Color localization data and code

This repository recreates the figures in the paper: "A Computational Approach to Search in Visual Working Memory"

Data

Run the function All_Data.m in the data-analysis folder. This script loads in Data_Wen-Chuang.mat to reformat the raw data into alldata.mat, which is a 1 * Nsubj struct with the field data, which each in turn have the following fields, all with size 1 * Ntrials (here 640), with the exception of stim_order and col_val, with size 8*640. The data contains the following fields:

• set_size: N in [2, 4, 6, 8]
• stim_order: stimulus indices organized from top center, going clockwise; 1 is always the place holder for the target stimuli, and 2 for the non-target/distractor
• spatial_dist: between target and nontarget, in [1,2,3,4]
• col_val: color values represented in radians from [-180°,180°]
• response: 1 (correct) or 0 (incorrect)
• reaction_time (seconds)
• col_dist: absolute circular_distance between target and non-target colors within domain of [0°,180°] (uniformly distributed)

For creation of simulated data, use the script sim_data_all_models.m that creates a simulated data structure like the real data. All the model fitting scripts described below should work for the simulated data. To check the parameter recovery, use the script param_recovery.m.

Model fitting

Resource Modeling

We explore 4 models in this approach:

• Equal Precision (EP) resource model
• Equal Precision model with fixed item limit (EPF) resource+slots model
• Variable Precision (VP) resource model
• Variable Precision model with fixed item limit (VPF) resource+slots model

The code for the modeling code for these models can be found in the resource_parametric folder. Note that for all the scripts here, an identifying tag variable mi is used to determine which model will be run (EP, EPF, VP, or VPF).

The function Master_fitting_real.m in the resource_parametric folder calls the function fit_pred.m and finds for each subject the parameters that maximize the loglikelihood LL.m and calculates the model predictions with the function Pred_change.m.

Both LL.m and Pred_change.m call the function calc_prob_corr.m. Additional section inside the modeling folder model_fits_cluster2 stores parameter values for all 4 models, 14 subjects, and all runs (currently set to 20).

Note that tau and lambda_alpha are optimized in log-space, while Jbar is optimized in regular exponentiated form. Both optimization are done with BADS.

Resource Modeling (non-parametric)

We also test a non-parametric instance of the best performing paramatric resource model from above (in this case, the VP model), and determine whether having no assumption that encoding precision decreases with set size according to a power law function. To run modeling for this, run the Master_Fitting.m script in the resource_non-parametric folder.

Resource-rational Modeling

In this approach, we use the encoding and decision-making rule according to the most optimal model of the resource models (VP) -- meaning, we assume variability in precision as represented by the parameter 'tau' and do not set an item limit.

We consider two variations of the resource-rational model---one with a linear neural cost, and the other with a neural cost defined by a power law function. The model-fitting scripts are in the resource-rational_linear-cost and resource-rational_power-law folders respectively.

In both folders, optim_normative.m holds the code for the first round of optimization (tau and lambda_alpha). This script then calls LL_cost.m which holds the observer's optimization of precision. LL_cost.m calls calc_prob_corr.m in its script to calculate the total cost value of the observer. The only difference in these two approaches is the cost function the observer is ultimately trying to minimize (which is defined in the Fun_Jbars_optimizeNEW_pow.m script)

Analysis and visualization scripts

All the plotting scripts are within one folder called plotting. Below is a list of the plotting script name and the figures it maps to:

• analysis_all_summary_statistics.m provides an analysis of proportion correct behavior across trials, with each experimental condition: set size, color distance, and spatial distance.
• analysis_all_parametric.m plots the parametric resource models. Note the script asks for an mi variable to be set which specifies the model index that the script will produce a figure for. This model index can be EP, EPF, VP, or VPF.
• analysis_all_model_non_parametric.m produces the modeling fits for the non-parametric VP resource model.
• analysis_all_model_comparison.m uses the summary paramater mat files for each model fit in the model_params_summary folder (which is automatically saved if you run the modeling fits using any of the above scripts), and creates a model comparision plot with the files that are loaded in the script. Note that by default, all the comparisions are relative to the third model---but this can be changed through the compare_index variable in this script.