Say I would like to use species as the random-effects term in the model. I have 800 species in total. Among them, 600 species have only one record, 100 have 2-4 records, and 100 have 5-15 records (to be more specific with the example, let's say 70 have 5-10 records, and the rest 30 have 11-15 records). Therefore, in this case, the number of levels of a grouping factor for the random effects is close to the number of observations -- would it generate a statistic problem because there is only one observation in most levels?
Is there a point that I "should" or "shouldn't" treat species as the random-effects term in this case?
This style of data is quite common in data sets compiled from literature, i.e. the majority of species are studied just once while a small portion of species have been studied over and over in different papers. Also, this data style is possible when you want to treat genus as the random effects, for example this paper -- see the 2nd paragraph on page 325 ( https://doi.org/10.1017/S0960258518000090).
Let's think about an extreme case that data record is used as the random-effects term and there is only one record in each level. Then, R will print a note: "Number of levels of a grouping factor for the random effects is equal to n, the number of observations". In this case, it is NOT a nested design, and there is no group. GLMM gives the same result as GLM in this extreme case. Is my understanding correct?
Many thanks!
I think it's not a problem.
Actually, to account for the notorious overdispersion in GLMM, people often add an observation-level random effect (OLRE) to a model. This is exactly the extreme case you mentioned. So, techinically, the model can run without problem with such random effect.
You mentioned that 'In this case, it is NOT a nested design, and there is no group. GLMM gives the same result as GLM in this extreme case. Is my understanding correct?'. This is not the case, after adding the observation-level random effect, you can imagine that you have 'two types of residuals' (one is the true residual, the other is the random effect) in the model. Then the GLMM gives a silightly different result with GLM.
As an example, you could try:
------------------------------------
set.seed(1001)
dat
思聪大师！今天刚好看到，说下我对这个问题的理解哈哈！
混合模型的实质就是要处理同属一个group水平的不同数据的彼此不独立性问题。所以
1）对于一般的混合模型，如果每个group只有一个数据，那么是否设置group为随机因素对结果没有任何影响，因为这种结构的数据根本不存在同属一个group level的不同数据这一问题。
2）对于广义混合模型，如果如果每个group只有一个数据，这时候设置group为随机因素可以处理数据的过度离散问题（但这一原理我没彻底搞明白）。
3）但对于你提到的实际数据结构，确实需要将group设置为随机效应，这也是混合模型的核心所在。混合模型并不要求每个group水平内的数据量相等，是都多少个都无所谓，只不过样本量越大的水平，将来在参数估计中发挥的作用就越大而已。
- Badges
- Science topic
- Similar topics
- Correction