|Multi-level and agent-based models: comparison and integration|
Multilevel models (MLM) have pioneered the analysis of data that have a hierarchical structure with two or more 'levels'. They have been developed within a statistical paradigm, primarily as a method of describing and analysing large data-sets. Agent-based models (ABM) are also used to analyse social phenomena in which are there are two or more 'levels' involved, often called the micro- and macro- levels. ABM were developed from a non-statistical background, drawing on artificial intelligence and physics. Agent-based modelling usually follow a deductive or abductive methodology, testing a model against data, while multi-level modelling is often inductive, deriving a model from data. MLM allow the user to make inferences with known confidence, which is generally not true of ABM, while ABM are capable of modelling non-linear, complex systems with emergent behaviour. Thus to some extent the two modelling 'paradigms' are interested in the same kind of issues but approach them from entirely different directions and have different strengths. The aim of this short study is to clarify the similarities and differences between the two styles of modelling, attending to the modelling of levels, and to investigate whether there is value in the integrating some aspects.
There are a few papers comparing the merits of 'equation-based models' and ABM, but none compare MLM with ABM.
To provide a basis for the comparison, we shall take a well-known example data set, the Inner London Education Authority (ILEA) school effectiveness data consisting of examination records from 140 secondary schools in years 1985, 1986 and 1987 for which a MLM has been well studied, and attempt to build an ABM based on this MLM that reproduces the data adequately.