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.
Assessing the correlations between psychological variabless, such as abilities and improvements, is one essential goal of psychological science. However, psychological variables are usually only available to the researcher as estimated parameters in mathematical and statistical models. The parameters are often estimated from small samples of observations for each research participant, which results in uncertainty (aka sampling error) about the participant-specific parameters. Ignoring the resulting uncertainty can lead to suboptimal inferences, such as asserting findings with too much confidence. Hierarchical models alleviate this problem by accounting for each parameter's uncertainty at the person- and average levels. However, common maximum likelihood estimation methods can have difficulties converging and finding appropriate values for parameters that describe the person-level parameters' spread and correlation. In this post, I discuss how Bayesian hierarchical models solve this problem, and advocate their use in estimating psychological variables and their correlations.