An Algorithm for Estimating Multivariate Castastrophe Models: Gemcat Ii
60 Pages Posted: 29 Mar 2006
Following the framework found in Oliva et al. 1987, GEMCAT II implements a felxible method to test catastrophe models containing multivariate (i.e., latent) variables while allowing for a prioi 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 catastrohe models as well as linear models. Two simulation studes are reported. Based on 61,250 simulated data setw 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 prositives in model identification. The results strongly support the vaibility GEMCAT II over a wide range of reasonable indicator reliabilities and sample sizes. Moreover, it proved possible to distinguish reliability betwee cusp catastrophes and linear models based on the Pseudo-R2 values. Finally a GEMCAT II application to actual market data is provided in order to demonstrate its use in an economic and research context. Using 34 quarters of panel data supplied by Techtel Corporation, Emeryville, CA, 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.
Keywords: Catastrophe theory, estimation techniques, catastrophe model parameter tests, organizational adoption, standards
JEL Classification: B14, C13, C10, C51, D21, L20, M39, O30
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