally distributed but the predictors will be normally distributed?
Hi Alex, similar to regression, the assumptions for linear multilevel models are generally about the residuals, not about the variables used in the models themselves. Introductory texts will generally outline the assumptions for you. Standardizing doesn't actually change the distribution, just the scaling, so that's not going to matter. It might make it harder to interpret your results because you lose the interpretation in the original metric of the predictor variables. Without knowing your underlying distributions, I am not sure how using the maximum scores for each subject might affect the distributions as compared with the means. Typically, multilevel modeling software uses empirical Bayes shrinkage estimators, which can produce less extreme residuals in linear multilevel modeling than you might get with linear regression modeling.
If, for example, this maximum score thing, gives a very skewed distribution, you might actually have something that fits a specific non-linear model (hierarchical generalized linear model or generalized linear mixed model) which has a link function, such as a Poisson model or a negative binomial. All of these (plus model assumptions, EB shrinkage estimators, and working with residuals) would be treated in a thorough introductory text such as Raudenbush SW and Bryk AS (2002; Sage); there are several others, such as Snijders and Bosker. In terms of using the outcome variable and predictors you describe, if you use a linear model and assumptions about the residuals are not met, typical transformations of the variables (logs, squaring, all that) can be useful to help meet the assumptions about the residuals. For more help, see the multilevel listserv: http://www.jiscmail.ac.uk/lists/multilevel.html Bob
As Robert reports - the key issue is the distribution of the response given the predictors, so the assumption is about the residuals not the response. There are a range of informal diagnostics around ( see volume 1 below).If the data are counts then you should think about the Loge response and Poisson/NBD family of models for the level 1 distribution (see volume 2) below). Iif there is non-normal continuous data, then try the rankit of the response to see if the conclusions change (the rankit is based on the normal score of the ranks; see http://en.wikipedia.org/wiki/Rankit)
Kelvyn Jones, VS Subramanian Book: Developing multilevel models for analysing contextuality, heterogeneity and change using MLwiN, Volume 1
Kelvyn Jones, VS Subramanian Developing multilevel models for analysing contextuality, heterogeneity and change using MLwiN, Volume 2
Both volumes are on Research Gate
To gauge the effects or non-normality the following is worth reading
Cora J. M. Maas and Joop J. Hox (2004) Robustness issues in multilevel regression analysis Statistica Neerlandica (2004) Vol. 58, nr. 2, pp. 127–137
Hello Dr. Brennan and Dr. Jones,
Thank you both for your detailed responses. My knowledge of multi-level modeling is still limited. I am reading up on the sources you suggested. Thank you very much!
Alex
Dr Brennan,
I tried to access the multilevel listserv but it is telling me I need a username and password. Is there any way I can access it?
Thanks!
Alex
I have a data set with an exponentially distributed outcome variable including values of zero. Is there a way to fit a linear mixed model to this data?
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