knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
To perform model selection, the dev version of quickspy is necessary.
Model selection is quite flexible in quickpsy
as in the fun
argument you can introduce any arbitrary set of functions with all possible combinations of shared parameters (see the last subsection of the functions section)
To perform model selection, quickpsy
uses likelihood ratio tests and the Akaike Information Criterion (see References).
Let's fit a model for each participant in which the slope does not change across conditions
library(quickpsy) library(dplyr) # the shared parameter is p[2] fun_1_df <- tibble(cond = c("cond1", "cond2"), fun = c(function(x, p) pnorm(x, p[1], p[2]), function(x, p) pnorm(x, p[3], p[2]))) fit_1 <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"), fun = fun_1_df, parini = c(-100, 50, -100), bootstrap = "none") plot(fit_1, color = cond)
We can look at the likelihoods of the models
fit_1$logliks
or the AICs
fit_1$aic
Now let's fit a model in which for each participant the slope can change across conditions
fun_2_df <- tibble(cond = c("cond1", "cond2"), fun = c(function(x, p) pnorm(x, p[1], p[2]), function(x, p) pnorm(x, p[3], p[4]))) fit_2 <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"), fun = fun_2_df, parini = c(-100, 50, -100, 50), bootstrap = "none") plot(fit_2, color = cond)
The quickpsy
function model_selection_lrt
performs the likelihood ratio tests using the chi square distribution. The inputs are the likelihoods of each model.
model_selection_lrt(fit_1$logliks, fit_2$logliks)
Using the default 5% criterion of significance, the Model 2 (allowing a different slope for each condition) does not improve the fit for any participant. There is some evidence, however, that for Participant 1 the Model 2 might be better.
To perform the model selection using quickpsy
, you need to introduce in the model_selection_aic
function the AICs of each model.
model_selection_aic(fit_1$aic, fit_2$aic)
Using Akaike Information Criterion the Model 1 is preferred for Participant 2 and 3 and the Model 2 is preferred for Participant 1. The p
indicates the relative probability of each model.
Kingdom FAA, Prins N. 2016. Psychophysics: A Practical Introduction. Elsevier Science.
Knoblauch, K., & Maloney, L. T. (2012). Modeling psychophysical data in R (Vol. 32). Springer Science & Business Media.
Prins, N. (2018). Applying the model-comparison approach to test specific research hypotheses in psychophysical research using the Palamedes toolbox. Frontiers in psychology, 9, 1250.
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