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Theories are sets of causal relationships between constructs and their proxy indicator variables. Theories are tested and their numerical parameters are estimated using statistical models of latent and observed variables. A considerable amount of theoretical development in Information Systems occurs by theory extension or adaptation. Moreover, researchers are encouraged to reuse existing measurement instruments when possible. As a consequence, there are many cases when a relationship between two variables (latent and/or observed) is re-estimated in a new study with a new sample or in a new context. To aid in cumulative theory building, a re-estimation of parameters should take into account our prior knowledge about their likely values. In this paper, we show how Bayesian statistical models can provide a statistically sound way of incorporating prior knowledge into parameter estimation, allowing researchers to keep a “running tally” of the best estimates of model parameters.

Bayesian Structural Equation Models for Cumulative Theory Building in Information Systems―A Brief Tutorial Using BUGS and R