Analyzing imputed financial data: a new approach to cluster analysis

The authors introduce a novel statistical modeling technique to cluster analysis and apply it to financial data. Their two main goals are to handle missing data and to find homogeneous groups within the data. Their approach is flexible and handles large and complex data structures with missing observations and with quantitative and qualitative measurements. The authors achieve this result by mapping the data to a new structure that is free of distributional assumptions in choosing homogeneous groups of observations. Their new method also provides insight into the number of different categories needed for classifying the data. The authors use this approach to partition a matched sample of stocks. One group offers dividend reinvestment plans, and the other does not. Their method partitions this sample with almost 97 percent accuracy even when using only easily available financial variables. One interpretation of their result is that the misclassified companies are the best candidates either to adopt a dividend reinvestment plan (if they have none) or to abandon one (if they currently offer one). The authors offer other suggestions for applications in the field of finance.

Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

On the Overspecification of Multinomial and Nested Logit Models Due to Alternative Specific Constants

. Discrete choice models as demand forecasting techniques have been used for transportation applications for more than thirty years. The multinomial and nested logit models are probably the most widely applied in this context. Alternative specific constants (ASCs), although playing an important role in these models, have received very little attention in theoretical studies. In this paper, we try to fill this gap by providing an analysis of the overspecification caused by ASCs to the log-likelihood function of multinomial and nested logit models. The theoretical results lead directly to a particular strategy of ASC specification, called here the orthogonal strategy. The analysis of the relationship between any two arbitrary strategies and the derivation of an interesting geometrical property of the orthogonal strategy provide a motivation to prefer the latter. 1 Intelligent Transportation Systems Program Massachusetts Institute of Technology, Cambridge, Ma E-mail: michel@..