Advantages of Latent Class Models over Continuous Mixture Models in Capturing Heterogeneity
S Hess, ITS, University of Leeds, UK; M Ben-Akiva, Massachusetts Institute of Technology, US; D Gopinath, Choicestream, US; J Walker, Boston University, US
This paper presents some new developments in the context of latent class modelling and highlights the model's advantages over Mixed Logit
The paper discusses the way in which the parameters of a discrete choice model can be used and how estimation errors in those parameters propagate to the functions derived from them which are commonly used in practical analysis. It is assumed that the parameters are initially estimated by maximum likelihood methods.
Independently of the model structure and utility specification used in choice analysis, the final estimates consist of a vector of parameters beta and a covariance matrix Omega. However, in many cases, the values of interest to analysts are in fact not the elements of the vector beta itself but functions of individual elements of beta. A simple but very important example is the ratio between two marginal utility coefficients in a linear model, with more complicated examples including welfare measures and the correlation between different randomly distributed marginal utility coefficients.
The calculation of these derived measures is well documented in the existing literature. However, what has received less attention are levels of confidence for these derived quantities. As a result, many studies still report derived measures without the associated standard errors. While the calculation of standard errors is in fact not analytically difficult, it can be tedious in some cases.
This paper builds on earlier work by Daly and de Jong (2006) which presented a general method for calculating these standard errors and discusses their quite attractive properties. The present paper starts by developing formulae for the standard errors of sums, differences, products, ratios and reciprocals of parameters. This is then extended to the case of non-linearities before looking at standard errors for the correlation in Nested Logit and Cross-Nested Logit models. Next, we present standard errors for the moments of transformed distributions, including Triangular and Lognormal, before looking at standard errors for the correlation in multi-variate Normal distributions. Finally, we develop standard errors for a number of measures used in appraisal and forecasting, such as consumer surplus, aggregate predictions and elasticities.
To allow readers to exploit the formulae developed in this paper, freeware software is being made available, and the use of this software is illustrated in the paper. The paper closes with a numerical example that shows the advantages of using the formulae developed in this paper over simulation methods, which are shown to work poorly in the important example of ratio estimation.
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