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

Area of Science:

• Mathematical Psychology
• Computational Social Science

Background:

• Psychological research extensively uses multivariate statistics but less frequently employs mathematical modeling techniques like Integer Programming (IP).
• Integer Programming (IP) is an optimization method extending linear programming (LP) by requiring decision variables to have integer values.

Purpose of the Study:

• To provide a historical overview of Integer Programming (IP) methodology.
• To review existing applications of IP in various psychological domains.
• To identify potential future applications of IP in emerging psychological fields.

Main Methods:

• Review of Integer Programming (IP) history and applications in psychology.
• Illustrative example using IP for clustering respondents in substance abuse disorder research.

Main Results:

• Integer Programming (IP) has a history of successful applications in psychology, including test assembly, cluster analysis, classification, seriation, and unidimensional scaling.
• An example demonstrates IP's utility in clustering individuals based on substance abuse disorder data.

Conclusions:

• Integer Programming (IP) is a valuable, albeit underutilized, tool in psychological research.
• IP shows promise for application in emerging areas like network psychometrics.