Random Coefficient Logit Model for Large Datasets
We present an approach for analyzing market shares and products price elasticities based on large datasets containing aggregate sales data for many products, several markets and for relatively long time periods. We consider the recently proposed Bayesian approach of Jiang et al [Jiang, Renna, Machanda, Puneet and Peter Rossi, 2009. Journal of Econometrics 149 (2) 136-148] and we extend their method in four directions. First, we reduce the dimensionality of the covariance matrix of the random effects by using a factor structure. The dimension reduction can be substantial depending on the number of common factors and the number of products. Second, we parametrize the covariance matrix in terms of correlations and standard deviations, like Barnard et al. [Barnard, John, McCulloch, Robert and Xiao-Li Meng, 2000. Statistica Sinica 10 1281-1311] and we present a Metropolis sampling scheme based on this specification. Third, we allow for long term trends in preferences using time-varying common factors. Inference on these factors is obtained using a simulation smoother for state space time series. Finally, we consider an attractive combination of priors applied to each market and globally to all markets to speed up computation time. The main advantage of this prior specification is that it let us estimate the random coefficients based on all data available. We study both simulated data and a real dataset containing several markets each consisting of 30 to 60 products and our method proves to be promising with immediate practical applicability.