I recently received a great question in a comment about whether the assumptions of normality, constant variance, and independence in linear models are about the errors, εi, or the response variable, Yi.
The asker had a situation where Y, the response, was not normally distributed, but the residuals were.
Quick Answer: It’s just the errors.
In fact, if you look at any (good) statistics textbook on linear models, you’ll see below the model, stating the assumptions: (more…)
A well-fitting regression model results in predicted values close to the observed data values. The mean model, which uses the mean for every predicted value, generally would be used if there were no useful predictor variables. The fit of a proposed regression model should therefore be better than the fit of the mean model. But how do you measure that model fit?
There are not a lot of statistical methods designed just to analyze ordinal variables.
But that doesn’t mean that you’re stuck with few options. There are more than you’d think.
Some are better than others, but it depends on the situation and research questions.
Here are five options when your dependent variable is ordinal.
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Are you learning Multilevel Models? Do you feel ready? Or in over your head?
It’s a very common analysis to need to use. I have to say, learning it is not so easy on your own. The concepts of random effects are hard to wrap your head around and there is a ton of new vocabulary and notation. Sadly, this vocabulary and notation is not consistent across articles, books, and software, so you end up having to do a lot of translating.
What do you do if the assumptions of linear models are violated?
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Interactions in statistical models are never especially easy to interpret. Throw in non-normal outcome variables and non-linear prediction functions and they become even more difficult to understand. (more…)