From 704fd11fee409d40568c22d4d9e62eecc2d5d883 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Fri, 12 Jul 2024 21:17:58 +0100 Subject: [PATCH] Beta animation --- content/3_scales.qmd | 42 ++++- content/4a_rt_descriptive.qmd | 4 +- content/4b_rt_generative.qmd | 8 +- content/media/animations_scales.jl | 122 ++++++--------- content/media/scales_BetaMean.gif | Bin 0 -> 203899 bytes content/media/scales_betamod.gif | Bin 270011 -> 0 bytes data/make_data.R | 23 ++- data/makowski2023.csv | 243 +++++++++++++++++++++++++++++ 8 files changed, 356 insertions(+), 86 deletions(-) create mode 100644 content/media/scales_BetaMean.gif delete mode 100644 content/media/scales_betamod.gif create mode 100644 data/makowski2023.csv diff --git a/content/3_scales.qmd b/content/3_scales.qmd index 7895012..e817f78 100644 --- a/content/3_scales.qmd +++ b/content/3_scales.qmd @@ -4,9 +4,30 @@ In many situations, the dependent variable is not continuous, nor is it even normally distributed. -## Slider (aka "Analog") Scales +## Bounded Variables -### Beta Models +While might be tempted to believe that most variables in psychological science are true **continuous** variables, this is often not the case. +In fact, many variables are **bounded**: there values are delimited by hard bounds. +This is typically the case for slider (aka "analog" scakes), dimensions scores (average or sum) from multiple Likert scales, percentages, proportions, etc. + +Most psychometric indices are bounded. +For instance, the minimum and maximum values for the IQ test (WAIS-IV) are 45-155. It is 0 and 63 for the depression scale BDI-II, 20 and 80 for the STAI. + +Despite this fact, we still most often use **linear models** to analyze these data, which is not ideal as it assumes that the dependent variable is continuous and normally distributed. + +### The Problem with Linear Models + + + +### Rescaling + +```{julia} +#| code-fold: false + + +``` + +### Beta Models ```{julia} #| code-fold: false @@ -15,12 +36,11 @@ using Distributions, Random using Turing # Reparameterized Beta distribution -function MeanVarBeta(μ, σ²) - if σ² <= 0 || σ² >= μ * (1 - μ) - error("Variance σ² must be in the interval (0, μ*(1-μ)=$(μ*(1-μ))).") +function BetaMean(μ, σ) + if σ <= 0 || σ >= sqrt(μ * (1 - μ)) + error("Standard deviation σ must be in the interval (0, sqrt(μ*(1-μ))=$(sqrt(μ*(1-μ)))).") end - - ν = μ * (1 - μ) / σ² - 1 + ν = μ * (1 - μ) / σ^2 - 1 α = μ * ν β = (1 - μ) * ν @@ -28,6 +48,13 @@ function MeanVarBeta(μ, σ²) end ``` +::: {.callout-caution} +TODO: Replace if it is supported somewhere (e.g., [Distributions.jl](https://github.com/JuliaStats/Distributions.jl/issues/1877)) +::: + + +![](media/scales_BetaMean.gif) + ```{julia} #| eval: false @@ -42,7 +69,6 @@ chains = sample(model_Beta(rand(MeanVarBeta(0.5, 0.2), 200)), NUTS(), 500; initial_params=[0.5, 0.1]) ``` -- https://github.com/JuliaStats/Distributions.jl/issues/1877 ### OrdBeta Models diff --git a/content/4a_rt_descriptive.qmd b/content/4a_rt_descriptive.qmd index 78b7563..61fce9f 100644 --- a/content/4a_rt_descriptive.qmd +++ b/content/4a_rt_descriptive.qmd @@ -572,7 +572,7 @@ The `loo_compare()` function orders models from best to worse based on their ELP As one can see, traditional linear models perform