# LDDMM

An R package for Longitudinal Drift-Diffusion Mixed Models (LDDMM), v0.3.

Authors: Giorgio Paulon, Abhra Sarkar

### Overview

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.

### Installation

To install the package in R, first install the devtools package, and then use the commands

library(devtools)
install_github('giorgiopaulon/lddmm')

If you are using a Windows machine, you might have to also install and configure Rtools using the following instructions.

### Usage

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")

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. Auxiliary functions that assume constant boundary parameters over time ($$b_{d,s}^{(i)}(t) = b_{d,s}$$ using the article notation) or fix the boundaries to the same level across input predictors ($$b_{d,s}^{(i)}(t) = b_{d}$$ using the article notation) can be called with the options boundaries = "constant" and boundaries = "fixed", respectively.

### Questions or bugs

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

### Citation

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