An introduction to Bayesian hierarchical models with an application in the theory of signal detection

By Jeffrey N. Rouder, Jun Lu. Psychonomic Bulletin & Review, 2005

408 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Developmental and Educational Psychology

View Paper: https://www.semanticscholar.org/paper/5a1dd2f8b0a8c0299e44e698404bf73b0b10818e

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Citations in the corpus

A practical solution to the pervasive problems ofp values (2007, background): “…is conceptually straightforward and can be easily extended to more complicated situations, such as those that require (possibly nonlinear) hierarchical models (see, e.g., Rouder & Lu, 2005; Rouder, Lu, Speckman, Sun, & Jiang, 2005) or order-constrained inference (Klugkist, Laudy, & Hoijtink, 2005).”
Bayesian just-so stories in psychology and neuroscience. (2012, methodology): “Nor do we dispute the promise of Bayesian analysis methods in the evaluation of cognitive models (e.g., Lee, 2008; Rouder & Lu, 2005; Wagenmakers, Lodewyckx, Kuriyal, & Grasman, 2010).”
Methodological and empirical developments for the Ratcliff diffusion model of response times and accuracy (2009, background): “In the field of psychology, Jeff Rouder and colleagues have repeatedly illustrated the theoretical advantages and practical relevance of a Bayesian hierarchical analysis of common experimental data (Rouder & Lu, 2005 ; Rouder, Lu, Speckman, Sun, & Jiang, 2005 ; Rouder et al, 2007 ).”
Hierarchical Bayesian parameter estimation for cumulative prospect theory (2011, methodology): “In order to facilitate hierarchical modeling, we followed Rouder and Lu (2005) and first transformed these parameters to the probit scale, that is, αϕi = Θ −1(αi), β ϕ i = Θ−1(βi), γ ϕ i = Θ −1(γi), δ ϕ i = Θ −1(δi), where Θ−1 denotes the inverse cumulative distribution function of the standard…”
Using MCMC chain outputs to efficiently estimate Bayes factors (2011, methodology): “To estimate the marginal posterior density, we sampled from the marginal posterior distributions of all parameters using Gibbs sampling (Geman & Geman, 1984; see Rouder & Lu, 2005) for a tutorial for psychologists).”
On a signal detection approach to m-alternative forced choice with bias, with maximum likelihood and Bayesian approaches to estimation (2012, methodology): “Hierarchical Bayesian models have previously been used for basic SDT models, see for example Lee (2008), Morey, Pratte, and Rouder (2008) and Rouder and Lu (2005); also see the February 2011 issue of the Journal of Mathematical Psychology, which is a special issue on hierarchical Bayesian models.”
Default Bayes factors for ANOVA designs (2012, background): “Derivation of conditional posteriors is straightforward (see Rouder and Lu, 2005, for a tutorial in such derivations).”
To transform or not to transform: using generalized linear mixed models to analyse reaction time data (2015, background): “This has led Rouder and colleagues to develop hierarchical models that use Bayesian statistics to make the necessary computations tractable (e.g., Rouder and Lu, 2005).”
Safe models for risky decisions (2017, neutral): “…Kim, Busemeyer, & Brown, 2011; Horn, Pachur, & Mata, 2015; Lejarraga, Pachur, Frey, & Hertwig, 2016; Navarro, Griffiths, Steyvers, & Lee, 2006; Rouder & Lu, 2005; Rouder, Lu, Speckman, Sun, & Jiang, 2005; Rouder, Lu, Morey, Sun, & Speckman, 2008; Scheibehenne & Pachur, 2015; Shiffrin, Lee,…”
Hierarchical Multinomial Processing Tree Models: A Latent-Trait Approach (2006, methodology): “In recent years, there has been growing awareness, however, of problems implied by analyzing nonlinear models in this way (e.g., Klauer, 2006; Smith & Batchelder, 2008, 2009; Rouder & Lu, 2005; Rouder, Lu, Morey, Sun, & Speckman, 2008).”
Bayesian hypothesis testing for psychologists: a tutorial on the Savage-Dickey method. (2010, positive): “The prior for the group mean of the study-neither condition, l/, is a truncated standard Normal (i.e., greater than zero only on the positive real line), which on the rate scale translates to a uniform distribution from 0.5 to 1 (cf. Rouder & Lu, 2005, p. 588).”