An R package for Longitudinal Drift-Diffusion Mixed Models (LDDMM), v0.4.2.

**Authors**: Giorgio Paulon, Abhra Sarkar

Codes accompanying “Bayesian Semiparametric Longitudinal Drift-Diffusion Mixed Models for Tone Learning in Adults” by Paulon, Llanos, Chandrasekaran, Sarkar.

This package implements a novel generic framework for longitudinal functional mixed models that allows automated assessment of an associated predictor’s local time-varying influence. We build on this to develop a novel inverse-Gaussian drift-diffusion mixed model for multi-alternative decision-making processes in longitudinal settings. Our proposed model and associated computational machinery make use of B-spline mixtures, hidden Markov models (HMM) and factorial hidden Markov models (fHMM), locally informed Hamming ball samplers etc. to address statistical challenges.

The main function is `LDDMM`

; please see the following vignette for details, as well as the main article:

Paulon, G., Llanos, F., Chandrasekaran, B., Sarkar, A. (2021). Bayesian semiparametric longitudinal drift-diffusion mixed models for tone learning in adults. Journal of the American Statistical Association **116**, 1114-1127

The data included in this package was analyzed in:

Roark, C. L., Paulon, G., Sarkar, A., Chandrasekaran, B. (2021). Comparing perceptual category learning across modalities in the same individuals. Psychonomic Bulletin & Review **28**, 898-909

and is available here.

To install the package in R, first install the `devtools`

package, and then use the commands

If you are using a Windows machine, you might have to also install and configure `Rtools`

using the following instructions.

The following is a minimal example of a simple model fit. For numerical stability, the unit of measurement should be such that the numerical values of most response times should lie in \([0, 10]\).

```
# Load libraries
library(RColorBrewer)
library(ggplot2)
library(dplyr)
library(reshape2)
library(latex2exp)
library(lddmm)
theme_set(theme_bw(base_size = 14))
cols <- brewer.pal(9, "Set1")
# Load the data
data('data')
# Descriptive plots
plot_accuracy(data)
plot_RT(data)
# Run the model
hypers <- NULL
hypers$s_sigma_mu <- hypers$s_sigma_b <- 0.1
# Change the number of iterations when running the model
# Here the number is small so that the code can run in less than 1 minute
Niter <- 25
burnin <- 15
thin <- 1
samp_size <- (Niter - burnin) / thin
set.seed(123)
fit <- LDDMM(data = data,
hypers = hypers,
Niter = Niter,
burnin = burnin,
thin = thin)
# Plot the results
plot_post_pars(data, fit, par = 'drift')
plot_post_pars(data, fit, par = 'boundary')
# Compute the WAIC to compare models
compute_WAIC(fit)
```

To extract relevant posterior draws or posterior summaries instead of simply plotting them, one can use the functions `extract_post_mean`

or `extract_post_draws`

. The following auxiliary functions are available by selecting the corresponding argument in the `LDDMM()`

function:

`boundaries = "constant"`

: constant boundary parameters over time, \(b_{d,s}^{(i)}(t) = b_{d,s} + u_{d,s}^{(i)}\) using the article notation`boundaries = "fixed"`

: fixed boundaries across input predictors, \(b_{d,s}^{(i)}(t) = b_{d}(t) + u^{(i)}_{d}(t)\) using the article notation`boundaries = "fixed-constant"`

: fixed*and*constant boundaries, \(b_{d,s}^{(i)}(t) = b_{d} + u_{d}^{(i)}\) using the article notation

For bug reporting purposes, e-mail Giorgio Paulon (giorgio.paulon@utexas.edu).

Please cite the following publication if you use this package in your research: Paulon, G., Llanos, F., Chandrasekaran, B., Sarkar, A. (2021). Bayesian semiparametric longitudinal drift-diffusion mixed models for tone learning in adults. Journal of the American Statistical Association **116**, 1114-1127