An Algorithm for Estimating Multivariate Catastrophe Models: GEMCAT II

Abstract

Following the framework in Oliva et al. 1987, GEMCAT II implements a flexible method to test catastrophe models containing multivariate (i.e., latent) variables while allowing for a priori variable specifications. The system uses an efficient hybrid minimization algorithm combining the Downhill Simplex and Powell's Conjugate Gradient method. GEMCAT II is compiled in Delphi V3.0 and is sufficiently fast to allow for the use of resampling methods (bootstrap as well as jackknife) to determine the statistical significance of latent variables' indicator weights. In addition, a Pseudo-R2 index of model fit is provided, together with a test of significance, and options are included to facilitate competitive model tests of nested and non-nested catastrophe models as well as linear models. Two simulation studies are reported. Based on 61,250 simulated data sets of varying sizes, the first study addressed the effects of indicator reliability on the quality of the weight estimations, and the second dealt with the problem of false positives in model identification. The results strongly support the viability of the GEMCAT II approach over a wide range of reasonable indicator reliabilities and sample sizes. Moreover, it proved possible to distinguish reliably between cusp catastrophes and linear models based on the Pseudo-R2 values. Finally, GEMCAT II is applied to actual market data in order to demonstrate its use in an economic context. Using 34 quarters of panel data, we examine the fit of a cusp catastrophe model of organizational product adoption as applied to competing software standards in the presence of network externalities. The results are consistent with economic theory and published work on network externalities. This example also illustrates GEMCAT II's bootstrap tests for indicator weights and its options for competitive model testing.