Integer programming in psychology: A review and directions for future research

Integer programming (IP) is an extension of linear programming (LP) whereby the goal is to determine values for a set of decision variables (some or all of which have integer restrictions) so as to maximize or minimize a linear objective function of the variables subject to a set of linear constraints involving the variables. Although the psychological literature is replete with applications of multivariate statistics, implementations of mathematical modelling methods such as IP are comparatively far fewer. Nevertheless, over the decades, there have been a variety of important applications and the vast majority of these fall within the IP rather than the LP category. In this paper, we offer a brief overview of the history of IP methodology. We subsequently review some domains where IP has been gainfully applied in psychology, such as test assembly, cluster analysis and classification and seriation and unidimensional scaling. An illustrative example of using IP to cluster respondents measured on items pertaining to substance abuse disorder is provided. Finally, we identify areas where IP might be applied in emerging areas of psychology, such as in the domain of network psychometrics.