Nested or crossed random effect
I had this question when I was taking the Designing, Running, and Analyzing Experiments Coursera Course. So what is the difference between nested and crossed random effect and why do we care?
Refresher: What is random effect v.s. fixed effect?
In biostatistics, which is my academic background, the fixed effect is simply the population average, while random effect is the subject specific effects. According to Wiki,
- Fixed effect factor: Data has been gathered from all the levels of the factor that are of interest
- Random effect factor: The factor has many possible level, interest is in all possible levels, but only a random sample of levels is included in the data
A mixed-effects model (class III) contains experimental factors of both fixed and random-effects types, with appropriately different interpretations and analysis for the two types. The analysis of the data is different, depending on whether the factor is treated as fixed or as random. Consequently, inferences may be incorrect if the factor is classified inappropriately. Mistakes in classification are most likely to occur when there is more than one factor in the study.
For example, if we would like model the valuation of CLIP (credit line increase program) under different credit lines using mixed-effect model. The customer’s segment, credit score etc. will be the random effect, while the credit line increase amount would be the fixed effect we cared about.
Then: What is crossed and nested random effect?
Some answer can be found here
- Two factors are crossed when every category of one factor co-occurs in the design with every category of the other factor. In other words, there is at least one observation in every combination of categories for the two factors.
- A factor is nested within another factor when each category of the first factor co-occurs with only one category of the other. In other words, an observation has to be within one category of Factor 2 in order to have a specific category of Factor 1. All combinations of categories are not represented. Nesting is a property of the data, or rather the experimental design, not the model.
Finally: Why do we care?
If two factors are crossed, you can calculate an interaction. If they are nested, you cannot because you do not have every combination of one factor along with every combination of the other, which is important to consider when testing for the significance of online experiments.