terribly. -## Other Models + \ No newline at end of file diff --git a/content/4b_rt_generative.qmd b/content/4b_rt_generative.qmd index 52d40a0..5740182 100644 --- a/content/4b_rt_generative.qmd +++ b/content/4b_rt_generative.qmd @@ -49,9 +49,12 @@ While such "generative" models offer potential insights into the cognitive proce Interestingly, the **Wald** model is actually a special case of a more general type called the **Drift Diffusion Model (DDM)** (named as such because the evidence accumulation is assumed to be a "diffusion" process, i.e., a random walk). One of the main difference is that in the Wald model, the drift rate $\nu$ must be *positive*, as it tracks the time taken by the diffusion processes to reach only one "positive" threshold $\alpha$. -But what happens if we relax this and allow the drift rate to be null or negative? Many traces might never reach the upper threshold, and might instead reach high "negative" values. +But what happens if we relax this and allow the drift rate to be null or negative? Many traces might never reach the upper threshold, and might instead reach high "negative" values. +The idea is then to also consider a **lower threshold**, which would correspond to a different response. +Finally, one could also modulate the starting point of the process relative to the thresholds (i.e., how close to the upper or lower threshold the accumulation process starts). +This is, in essence, the core idea behind the **Drift Diffusion Model**. -Drift Diffusion Models are useful to **jointly model RTs and a binary outcome**, such as 2 different choices or accuracy (i.e., "correct" vs. "error"). +Drift Diffusion Models are useful to **jointly model RTs and a binary outcome**, such as 2 different choices or accuracy (e.g., "correct" vs. "error"). They allow, in theory, to delineate various cognitive processes, such as the **speed** of evidence accumulation (drift rate), the **amount of evidence** required to make a decision (threshold), and the starting point of the accumulation process (bias). ![](media/rt_ddm.gif) @@ -96,3 +99,4 @@ TODO. - [**Lindelov's overview of RT models**](https://lindeloev.github.io/shiny-rt/): An absolute must-read. - [**De Boeck & Jeon (2019)**](https://www.frontiersin.org/articles/10.3389/fpsyg.2019.00102/full): A paper providing an overview of RT models. - [https://github.com/vasishth/bayescogsci](https://github.com/vasishth/bayescogsci) +- [An expert guide to planning experimental tasks for evidence accumula6on modelling (Boag, 2024)](https://osf.io/preprints/psyarxiv/snqgp) \ No newline at end of file diff --git a/content/media/animations_scales.jl b/content/media/animations_scales.jl index c9d7c78..0de4279 100644 --- a/content/media/animations_scales.jl +++ b/content/media/animations_scales.jl @@ -25,111 +25,93 @@ end # BetaMod ======================================================================================= using Turing, Distributions, Random -# Reparameterized Beta distribution -function MeanVarBeta(μ, σ²) - if σ² <= 0 || σ² >= μ * (1 - μ) - error("Variance σ² must be in the interval (0, μ*(1-μ)=$(μ*(1-μ))).") +# # Reparameterized Beta distribution +# function MeanVarBeta(μ, σ²) +# if σ² <= 0 || σ² >= μ * (1 - μ) +# error("Variance σ² must be in the