Models and contrasts Example data Model Interpreting the model’s parameters hypothesis() More contrasts Directional hypotheses and posterior probabilities Multiple hypotheses Hierarchical hypotheses Conclusion brms (Bayesian Regression Models using Stan) is an R package that allows fitting complex (multilevel, multivariate, mixture, …) statistical models with straightforward R modeling syntax, while using Stan for bayesian inference under the hood. You will find many uses of that package on this blog.
Ratings provided on visual analog scales (VAS), or slider scales, are unlikely to be normally distributed. Nevertheless, researchers typically use the normal distribution to analyze analog scale ratings, such as when they perform ANOVAs, t-tests, and correlations. A potentially better model of analog ratings, which are typically skewed and have lower and upper limits, is the so called zero-one-inflated beta model. In this post, I explain this model, illustrate its use with simulated and data, and compare its performance to t-tests in comparing two groups slider ratings.
(This post is part 4 of a series of blog posts discussing Bayesian estimation of Signal Detection models.) In this blog post, I describe how to estimate the unequal variances Gaussian signal detection (UVSDT) model for confidence rating responses, for multiple participants simultaneously. I provide software code for the hierarchical Bayesian model in R.
(This post is part 3 in a series of blog posts discussing Bayesian estimation of Signal Detection models.) In this post, we extend the EVSDT model to confidence rating responses, and estimate the resulting model as an ordinal probit regression. I also describe how to estimate the unequal variance Gaussian SDT model for a single participant. I provide a software implementation in R.
This is a part of a series of blog posts discussing Bayesian estimation of Signal Detection models. In this post, I describe how to estimate the equal variance Gaussian SDT model's parameters for multiple participants simultaneously, using Bayesian generalized linear and nonlinear hierarchical models. I provide a software implementation in R.
Signal Detection Theory (SDT) is a common framework for modeling memory and perception. Calculating point estimates of equal variance Gaussian SDT parameters is easy using widely known formulas. More complex SDT models, such as the unequal variance SDT model, require more complicated modeling techniques. These models can be estimated using Bayesian (nonlinear and/or hierarchical) regression methods, which are sometimes difficult to implement in practice. In this post, I describe how to estimate the equal variance Gaussian SDT model's parameters for a single participant with a Generalized Linear Model, and a nonlinear model. I describe the software implementation in R.
2017 will be the year when social scientists finally decided to diversify their applied statistics toolbox, and stop relying 100% on null hypothesis significance testing (NHST). A very appealing alternative to NHST is Bayesian statistics, which in itself contains many approaches to statistical inference. In this post, I provide an introductory and practical tutorial to Bayesian parameter estimation in the context of comparing two independent groups' data.
Introduction Hello everybody! Recently, there’s been a lot of talk about meta-analysis, and here I would just like to quickly show that Bayesian multilevel modeling nicely takes care of your meta-analysis needs, and that it is easy to do in R with the rstan and brms packages. As you’ll see, meta-analysis is a special case of Bayesian multilevel modeling when you are unable or unwilling to put a prior distribution on the meta-analytic effect size estimate.