Is the DV a single 4-point item? Or is it the mean of several such items intended to measure the same thing? Only the latter would be considered a scale.

The fitted values from a linear mixed model (aka., multilevel linear model) are conditional means. So if you use that type of model, you are implicitly arguing that it is okay to report means--i.e., you are arguing that the DV has (at least approximate) interval scale properties. If you do not think you can reasonably argue that, multilevel ordinal logistic regression is another option. Try a search on , and add the name of the software you use. HTH.

Sum or average scores from Likert scale questionnaires are often treated as "quasi-continuous", which, strictly speaking, isn't correct. However, unless your score distribution is very asymmetrical, there usually aren't any substantial negative consequences of treating those scores as if they were truly continuous, especially when the scores are composed of a larger number of items. I would nonetheless recommend checking for distribution shape, outliers etc.

Bruce Weaver Thank you so much for your response. My DV's are not single 4-point items, but are transformed so that they form a score ranging from 0-100.

This is done with the following formula: score=((rawscore - 1) / 3) * 100.

In which rawscore is the 4-point item.

I will look into the multilevel ordinal logistic regression, thank you for this suggestion.

Christian Geiser Thank you for your response! When plotting my residuals, I see clearly some clusters in the plot (atleast, for some of my scores/DV's). Do you think this forms a problem in assuming the continuity?

Tamara de Haas, I think to answer Bruce Weaver 's question, it IS a four point scale, or just a linear transformation of one. 33.3 * rawscore - 33.3.