The coefficients for the attitude variables and their interaction with high political
awareness are statistically significant (at .05 level) in all but one referendum (the second
Irish referendum on the Nice Treaty), whilst the direct impact of attitudes remains
sig
al
awareness and EU attitudes are statistically significant in six of the eight referendums. This
indicates that people with higher levels of political awareness rely more heavily on their
EU attitudes when deciding in referendums than people with low levels of political
awareness. This supports the third hypothesis relating to the impact of differences in
political awareness. The interaction between political awareness and the remaining
independent variables, partisanship and government satisfaction, is not statistically
significant. Moreover, a likelihood ratio test of the model with and without interaction
terms, shows that the fit improves when the interaction terms are included.
However, while it is relatively straightforward to estimate and interpret interaction
effects in linear models, this is not the case in logit models, and there is no consensus in
the field about the most appropriate way to do this (Norton, Wang and Ai 2004; Nagler
1994; Berry 1999; Berry and Berry 1991). There are several difficulties with interpreting
the coefficients of interaction terms in the same way as one would do in linear model, since
the marginal effect of a change in both interacted variables is not equal to the marginal
effect of changing just the interaction terms. Moreover, the sign of the interaction term
coefficient may be different for different observations and the familiar odds-ratio
interpretation cannot be applied (Norton, Wang and Ai 2004; Ai and Norton 2003; Berry
1999). Furthermore, it has been argued that since logit models are inherently interactive
with respect to the effects of the independent variables (X
1,
X
2
) on the probability of the
dependent variable (Pr(Y=1)), it is not even necessary to include interaction terms in order
to detect interaction. In fact Berry (1999) argues that in cases where the dependent variable
of interest is whether some discrete event occurs (rather than the underlying unbounded
concept Z presumed to be measured by Y) – such as whether individuals vote ‘yes’ or ‘no’
in an EU referendum – you cannot perform a statistical test of the hypothesis that X
1,
and
X
2
interact in influencing Pr(Y=1) against the null hypothesis that there is no interaction,
because there can be no logit or probit model in which the effect of X
1
is on Pr(Y=1) is
ompletely independent of the value of X
2
.
Instead Berry recommends comparing the
changes in predicted probabilities, Pr(Y=1), across different levels of X
2
, using maximum
nificant. Moreover, the coefficients for the interaction between medium politic
c
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Convention