kber: Estimate the Strength of the Magnitude Effect

The magnitude effect is an effect where, as stimulus magnitude increases, it becomes more difficult to detect small increments in stimulus magnitude. You can read about why this is important and how to quantify how stimuli are perceived here:

Dixit, T., Apostol, A.L., Chen, K.-C., Fulford, A.J.C., Town, C.P. & Spottiswoode, C.N. (2022) Visual complexity of egg patterns predicts egg rejection according to Weber’s law. Proceedings of the Royal Society B: Biological Sciences. 289 (1978), 20220710. doi:10.1098/rspb.2022.0710.

This package aims to help researchers conduct similar analysis, in experiments which involve discriminating between two stimuli of different magnitudes.

Quantifying the magnitude effect

The ability to discriminate between stimuli often depends on both the absolute and relative differences between two stimuli. This can be summarised with this equation (modified from Dixit et al. 2022): $$\text{stimulus contrast} = \frac{ΔI}{I^k}$$ where stimulus contrast is a measure of the perceived difference between two stimuli, $ΔI$ is the absolute difference between these two stimuli, and $I$ is the stimulus magnitude. In this equation, $k$ is a measure of the strength of the magnitude effect. If $k=0$, stimulus magnitude has no effect on discrimination; only the distance betwen stimuli matters. The larger $k$ is, the stronger the magnitude effect.

Note: How should the stimulus magnitude $I$ be measured, when there are two stimuli? Historically, studies usually take $I$ to be the smaller magnitude of the pair. Some studies (eg. Nachev et al. 2013) have taken $I$ to be the mean magnitude of both stimuli. Depending on the experiment, one of the stimuli in the pair may have a stronger claim to being the "background" or "reference" stimulus, in which case this stimulus can be used as $I$ (eg. Dixit et al. 2022).

Installing kber

This package is not yet available on CRAN, but you can download it from GitHub using the package devtools. Install kber with the following code:

library(devtools) #allows downloads from github
install_github("mzw22/kber") #download package
library(kber)

CRAN install coming soon, perhaps?

About this package

estimate_k() estimates the value of $k$ which best describes discrimination between stimuli. stimulus_model() can be used to inspect the resulting model, and any other models (eg. $k = 0$ or $k = 1$). If you want to plot the predictions of this model, you can use stimulus_contrast() to compute contrast directly.

WARNING

All models should be used with caution and an understanding of their assumptions. This model of stimulus perception assumes that (a) discrimination can/should be described with a generalised linear model, and (b) discrimination varies with magnitude in an unidirectional manner which can be described by the parameter $k$.

I STRONGLY advise plotting your data against the model and using diagnostic plots to assess whether the output is sensible, as with any model fitting in R.

Feedback

Please send any questions, suggestions and bugs to mzwo142@gmail.com or open an issue at https://github.com/mzw22/kber.