Current Agriculture, Food & Resource Issues
G. Hailu, E. W. Goddard and S. R. Jeffrey
Ordered response regression recognizes the indexed nature of various response
variables. Underlying the indexing in such models is a latent but continuous descriptor of
the response. In an ordered probit regression, the random error associated with this
continuous descriptor is assumed to follow a normal distribution. The observed and coded
discrete behavioural intention variable (i.e., 1,2....,J), BI, is determined from the model as
follows:
n
(8) BIi = βo + βιAi + βSN1 + β3PBCi + ∑βjDemθjl + ɛ41,
j=1
where BIi* is a latent and continuous measure of behavioural intention for the i-th DM and
J represents possible values of BIi. The relationship between BIi* and BIi is defined in
terms of threshold parameters (μ's) to be estimated with β; that is, BIi =1, if μ0<BIi*≤μ1;
BIi=2, if μ1<BIi* ≤μ2,...; BIi=J, if BIi*>μ -1. In the above, the respondents have their own
intensity of behavioural intention. The intensity of behavioural intention depends on
observed exogenous variables, and unobservable factors, ε4i. The ordered probit model is
based on an assumption that respondents could respond to the question with their own BIi*
if asked to do so. Given only seven or five possible discrete answers (depending on the
question), respondents opt for the choice that most closely represents their own intentions
on the question (Greene, 2000). However, one of the undesirable consequences of
applying linear regression is that “it implicitly assumes that respondents who give the
same response have exactly the same attitude” (Daykin and Moffatt, 2002). This may not
be the case, as a particular response may be consistent with a range of attitudes, and
ignoring such differences may lead to biased estimates. The ordered probit model
accommodates such differences.
With the assumption that ε4i is distributed normally across sample observations, the
probability that BIi falls into the j-th category is given by
(9) Prob( BI = j ) = Φ ( μj-β ' x )-Φ ( μj4ι - β ' x ) ,
where Φ denotes the cumulative standard normal distribution function and μ and μ+1
denote the upper and lower threshold values, respectively, for the j-th category,
respectively. If j is the lower category, then the lower threshold value is -∞ and the upper
threshold value is zero. If j is the higher category, the upper threshold value is +∞. For all
probabilities to be positive, the ordering 0 < μ1 < μ2 <... < μJ_1 must hold. The estimated
coefficients from an ordered probit regression do not have an intuitive interpretation.
Therefore, marginal effects are calculated to provide more information. For the above
probabilities, the marginal effect of changes in the regressors for the j-th category is
(10) 9 ob(BI = j) = [φ(μl -β'x)-φ(μl+1 -βx)] ,
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