The DCE approach follows random utility theory, in which an individual, n, is assumed to choose the utility-maximising option i when presented with a choice set, Cn, containing alternative scenarios following:
where v is the systematic component, α refers to the ASC, β is related to the vector of coefficients, X is the vector of k attributes and εin relates to the random component (unobservable variation). A respondent is assumed to choose the scenario j among alternatives J if the utility derived from that alternative is greater than the utility from any other alternative in the choice set.
The model will estimate the probability of a chosen alternative, j, as a function of the attributes k. In the current study, the utility derived from the chosen option is described by:
Further details on discrete choice experiment analysis
The initial analysis employed the benchmark case of a conditional logit model (or clogit) which is based on three assumptions: (1) independence of irrelevant alternatives; (2) error terms are independent and identically distributed across observations; and (3) no preference heterogeneity (i.e. identical preferences across respondents). Alternative model specifications were also tested, including mixed logit and generalised multinomial logit models. Goodness-of-fit criteria, including Akaike and Bayesian information criteria, were used to determine the best model for the data.
Based on the data analysis plan, the objectives of the research, results of preliminary analyses, and Akaike and Baysian goodness-of-fit criteria, the mixed-effects logistic regression was deemed most appropriate. Mixed-logit regression models were optimal as they allow for the examination of unobserved preference heterogeneity: that is varying model estimates across individuals. Mixed-logit regression facilitated the examination of heterogeneity among respondents (which was expected) and relaxed the assumption of independence from irrelevant alternatives, which is an underlying assumption of the clogit model. The mixed-logit regression allowed for increased flexibility by specifying certain coefficients to be randomly distributed across individuals. Estimation by maximum simulated likelihood was undertaken using the user-written ‘mixlogit’ Stata programme (Arne Hole, Boston College Department of Economics, Boston, MA, USA). All estimation results reported were generated assuming the random parameters were normally distributed and using 250 Halton draws to simulate the likelihood functions to be maximised. There is an inherent trade-off between the number of Halton draws and the time taken to compute various models. It is suggested that an analysis build up models working from the default of 50, up to 100, 200, 250, 500 and up to 1000, if appropriate. However, given the number of random effects specified in the current study, it was not feasible to compute models with 500 or 1000 Halton draws and therefore 250 was set for each model.
Effects coding was used for the analysis. This refers to a way of using categorical predictor variables in estimation models. It is similar to dummy coding but uses ones, zeros and minus ones to represent information on factor levels. Effects coding facilitates reliable estimates of main effects and interaction effects (if included/required) and allows for estimation of all levels.134