interval (0, μ*(1-μ)=$(μ*(1-μ))).") +# end + +# ν = μ * (1 - μ) / σ² - 1 +# α = μ * ν +# β = (1 - μ) * ν + +# return Beta(α, β) +# end +# var(MeanVarBeta(0.3, 0.1)) +# mean(MeanVarBeta(0.3, 0.1)) + +function BetaMean(μ, σ) + if σ <= 0 || σ >= sqrt(μ * (1 - μ)) + error("Standard deviation σ must be in the interval (0, sqrt(μ*(1-μ))=$(sqrt(μ*(1-μ)))).") end - - ν = μ * (1 - μ) / σ² - 1 + ν = μ * (1 - μ) / σ^2 - 1 α = μ * ν β = (1 - μ) * ν return Beta(α, β) end -var(MeanVarBeta(0.3, 0.1)) -mean(MeanVarBeta(0.3, 0.1)) +std(BetaMean(0.3, 0.2)) +mean(BetaMean(0.3, 0.2)) + # Range of possible parameters fig = Figure() -ax = Axis(fig[1, 1], xlabel="μ", ylabel="variance σ²") -for μ in range(0.0, 1, length=200) - for σ in range(0, 1, length=200) - x = range(0, 1, length=100) - try - y = pdf.(MeanVarBeta(μ, σ), x) - scatter!(ax, μ, σ, color=:red) - catch - continue - end - end -end -ylims!(ax, 0, 0.5) -# ablines!(ax, [0, 1], [1, -1]; color=:black) -xaxis = range(0, 1, length=1000) -lines!(ax, xaxis, xaxis .* (1 .- xaxis); color=:black) -fig - - -using Turing, Distributions, Random - -# Reparameterized Beta distribution -function MeanVarBeta(μ, σ²) - if σ² <= 0 || σ² >= μ * (1 - μ) - error("Variance σ² must be in the interval (0, μ*(1-μ)=$(μ*(1-μ))).") - end - - ν = μ * (1 - μ) / σ² - 1 - α = μ * ν - β = (1 - μ) * ν - - return Beta(α, β) -end - -@model function model_Beta(x) - μ ~ Beta(1, 1) - σ ~ Uniform(eps(typeof(μ)), μ * (1 - μ) - eps(typeof(μ))) - for i in 1:length(x) - x[i] ~ MeanVarBeta(μ, σ) - end -end -chains = sample(model_Beta(rand(MeanVarBeta(0.5, 0.2), 200)), NUTS(), 500; initial_params=[0.5, 0.1]) - +μ = Observable(0.5) +σ = Observable(0.05) +ax1 = Axis(fig[1, 1], title="Possible parameter range", xlabel="μ", ylabel="σ", yticks=range(0, 0.5, 6)) +ylims!(ax1, 0, 0.6) +# ablines!(ax, [0, 1], [1, -1]; color=:black) +xaxis = range(0, 1, length=1000) +yaxis = sqrt.(xaxis .* (1 .- xaxis)) +band!(ax1, xaxis, 0, yaxis, color=:orange) +lines!(ax1, xaxis, yaxis; color=:red) +text!(ax1, 0, 0.55, text="max. σ = √(μ * (1 - μ))", align=(:left, :center), color=:red) +scatter!(ax1, @lift([$μ]), @lift([$σ]); color="#2196F3", marker=:xcross, markersize=15) +fig -μ = Observable(0.5) -σ = Observable(0.1) -# Initialize the figure -fig = Figure() -ax = Axis( - fig[1, 1], - title=@lift("BetaMod(μ = $(round($μ, digits = 1)), σ = $(round($σ, digits = 2)))"), +ax2 = Axis( + fig[1, 2], + title=@lift("BetaMean(μ = $(round($μ, digits = 1)), σ = $(round($σ, digits = 2)))"), xlabel="Score", ylabel="Distribution", yticksvisible=false, xticksvisible=false, yticklabelsvisible=false, ) -ylims!(ax, 0, 10) +ylims!(ax2, 0, 10) +xlims!(ax2, 0, 1) -x = range(0, 1, length=100) -y = @lift(pdf.(MeanVarBeta($μ, $σ), x)) +x = range(0, 1, length=1000) +y = @lift(pdf.(BetaMean($μ, $σ), x)) -lines!(ax, x, y) +band!