Bayesian Structural Equation Modeling: A Business Culture Application in Kenya

Abstract

Structural equation modeling (SEM) is a multivariate method that incorporates regression, path-analysis and factor analysis. Classical SEM requires the assumption of multivariate normality to be met and large sample size, also choice is made either to ignore uncertainties or treat the latent variables as observed. National culture Data gathered in a study or survey may be inform of ordered categories and may not follow the assumptions of multivariate normality. This restricts the use of frequentist method of estimation. A Bayesian approach to SEM allows inclusion of this uncertainty and directly models the uncertainties in predictive models. In addition Bayesian SEM does not require constant variance normal disturbances and the sample size can be a small number. The development and application of Bayesian SEM has been relatively slow but it has been made possible by Gibbs sampler. The main purpose of the study was model National Culture in Kenya based on Hofstede model and business performance. Maximum likelihood Estimation was used to estimate the parameters in Classical SEM. Gibbs sampler algorithm was employed in Bayesian approach to SEM. This study used non-informative priors. The convergence of parameter was evaluated using proportional scale reduction procedure and trace and density plots. Data was gathered from employees in Nairobi through structured questionnaires. Bayesian SEM with non-informative prior gave the best estimates indicating that personal distance, individualism and long term orientation were significantly related to business performance. However, Uncertainty Avoidance had no significant relationship with business performance.