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R code for the precision mixture modelling by Paul Bays
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Functions for modelling response errors in precision tasks

Bug Fix (2019-02-23)

It was pointed out by (Jim Grange)[] that these functions always seems to return very smaller non-target probabilities. This was due to an error in the JV10_df() function. The line

X <- as.matrix(df[, tar.var])
Tg <- as.matrix(df[res.var])

should have been

X <- as.matrix(df[, res.var])
Tg <- as.matrix(df[tar.var])

This has now been fixed. The issue primarily affects the estimated of the non-target probability (Pn) and guessing probability (Pu). That said, it can also affect the estimation of the target probability (Pt), where there are non-targets.

The variable names were also the wrong way round in JV10_df_error(). However, this did not effect the result as only the difference between the two columns was relevant to the function. Nevertheless, the function has now been corrected.


Translation of Paul Bays' Matlab functions for modelling precision data into R. Bays' guide to the functions and their usage can be found here. All the function names are the same as the Matlab functions. The code is also as close as possible to the Matlab code 'under the hood'. The model implemented is described in:

The precision of visual working memory is set by allocation of a shared resource. Bays PM, Catalao RFG & Husain M. Journal of Vision 9(10): 7, 1-11 (2009).

To use the functions here the easiest thing to do is have source("mixture_model_functions.R") at the top of your script, making sure that file is in your working directory. The individual functions are also provided as separate files but be aware that they depend on one another; you'll need to have most of them available in your working directory.

If you use this code please refer to the paper above and Paul Bays' website

Overview of functions

Below is a list of all the functions provided here. Most of them exist to be called by other functions. I've given more details on the main functions below. You can also see Paul Bays' guide linked above. Bear in mind there are some differences in outputs.

Function name Use Input Output
cmean Circular mean Vector of radians Single value
cstd Circular SD Vector of radians Single value
randomvonmises Random samples from a Von Mises distribution N, Mu, concentration K Vector of samples
vonmisespdf PDF for Von Mises distribution Vector of radians, Mu, concentration K Vector of probabilities
k2sd Convert from Von Mises K to circular SD (Vector of) K (Vector of) SD
sd2k Convert circular SD to Von Mises K (Vector of) SD (Vector of) K
wrap Degrees to radians from -pi to pi Vector of degrees Vector of radians
JV10_error Calculate bias and precision See below See below
JV10_likelihood Estimate mixture model likelihood Starting parameters, responses, targets (Non-targets) Dataframe with likelihood and log-likelihood
JV10_function The main modelling function Responses, targets (Non-targets), (Starting values) List of parameters and log-likelihood
JV10_fit High level function that runs JV10_function for a range of starting values See below Dataframe or list (see below)
JV10_df Runs JV10_fit over a dataframe See below See below
JV10_df_error Runs JV10_error over a datframe See below See below

Estimating bias and precision

If we want to calculate bias (central tendency) or precision (inverse SD) all you need to do is call

JV10_error(X, Tg)

where X is a vector of responses and Tg is a vector of targets. Importantly these inputs must be in the range -pi to pi. To get your degrees to this range use the wrap function. JV10_error return a dataframe with two columns P for the precision value and B for the bias value. If the vector of target orientations isn't included then it defaults to 0. When calling wrap you should divide the input by 180*pi if the range of unique values is 0 to 360 degrees. If the range of unique values is 0 to 180 degrees (e.g. bar orientations) then divide by 90*pi.

If you want to apply this function to a dataframe you can use:

JV10_df_error(d, id.var = "id", tar.var = "target", res.var = "response")

where d is a data.frame, id.var is the columns that identifies your participants, tar.var is the name of the target orientations (in radians) and res.var is the name of the columns for response orientations also in radians.

Mixture modelling

To do the mixture modelling described in Bays et al. 2009 you call JV10_fit(X, Tg, NT, return.ll). This function has two required argument and two optional argument. The required arguments are X (a vector of response orientations in radians) and Tg (a vector of target orientations in radians). NT is the orientation(s) on your non-target items and should be a vector/matrix with the same number of rows as X and Tg. Clearly the first rows of X, Tg, and NT should be the single trial, and so on. return.ll is a logical argument for whether you want the log-likelihood of the final estimates to be returned. return.ll defaults to TRUE meaning that JV10_fit will return a list containing B (a dataframe of parameter estimates) and LL the log-likelihood. If return.ll = FALSE then you will just get the dataframe B back.

Working with a dataframe

I've written a function JV10_df for cases where you want to apply the mixture modelling to a dataframe.

estimates <- JV10_df(df, id.var = "id", tar.var = "target", res.var = "response", nt.vars = NULL)

The df argument is your dataframe. id.var is the name of the column that contains a factor that you want to estimate the parameters for each level of. tar.var is the name of your target column and res.var is the name of your response variable. Use nt.vars if you have non-targets. This can either be a single column or a set of columns, e.g. c("nt1", "nt2"). You don't get the logliklihood back here but I may update this at some point.

The file "test_analysis.R" shows what using this function would look like and runs in conjunction with the file "test_data.csv".


I've tested the code against the Matlab version but if you find any issues let me know ( Should you use this code for a paper you might want to double-check there haven't been any updates/error-fixes posted here before publishing.

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