Isotonic regression: Theory and empirical applications for psychological studies using intrinsic religious orientation

摘要

Isotonic regression is a technique for detecting trends that have the property of being non-decreasing or non-increasing. The first purpose of this study is to present the theory and computational procedures to conduct isotonic regression analysis for a one-way analysis of variance experimental design. The second purpose is to illustrate the use of the isotonic regression technique in analyzing psychological data. Using a data set from Hossack (1997), the property of isotonicity is tested by using a technique that preserves the order of group means. In this study, groups of Intrinsic Religious Orientation (IRO) are hypothesized to be significantly different for Attachment to Mother (ATM), Attachment to Father (ATF), Sense of Coherence (SOC) and Satisfaction with Life (SWL) at the 0.05 level of significance. Moreover, there is no expected significant difference hypothesized between IRO groups for Agreeableness (AGR), Conscientiousness (CON) or Neuroticism (NEU) at the same level of significance. Results confirm these hypotheses under both ANOVA and isotonic regression analyses. However, there are three exceptions. For ANOVA, the IOR groups were significantly different for CON (p < 0.01) when a non-significant result was expected. For isotonic regression, the IOR groups were significantly different for NEU and AGR (p < 0.05), when a non-significant result was expected. In addition, the goodness of fit values using isotonic regression estimates were greater than goodness of fit values using sample mean estimates for each of the criterion variables. Besides the linear ANOVA-typed model, isotonic regression techniques are also used with some nonlinear models such as exponential and logistic functions. The implications are that isotonic parameter estimates should be used instead of sample mean estimates. In the conclusion, the advantages and disadvantages of isotonic regression are discussed.