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In response to the importance of individual-level effects, the purpose of this paper is to describe the new randomization permutation (RP) test for a mediation mechanism for a single subject. We extend seminal work on permutation tests for individual-level data by proposing a test for mediation for one person. The method requires random assignment to the levels of the treatment variable at each measurement occasion, and repeated measures of the mediator and outcome from one subject. If several assumptions are met, the process by which a treatment changes an outcome can be statistically evaluated for a single subject, using the permutation mediation test method and the permutation confidence interval method for residuals. A simulation study evaluated the statistical properties of the new method suggesting that at least eight repeated measures are needed to control Type I error rates and larger sample sizes are needed for power approaching .8 even for large effects. The RP mediation test is a promising method for elucidating intraindividual processes of change that may inform personalized medicine and tailoring of process-based treatments for one subject.

Abstract. Common model fit indices behave poorly in structural equation models for experience sampling data which typically contain many manifest variables. In this article, we propose a block-wise fit assessment for large models as an alternative. The entire model is estimated jointly, and block-wise versions of common fit indices are then determined from smaller blocks of the variance-covariance matrix using simulated degrees of freedom. In a first simulation study, we show that block-wise fit indices, contrary to global fit indices, correctly identify correctly specified latent state-trait models with 49 occasions and N = 200. In a second simulation, we find that block-wise fit indices cannot identify misspecification purely between days but correctly rejects other misspecified models. In some cases, the block-wise fit is superior in judging the strength of the misspecification. Lastly, we discuss the practical use of block-wise fit evaluation and its limitations.

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