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bmm

R-CMD-check test-coverage

Overview

The goal of the bmm (Bayesian Measurement Models) package is to make it easier to estimate common cognitive measurement models for behavioral research. It achieves this by combining the flexibility of the ‘brms’ package for specifying linear model syntax with custom functions that translate cognitive measurement model into distributional families that can be estimated using Bayesian hierarchical estimation. Cognitive measurement models provide a more refined representation of the cognitive processes underlying observed behavior, because they decompose observed behavior into several theoretically meaningful parameters that each represent distinct cognitive processes.

Available models

Currently the bmm package implements mainly models used in the domain of visual working memory research:

Visual working memory

  • Interference measurement model by Oberauer and Lin (2017).
  • Two-parameter mixture model by Zhang and Luck (2008).
  • Three-parameter mixture model by Bays et al (2009).
  • Signal Discrimination Model (SDM) by Oberauer (2023)

However, the setup of the bmm package provides the foundation for the implementation of a broad range of cognitive measurement models. In fact, we are already working on implementing additional models, such as:

  • Signal-Detection Models
  • Evidence Accumulation Models
  • Memory Models for categorical response

If you have suggestions for models that should be added to the package, feel free to create an issue. Ideally this should describe the model, point towards literature that gives details on the model, and if possible link to code that has already implemented the model.

Given the dynamic nature the bmm package is currently in, you can always view the latest list of supported models by running:

bmm::supported_models()
#> The following models are supported:
#> 
#> -  IMMabc(non_targets, setsize) 
#> -  IMMbsc(non_targets, setsize, spaPos) 
#> -  IMMfull(non_targets, setsize, spaPos) 
#> -  mixture2p() 
#> -  mixture3p(non_targets, setsize) 
#> -  sdmSimple() 
#> 
#> Type  ?modelname  to get information about a specific model, e.g.  ?IMMfull

Installation

Currently, we are working on getting the package ready to be submitted to CRAN. For now, you have to install the development version of bmm from GitHub with:

# install.packages("devtools")
devtools::install_github("venpopov/bmm")

All the vignettes are also available on the bmm website.

The package was significantly updated on Feb 03, 2024. If you are following older versions (earlier than Version 6) of the Tutorial preprint, you need to install the 0.0.1 version of the bmm package with:

# install.packages("devtools")
devtools::install_github("venpopov/[email protected]")

The general structure of the bmm package

The main building block of the bmm package is that cognitive measurement models can often be specified as distributional models for which the distributional parameters of the generalized linear mixed model are a function of cognitive measurement model parameters. These functions that translate the cognitive measurement model parameters into distributional parameters is what we implement in the bmm package.

As these function can become complicated and their implementation changes with differences in experimental designs, the bmm package provides general translation functions that eases the use of the cognitive measurement models for end users. This way researchers that face challenges in writing their own STAN code to implement such models themselves can still use these models in almost any experimental design.

Fitting models using the bmm

The core function of the bmm package is the fit_model function. This function takes:

  1. a linear model formula specifying how parameters of the model should vary as a function of experimental conditions
  2. data containing the dependent variables, the variables predicting model parameters, and potentially additional variables providing information to identify the model
  3. the model that should be fit

You can get more detailed information on the models implemented in bmm by invoking the documentation of each model typing ?bmmmodel into your console. For example, calling the information on the full version of the Interference Measurement Model would look like this:

?IMMfull

The function will then call the appropriate functions for the specified model and will perform several steps:

  1. Configure the Sample (e.g., set up prallelization)
  2. Check the information passed to the fit_model function:
    • if the model is installed and all required arguments were provided
    • if a valid formula was passed
    • if the data contains all necessary variables
  3. Configure the called model (including specifying priors were necessary)
  4. Calling brms and passing the specified arguments
  5. Posprocessing the output and passing it to the user

This process is illustrated in the Figure below:

A complete call to fit a model using bmm could look like this. For this example, we are using the OberauerLin_2017 data that is provided with the package.

library(bmm)
data <- OberauerLin_2017

For this quick example, we will show hot to setup fitting the Interference Measurement Model to this data. If you want a detailed description of this model and and in depth explanation of the parameters estimated in the model, please have a look at vignette("IMM").

model_formula <- brms::bf(dev_rad ~ 1,
                          c ~ 0 + SetSize,
                          a ~ 0 + SetSize,
                          s ~ 0 + SetSize,
                          kappa ~ 0 + SetSize)

model <- IMMfull(non_targets = paste0("Item",2:8,"_Col"),
                 spaPos = paste0("Item",2:8,"_Pos"))

fit <- fit_model(
  formula = model_formula,
  data = data,
  model = model
)

Using this call, the fit object will save all the information about the fitted model. As bmm calls brms to fit the models, these objects can be handled the same way a normal brmsfit object is handled:

# print summary
summary(fit)

# plot posterior predicitive plot
brms::pp_check(fit)

You can have a look at examples for how to fit all currently implemented models by reading the vignettes for each model here for the released version of the package or here for the development version.

Exploring cogntive measurement models

To aid users in improving their intuition about what different models predict for observed data given a certain parameter set, the bmm package also includes density and random generation function for all implemented models.

These function provide an easy way to see what a model predicts for data given a certain set of parameters. For example you can easily plot the probability density function of the data for the Interference Measurement model using the dIMM function. In similar fashion the random generation function included for each model, generates random data based on a set of data generating parameters. For the IMM, you can use rIMM to generate data given a set of parameters. Plotting the random data against the density illustrates that the data follows the theoretically implied density.

library(ggplot2)

simData <- data.frame(
  x = bmm::rIMM(n = 500,
           mu = c(0,-1.5,2.5,1),
                            dist = c(0, 2, 0.3, 1),
                            c = 1.5, a = 0.3, b = 0, s = 2, kappa = 10)
)

ggplot(data = simData, aes(x = x)) +
  geom_histogram(aes(y = after_stat(density))) +
  geom_function(fun = bmm::dIMM,
                args = list(mu = c(0,-1.5,2.5,1),
                            dist = c(0, 2, 0.3, 1),
                            c = 1.5, a = 0.3, b = 0, s = 2, kappa = 10)) +
  scale_x_continuous(limits = c(-pi,pi))

Contributing to the bmm package

Should be interested in contributing a model to the bmm package, you should first look into the Developer Notes. These give a more in depth description of the package architecture and the steps necessary to add your own model to the package.

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An R package for easy and flexible Bayesian Measurement Modeling

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