10. Modeling Contextual Effects
Goal of exercise is to engage user to understand the importance of and difference between random and fixed effects.
Below are two statements. For each statement, select whether the appropriate strategy is fixed or random.
The researcher wishes to quantify the association between density of fast food restaurants in a neighborhood and individual BMI.
Answer: Random. A multilevel model with neighborhoods specified as a random effect is required as specifying neighborhoods in the fixed part of the model (i.e., treating them as variables as opposed to levels) will consume all degrees of freedom not permitting an estimation of the effect of neighborhood fast food density..
The researcher wishes to ascertain the effect of individual SES on individual BMI.
If Random is selected:
Either could be correct based on the following. There is an implicit assumption that there are other factors at the neighborhood level that are also important for explaining variation in BMI. We also assume that such effects are not correlated with the fixed part in any systematic manner. The model provides high degree of efficiency, however there is a possibility of bias.
If Fixed is selected:
Either could be correct based on the following. Specifying neighborhoods as a fixed effect implicitly assumes that neighbors are primarily confounders to the individual SES-BMI relationship. This strategy can be extremely inefficient as with the presence of lots of neighborhoods these need to specify as dummy variables. However, if the assumption of neighborhoods as confounders is true, the effect of SES is less biased.
The choice of fixed or random (multilevel) should be based on substantive target of inference, and with an eye on the potential trade-offs between statistical efficiency and statistical bias.