We can also say something about the variation between families we would expect 95% of families to have a mean young adult BMI of between μ − 1.96 σ u 0 2 μ + 1.96 σ u 0 2 or (16.99, 28.69). The total variance in the sample is 22.84 and so the standard deviation σ is 4.779 with a reported mean BMI of 25.38, we would expect 95% of the young adults to have a BMI of between ( μ − 1.96 σ, μ + 1.96 σ) = (16.01, 34.75).

This means that they found 39.1% of the variation in BMI in young adulthood to be attributable to the family level, with the remaining 60.9% being due to differences between young adults within families. Omitting a relevant level has consequences for the estimation of the amount of variation associated with the remaining levels.

The specification of levels is important, both from a theoretical and a statistical point of view. More variance at a higher level means that we need more observations to achieve the same power as when there is little variation at the higher level. The clustering of observations within higher level units also informs power calculations. The higher level variance estimated from multilevel logistic regression models tends to be low leading to the question as to whether this small variance is still important. This can be done by transforming the difference between the 2.5 and 97.5 centile into an odds ratio or by using the median odds ratio, both of which can be interpreted in the same way as the odds ratio of a specific fixed effect. We discuss ways of clarifying and interpreting the importance of the higher level variance in logistic multilevel regression analysis. Partitioning the variance between levels is straight forward in two-level linear models, but more complicated when we consider more than two levels or when our outcome is dichotomous. Several issues concerning variances at all levels are discussed in this chapter. The starting point of multilevel analysis is to separate the variance in an outcome into the parts that are associated with the levels we distinguish.

What does high variance in data mean