Value sets for the EQ-5D-5L are required to facilitate its use in estimating quality-adjusted life years. An international protocol has been developed to guide the collection of stated preference data for this purpose and has been used to generate EQ-5D-5L valuation data for England. The aim of this paper is report the innovative methods used for modelling those data to obtain a value set. Nine hundred and ninety-six members of the English general public completed time trade-off (TTO) and discrete choice experiment (DCE) tasks. We estimate models, with and without interactions, using DCE data only, TTO data only, and TTO/DCE data combined. TTO data are interpreted as both left and right censored. Heteroskedasticity and preference heterogeneity between individuals are accounted for. We use Bayesian methods in the econometric analysis. The final model is chosen based on the deviance information criterion (DIC). Censoring and taking account of heteroskedasticity have important effects on parameter estimation. For DCE data only, TTO data only, and DCE/TTO data combined, models with parameters for all dimensions and levels perform best, as judged by the DIC. Taking account of heterogeneity improves fit, and the multinomial model reports the lowest DIC. This paper presents approaches that suit observed characteristics of EQ-5D-5L valuation data and recognise respondents' preference heterogeneity. The methods described are potentially relevant to other value set studies.