I am reading a paper that is using mixed-level modelling to investigate the effect of individual (level 1) and household-level (level 2) exposures on malaria infection (level 1). 

The authors have justified their use of an MLM approach based on the ICC of the null model (intercept terms only) being statistically significant (ICC: 0.19, p = 0.046). However, I am reading in another paper - A practical guide to multilevel modelling. Peugh J. *Journal of School Psychology* 48 (2010) 85 - 112 - that "a non-zero ICC estimate does not necessarily indicate the need for multilevel analyses". 

Rather, it is, according to these authors, also dependent on the design effect:

DE = 1 + (n - 1)ICC

Where n is the average number of individuals in each cluster, which, in the paper above is 4.2. Also, in the above paper ICC = 0.19.

Using the numbers from this paper gives me a DE = 1.608.

Peugh goes on to say that "some researchers believe that design effect estimates greater than 2.0 indicate a need for MLM", which, given the values from the malaria paper indicates that an MLM approach was not needed after all.

Were the authors of the malaria paper wrong to have used an MLM approach? Could they have used traditional multivariable logistic regression modelling?