Assessing risk perception by means of ordinal models 81In Table 1 we list the estimation of parameters of aCUB(0,3) with gender (Gen),
working years (Year) and serious injury (Serinj) as sensible covariates.
Ta b le 1 .Parameters
Covariates Parameters Estimates (Standard errors)
Uncertainty π 0. 440 (0.060)
Constant γ 0 1. 515 (0.319)
Gender γ 1 1.^029 (0.573)
Working years γ 2 − 0. 032 (0.015)
Serious injury γ 3 − 0. 928 (0.323)Log-likelihood functions ofCUB(0,0) andCUB(0,3) estimated models are 00 =
− 660 .07 and 03 =− 651 .81, respectively. As a consequence, the model with co-
variates adds remarkable information to the generating mechanism of the data since
2 ∗( 03 − 00 )= 16 .52 is highly significant when compared to theχ 02. 05 = 7. 815
percentile withg=3 degrees of freedom.
We may express the feeling parameters as a function of covariates in the following
way:
ξi=1
1 +e−^1.^515 −^1.^029 Geni+^0.^032 Yeari+^0.^928 Serinji, i= 1 , 2 ,...,n, (3)which synthesises the perception of danger of fire/explosion risk with respect to the
chosen covariates. More specifically, this perception increases for men and for those
who have worked for many years (a proxy of experience) and decreases for the part
of sample that had not suffered from a serious accident. For correct interpretation, it
must be remembered that if items are scored (as a vote, increasing from 1 tomas
liking increases) then (1−ξ) must be considered as the actual measure of preference
[10]. Although the value of the response is not metric (as it stems from a qualitative
judgement), it may be useful for comparative purposes to compute the expected value
ofR, since it is related to the continuous proxy that generates the risk perception.
More specifically, Figure 2 shows the expectation and its relation to the varying
working years and for all the profiles of gender and serious injury.
4 Conclusions
In this paper, we obtained some results about direct inference on the feeling/risk
awareness and uncertainty parameters by means ofCUBmodels with and without
covariates. The experiments confirmed that this new statistical approach gives a dif-
ferent perspective on the evaluation of psychological processes and mechanisms that
generate/influence risk perception in people. The results show thatCUBmodels are a