(ax2, x, 0, y, color="#2196F3") fig function make_animation(frame) - if frame < 0.15 - μ[] = change_param(frame; frame_range=(0.0, 0.15), param_range=(0.5, 0.9)) + if frame < 0.20 + σ[] = change_param(frame; frame_range=(0.0, 0.20), param_range=(0.05, 0.46)) end if frame >= 0.25 && frame < 0.45 - μ[] = change_param(frame; frame_range=(0.25, 0.45), param_range=(0.9, 0.1)) + μ[] = change_param(frame; frame_range=(0.25, 0.45), param_range=(0.5, 0.2)) + σ[] = change_param(frame; frame_range=(0.25, 0.45), param_range=(0.46, 0.2)) end - if frame >= 0.55 && frame < 0.65 - σ[] = change_param(frame; frame_range=(0.55, 0.65), param_range=(0.1, 0.3)) + if frame >= 0.50 && frame < 0.65 + μ[] = change_param(frame; frame_range=(0.50, 0.65), param_range=(0.2, 0.85)) + σ[] = change_param(frame; frame_range=(0.50, 0.65), param_range=(0.2, 0.1)) end # Return to normal if frame >= 0.7 && frame < 0.9 - μ[] = change_param(frame; frame_range=(0.7, 0.9), param_range=(0.1, 0.5)) - σ[] = change_param(frame; frame_range=(0.7, 0.9), param_range=(0.3, 0.1)) + μ[] = change_param(frame; frame_range=(0.7, 0.9), param_range=(0.85, 0.5)) + σ[] = change_param(frame; frame_range=(0.7, 0.9), param_range=(0.1, 0.05)) end end # animation settings frames = range(0, 1, length=120) -record(make_animation, fig, "scales_MeanVarBeta.gif", frames; framerate=20) +record(make_animation, fig, "scales_BetaMean.gif", frames; framerate=10) diff --git a/content/media/scales_BetaMean.gif b/content/media/scales_BetaMean.gif new file mode 100644 index 0000000000000000000000000000000000000000..3ef736638998c91954bbf127172c0212227f5fd9 GIT binary patch literal 203899 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za`XFQPh@vyVYPh$wL+x3FN0ZpjB8NpY>4pH* zB7CbH#v_v^GOqf)A6@b>E@@(lBpFOb75gb92;~<-224~VKr{-3Az%@= z00#je4A61`G7p7RGLRNIf&~8MM~gh2n^`7XjL0D^a@2qd>c_~v-V|V84ry^9t9l3? w*W6EoynTfY_pzMe#odz4<^NXR*a*syWE=_+c4$BajsEA^@V^iK|CPA?4_$E0rvLx| diff --git a/data/make_data.R b/data/make_data.R index 74b8bb1..f425792 100644 --- a/data/make_data.R +++ b/data/make_data.R @@ -47,10 +47,25 @@ df <- df |> df <- df[complete.cases(df),] -# df |> -# group_by(Gender) |> -# summarize(Neuroticism = mean(Neuroticism), -# Agreeableness = mean(Agreeableness)) write.csv(df, "harman1967.csv", row.names = FALSE) + + +# Patho Personality ------------------------------------------------------------- + + +df <- read.csv("https://raw.githubusercontent.com/RealityBending/IllusionGameValidation/main/data/study3.csv") |> + select(starts_with("IPIP6_"), starts_with("PID5_"), -PID5_SD, -IPIP6_SD) |> + mutate(across(starts_with("IPIP6_"), \(x) datawizard::rescale(x, range=c(0, 100), to=c(1, 7))), + across(starts_with("PID5_"), \(x) datawizard::rescale(x, range=c(0, 100), to=c(0, 3))) ) + +df <- df[complete.cases(df),] + +ggplot(df, aes(x=PID5_Disinhibition)) + + geom_histogram(bins = 60) + +write.csv(df, "makowski2023.csv", row.names = FALSE) + + + diff --git a/data/makowski2023.csv b/data/makowski2023.csv new file mode 100644 index 0000000..f82e33e --- /dev/null +++ b/data/makowski2023.csv @@ -0,0 +1,243 @@ +"IPIP6_Extraversion","IPIP6_Conscientiousness","IPIP6_Neuroticism","IPIP6_Openness","IPIP6_HonestyHumility","IPIP6_Agreeableness","PID5_Disinhibition","PID5_Detachment","PID5_NegativeAffect","PID5_Antagonism","PID5_Psychoticism" +2.53,2.455,5.515,5.59,6.91,5.935,0.042,1.122,2.202,0.018,1.02 +4.66,4.21,4.045,5.53,3.4,4.63,1.368,0.858,1.488,1.38,1.77 +3.91,5.635,2.425,6.775,4.51,4.06,1.242,1.05,0.054,0.744,0.39 +1,4.165,6.235,5.275,4.33,4.06,0.45,1.62,1.626,1.698,1.32 +5.725,5.845,3.52,5.785,3.715,5.41,0.612,0.318,0.126,0.81,0.162 +2.185,3.49,1,5.875,6.79,3.43,0.708,2.112,0,0.12,1.14 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