Assessing risk perception by means of ordinal models 77D’Elia and Piccolo [8]) and we useCUBmodels when we relate the responses to sub-
jects’ covariates. The presence of Uniformand shifted Binomial distributions and the
introduction of Covariates justify the acronymCUB. This model combines a personal
feeling (risk awareness) towards the object and an inherent uncertainty in the choice
of the ordinal value of responses when people are faced with discrete choices.
The result for interpreting the responses of the raters is a mixture model for ordered
data in which we assume that the rankris the realisation of a random variableRthat
is a mixture of Uniform and shifted Binomial random variables (both defined on the
supportr= 1 , 2 ,...,m), with a probability distribution:
Pr(R=r)=π(mr−− 11 )( 1 −ξ)r−^1 ξm−r+( 1 −π)1
m, r= 1 , 2 ,...,m. (1)The parametersπ∈( 0 ,1] andξ ∈[0,1], and the model is well defined for a
givenm>3.
The risk-as-feelings hypothesis postulates that responses to risky situations (in-
cluding decision making) result in part from direct (i.e., not correctly mediated) emo-
tional influences, including feelings suchas worry, fear, dread or anxiety. Thus, the
first component,feeling-risk awareness, is generated by a continuous random vari-
able whose discretisation is expressed by ashifted Binomialdistribution. This choice
is motivated by the ability of this discrete distribution to cope with several differ-
ent shapes (skewness, flatness, symmetry, intermediate modes, etc.). Moreover, since
risk is a continuous latent variable summarised well by a Gaussian distribution, the
shifted Binomial is a convenient unimodal discrete random variable on the support
{ 1 , 2 ,...,m}.
At the same time, feeling states are postulated to respond to factors, such as the
immediacy of a risk, that do not enter into cognitive evaluations of the risk and also
respond to probabilities and outcome values in a fashion that is different from the way
in which these variables enter into cognitive evaluations. Thus, the second compo-
nent,uncertainty, depends on the specific components/values (knowledge, ignorance,
personal interest, engagement, time spent to decide) concerning people. As a conse-
quence, it seems sensible to express it by a discreteUniformrandom variable. Of
course, the mixture (1) allows the perception of any people to be weighted with re-
spect to this extreme distribution. Indeed, only ifπ=0 does a person act as motivated
by a total uncertainty; instead, in real situation, the quantity( 1 −π)measures the
propensity of each respondent towards the maximal uncertainty.
An important characterisation of this approach is that we can map a set of ex-
pressed ratings into an estimated model via(π,ξ)parameters. Thus, an observed
complex situation of preferences/choices may be simply related to a single point in
the parametric space.
In this context, it is reasonable to assume that the main components of the choice
mechanism change with the subjects’ characteristics (covariates). Thus,CUBmodels
are able to include explanatory variables that are characteristics of subjects and which
influence the position of different response choices. It is interesting to analyse the
values of the corresponding parameters conditioned to covariate values.