The Dictionary of Human Geography

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new norms into the international system and

thereby added a further dimension to multilat-

eralism (see alsocosmopolitanism). Argu-

ments about humanitarian intervention in the

face of state failure and environmental disas-

ters have suggested a more activist stance for

international institutions in the face of human

suffering, and in the process challenged the

UN norm of non-intervention. Advocates

insist that all states have a responsibility to

protect their citizens and that, in extreme

cases when they obviously fail to do so, inter-

vention from abroad is justified (International

Commission on Intervention and State

Sovereignty, 2001): a claim that is controver-

sial precisely because it overrides the territorial

integrity principle of the UN.

Simultaneously, in the aftermath of 11 Sep-

tember 2001, the Bush administration in the

USA frequently preferred to act alone in a

unilateral manner, and refused multilateral

co-operation on such matters as the Inter-

national Criminal Court and the Kyoto Proto-

col on climate change. This stance makes

multilateral action more difficult on many

issues, and yet, given the increasing number

of international agreements on numerous mat-

ters, multilateralism as a foreign policy ap-

proach has now become a widely accepted

and routine diplomatic practice. But in the

process territorial sovereignty has become a

more fluid principle ininternational rela-

tions(Agnew, 2005b). sd

Suggested reading

Ruggie (1993).

multi-level models quantitative methods

that can analyse research problems with a

complex data structure. In a hierarchical

structure, the lower-level unit is nested in

one and only one unit – for example, people

in neighbourhoods in a two-level structure,

and people in neighbourhoods inregionsin

a three-level structure. Other examples are

repeated measures of individuals as in a panel

study (cf.longitudinal data analysis) and a

multivariate design when there is more than

one response variable, so that it is possible to

model several aspects of individual behaviour

simultaneously. There are two types of non-

hierarchical structure. In a cross-classified de-

sign, lower units may nest within more than

one set of higher-level units, so that pupil per-

formance may be affected by individual,

school and neighbourhood characteristics (cf.

neighbourhood effect). Both schools and

neighbourhoods are higher-level units, but

they are not nested within each other. The

remaining type is a multiple membership

model in which lower-level units are affected

by more than one higher-level unit, so that

people’s voting behaviour may be affected by

the different households and neighbour-

hoods they have been members of, with a

weight proportional to the relative time spent

in each. It is possible to combine these struc-

tures in a rich fashion, so that spatialmodels

(e.g.geographically weighted regression)

can have a hierarchical structure in which in-

dividuals are affected by the area they live in,

and a multiple membership relation by which

they are affected by spillover effects from

nearby neighbourhoods (seeecometrics).

Such models can handle continuous and

categorical data responses and variables

and, indeed, interactions between predictor

variables at each level of the structure (cf.

measurement). In terms of specification, in

addition to the usualregressioncoefficients

that estimate the mean (or fixed) relationship

across all structures, there is considerable de-

velopment of the random stochastic part of the

model (seestochastic process) so that it is

possible to separate between-individual from

between-neighbourhood variation and, in-

deed, to allow a variable to have a differential

effect on the outcome in different neighbour-

hoods. Because of this specification, these are

also known as random coefficient or mixed

models (fixed and random).

Multi-level models are increasingly being

used in social science research, as they have a

number of advantages. Technically, they can

model complex data dependencies, including

spatial and temporalcorrelation, and there-

by give correct standard errors for the fixed

estimates; this is particularly important for

variables measured at the higher level. They

also allow explicit modelling of heterosce-

dasticity at any level of the model. Substan-

tively, by modelling simultaneously at the

micro- and macro-levels, they overcome the

atomistic fallacy of modelling individuals and

ignoring context, as well as theecological

fallacy,of not modelling at the individual

level. Most importantly, they can incorporate

an element of context so that there does not

have to be a single relationship fitted for all

times and places, so that the class effects on

individual voting can be allowed to vary from

place to place (Jones, Johnston and Pattie,

1992). kj

Suggested reading

Jones (1991); Jones and Duncan (1998).

Gregory / The Dictionary of Human Geography 9781405132879_4_M Final Proof page 483 1.4.2009 3:19pm

MULTI-LEVEL MODELS