Theories and models in cognitive psychology tend to be nonlinear, e.g. Process Dissociation Model of Memory, but statistical methodology for assessing these theories is based on linear models. As a consequence, psychologists using nonlinear models have no suitable means of accounting for extraneous variability from the selection of items and participants. In these nonlinear contexts, unaccounted variability often leads to asymptotic bias in estimation and may lead to flawed inference in hypothesis testing. To fill this void, we propose a series of hierarchical nonlinear models to capture psychological processes of interest. Although models are custom-tailored for specific applications, the form of these models and the corresponding analytic techniques will have broad applicability across experimental psychology. Our overall strategy is to place linear models on parameters in nonlinear processes. For example, to account for item and participant variability in a signal detection analysis of memory performance, we assume that each individual and each item have separate effects on sensitivity. These items and participant effects are assumed to be random effects from parent distributions and modeled accordingly. The overall benefit is accurate estimation and vastly improved inference. In the course of specifying these models for psychological process, we necessarily make significant progress in Bayesian methodology, most notably in improving mixing and implementing Bayes Factor computations in hierarchical models with non-informative priors.
| Rouder, Jeffrey N; Pratte, Michael S; Morey, Richard D (2010) Latent mnemonic strengths are latent: a comment on Mickes, Wixted, and Wais (2007). Psychon Bull Rev 17:427-35 |
| Min, Xiaoyi; Sun, Dongchu; He, Zhuoqiong et al. (2010) A Bayesian hierarchical model of nontraumatic lower-extremity amputation rates. Spat Spatiotemporal Epidemiol 1:169-76 |
| Pratte, Michael S; Rouder, Jeffrey N; Morey, Richard D (2010) Separating mnemonic process from participant and item effects in the assessment of ROC asymmetries. J Exp Psychol Learn Mem Cogn 36:224-32 |
| Lin, Xiaoyan; Sun, Dongchu (2010) A Note on the Existence of the Posteriors for One-way Random Effect Probit Models. Stat Probab Lett 80:57-62 |
| Pratte, Michael S; Rouder, Jeffrey N; Morey, Richard D et al. (2010) Exploring the differences in distributional properties between Stroop and Simon effects using delta plots. Atten Percept Psychophys 72:2013-25 |
| Rouder, Jeffrey N; Speckman, Paul L; Sun, Dongchu et al. (2009) Bayesian t tests for accepting and rejecting the null hypothesis. Psychon Bull Rev 16:225-37 |
| Cowan, Nelson; Rouder, Jeffrey N (2009) Comment on ""Dynamic shifts of limited working memory resources in human vision"". Science 323:877; author reply 877 |
| Pratte, Michael S; Rouder, Jeffrey N (2009) A task-difficulty artifact in subliminal priming. Atten Percept Psychophys 71:1276-83 |
| Rouder, Jeffrey N; Morey, Richard D (2009) The nature of psychological thresholds. Psychol Rev 116:655-60 |
| Thapar, Anjali; Rouder, Jeffrey N (2009) Aging and recognition memory for emotional words: a bias account. Psychon Bull Rev 16:699-704 |
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