Identifying Structural Parameters of Social " Processes Using

In this paper we present examples illustrating five important issues involved in the identification of structural information about social processes using the fragmentary data which is usually available for this purpose. These issues are listed below. (i) It is of considerable importance to use continuous-time models to desi;ribe processes for which there is no substant~ve basis for a choice of basi.c unit time interval between state changes. Failure to observe this point can, result in conclusions about compatibility of data ,with a discrete-time model which are dependent simply on an ad-hoc choice of unit time interval. (11.) The trade-off between parsimony and realism in the selection of base-line models is closely linked to a consideration of the currently as well as potentially available data bases which can be used for the purpose of identifying structural mechanisms. Examples of some major sociological data bases are described in order to explicitly illustrate the fragmentary nature of the observations. In addition, special mixtures of Markov and semi-,Markov processes are presented as 'examples of models which are both moderately realistic and simple enough to allow for identification of structural parameters using rather limited data. (iii) Very little attention has been paid to the development of strategies for discriminating between several apriori plausible models all fitted to the same data. We present an example of testing data for compatibility with the class of continuous-time Markov chains (null hypothesis)vs. a restricted class of mixtures of Markov chains as art alternative. (iv) The evenly-spaced sampling of Markov semi-groups can lead to the aliasing of intensity matrices. This phenomenon is analogous to the familiar aliasing of frequencies in the evenly-spaced sampling of stationary time series. (v) Two strategies are presented for assessing the sensitivity of conclusions about structural parameters compatible with a given data set to noise and other uncontrollable sources of variability.