Piecewise Propensity Score Analysis: A New Method for Conducting Propensity Score Matching With Polytomous Ordinal Independent Variables

Abstract

One common purpose of research is to determine the effect of an intervention on an outcome. The gold standard for determining effects is a randomized control trial. A randomized control trial controls for unmeasured variables that may affect the outcome by randomly placing participants in either a treatment or control condition. This works well in cases in which participants can be randomized, but in many cases it is impossible to do so. For example, assigning people to psychological conditions, race, or gender is impossible. To address this, many people use a procedure called propensity score matching (PSM). One current method that is used for PSM is marginal mean weighting through stratification. This analysis is complicated to conduct and suffers from other disadvantages. To address these concerns, we propose a new method to conduct PSM called piecewise propensity score analysis (PPSA). PPSA is a method that can assist researchers in identifying causal effects when random assignment is not possible. Creating methods to accurately determine the effect of interventions is extremely important in educational research, psychological research, and behavioral and cognitive science research. PPSA is a method that can support researchers and practitioners in trying to understand human processes in order to improve them. S C I E N T I F I C A B S T R A C T Propensity score analysis is widely used for simulating random assignment in observational studies when true random assignment is not possible. In propensity score modeling, a number of covariates are used to estimate the probability that an individual will belong to 1 of 2 groups. Prospective participants are then matched on their probabilities of belonging to the 2 groups rather than on the exact set of covariate values (as in traditional matching methods). However, traditional propensity score analysis can only be used in studies with 2 groups, such as an experimental and a control group. In this article, we propose a new method called piecewise propensity score analysis (PPSA) for ordinal polytomous grouping variables. We compared PPSA with another method of conducting propensity score analysis with ordered categories, marginal mean weighting through stratification (MMW-S; Hong, 2010, 2012) in a 3 5 4 study across three model misspecification conditions, five matching methods, and four sample sizes (1,000, 5,000, 10,000, 21,753). We found no significant difference between PPSA and MMW-S methods across conditions. We recommend linear regression, simple mean difference, or propensity stratification methods for simulating causal inference.