Within HLM, there are two ways of reporting an analysis of the data depending upon the aims of the research. Unit-specific models attempt to describe how the affects of independent variables vary across the particular units. The value of a random effect is held constant as the results are compared from unit to unit. The scale of the interpretation is limited to the groups and levels of the study and does not attempt to expand beyond that.
Population average models are used for estimating probabilities for the entire population. The random effect is averaged, and the results of it are looked at over the population as a whole. The statistical interpretations derived from the study are not limited to the subjects and groups involved in the study but are extrapolated to include a much larger group.
Statistically, unit-specific results are more sensitive to the specifics of the research design and make more assumptions about the variables and the data. Erroneous assumptions about variable effects and distributions may distort results in unit-specific models. Population average models rely on fewer assumptions, so they usually have stronger standard error measures.
The unit-specific approach is appropriate when you look at how particular independent variables affected dependent variables in specific locations or groups. For example, how class size and student socioeconomic status, or SES, affected the probability of grade repetition in local schools would probably be reported using the unit-specific model. The population average model would be appropriate if you were seeking to make predictions regarding how a variable would have the same effects across the nation.