Missing data can lead to biased and inefficient parameter estimates in statistical models, depending on the missing data mechanism. Count regression models are no exception, with missing data leading to incorrect inferences about the effects of explanatory variables. A convenient approach for dealing with missing data is to remove observations with incomplete records prior to the analysis – often referred to as case-wise deletion. Removing incomplete records, however, reduces the sample size, increases standard errors and, if data are not missing completely at random, produces biased parameter estimates. A more complex approach is multiple imputation, which provides an estimate of the modelling uncertainty created by the data ‘missing-ness’, as distinct from the natural variation in the data. However, multiple imputation produces biased parameter estimates if the probability of missing data is related to the observed data – or is endogenous. Latent variable modelling has recently been introduced as an alternative approach for dealing with missing data, but it comes at a high computational cost and complexity. Despite fairly extensive methodological advancements in statistical literature, case-wise deletion is commonly employed to deal with missing data in statistical models of transport, while the multiple imputation and latent variable approaches remain relatively unexplored. More importantly, the performance of these approaches has not been tested across different types of data missing-ness. To address these gaps, this study aims to contrast case-wise deletion with multiple imputation and latent variable approaches in dealing with missing data in count regression models. We compare the performance of these three approaches using crash count models estimated against empirical data obtained from state controlled roads in Queensland, Australia. A quasi-experimental evaluation of data missing-ness is then conducted by extracting three data subsets from the original dataset, each with a unique missing data mechanism (with terminology adopted from the statistical literature): missing completely at random, missing at random, and missing not at random. The three approaches are then applied to each data subset and the results are compared in terms of bias, precision of parameter estimates, and goodness-of-fit. The findings indicate that multiple imputation is the most effective approach when data are missing either completely at random or at random, whereas the latent variable approach is more effective when data are missing not at random. However, the effectiveness of the latent variable approach is dependent on the availability of suitable variables as instruments in the data.@en

As discrete choice models may be misspecified, it is crucial for choice modellers to have knowledge on the robustness of their modelling outcomes towards misspecification. This study investigates the robustness of Random Regret Minimization (RRM) modelling outcomes towards one sort of model misspecification: the omission of relevant attributes. We explore the effect of omitted attributes (orthogonal and correlated) in the context of labelled and unlabeled data. In the context of labelled data, we show that - just as in RUM models - in RRM models Alternative Specific Constants (ASCs) can be used to capture the average effect of omitted attributes. However, in contrast to RUM models, ASCs in RRM models are choice set composition specific. This implies that in order to achieve consistent parameter estimates when the choice set composition varies across choice observations, different sets of ASCs need to be estimated for each unique choice set composition. In the context of unlabeled data, we show - using Monte Carlo simulations - that RRM models are fairly robust towards the presence of an orthogonal omitted attribute, though not as robust as the linear-additive RUM model. Specifically, we find that: (1) Aggregate Demand Elasticities (ADEs) implied by RRM models are less robust towards the presence of an orthogonal omitted attributes than those implied by linear-additive RUM models, and (2) Average Sample Effects (ASEs) implied by RRM models are - in the presence of an omitted orthogonal attribute - more sensitive towards misspecification in terms of the underlying decision rule than those implied by its linear-additive RUM counterpart.

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This paper derives a trick to account for variation in choice set size in Random Regret Minimization (RRM) models. In many choice situations the choice set size varies across choice observations. As in RRM models regret level differences increase with increasing choice set size, not accounting for variation in choice set size results in RRM models to predict relatively deterministic choice behaviour in observations where the choice set is large and relatively random choice behaviour in observations where the choice set is small. Such variation in choice consistency across observations is behaviourally unrealistic and leads to inferior performance of RRM models in the context of data sets with varying choice set sizes. The proposed trick resolves this in an econometrically pragmatic and behaviourally meaningful way by rescaling the regret levels as a function of the choice set size. The trick can be applied in the estimation phase when the choice set size varies across choice observations as well as in the forecasting phase when forecasts are made over choice sets of varying sizes.@en