### A Pluto.jl notebook ###
# v0.16.1

using Markdown
using InteractiveUtils

# ╔═╡ c8032155-0298-438c-8d2e-e711ce8a3055
begin 
	using Arrow
	using AlgebraOfGraphics
	using CairoMakie   # for displaying static plots in a Pluto notebook
	using CategoricalArrays
	using Chain
	using DataFrames
	using DataFrameMacros
	using MixedModels
	using MixedModelsMakie
	using Random
	using Statistics
	using StatsBase
	using StatsPlots
	using AlgebraOfGraphics: density
	using AlgebraOfGraphics: boxplot
	using MixedModelsMakie: qqnorm
	using MixedModelsMakie: ridgeplot
	using MixedModelsMakie: scatter
	const rng = MersenneTwister(1234321)
	CairoMakie.activate!(type="svg") # use SVG (other options include PNG)
	Base.show(io::IO, ::MIME"text/html", 
		       x::CategoricalArrays.CategoricalValue) = print(io, get(x)) 
end

# ╔═╡ e53c82d6-6deb-4a2c-a127-9cd6805cc74b
md"""
# RePsychLing Kliegl, Kuschela, & Laubrock (2015)

## Date: 2021-09-29

## Background

This is a follow-up to ([Kliegl et al., 2011; Frontiers](https://doi.org/10.3389/fpsyg.2010.00238); see also script `kwdyz.jl`) from an experiment looking at a variety of effects of visual cueing under four different cue-target relations (CTRs). In this experiment two rectangles are displayed (1) in horizontal orientation , (2) in vertical orientation, (3) in left diagonal orientation, or in (4) right diagonal orientation relative to a central fixation point. Subjects react to the onset of a small or a large visual target occuring at one of the four ends of the two rectangles. The target is cued validly on 70% of trials by a brief flash of the corner of the rectangle at which it appears; it is cued invalidly at the three other locations 10% of the trials each. This implies a latent imbalance in design that is not visiable in the repeated-measures ANOVA, but we will show its effect in the random-effect structure and conditional modes. 

There are a couple of differences between the first and this follow-up experiment, rendering it more a conceptual than a direct replication. First, the original experiment was carried out at Peking University and this follow-up at Potsdam University. Second, diagonal orientations of rectangles and large target sizes were not part of the design of Kliegl et al. (2011). To keep matters somewhat simpler and comparable we ignore them in this script.  

We specify three contrasts for the four-level factor CTR that are derived from spatial, object-based, and attractor-like features of attention.  They map onto sequential differences between appropriately ordered factor levels. Replicating Kliegl et al. (2011), the attraction effect was not significant as a fixed effect, but yielded a highly reliable variance component (VC; i.e., reliable individual differences in positive and negative attraction effects cancel the fixed effect). Moreover, these individual differences in the attraction effect were negatively correlated with those in the spatial effect.

This comparison is of interest because a few years after the publication of Kliegl et al. (2011), the theoretically critical correlation parameter (CP) between the spatial effect and the attraction effect was determined as the source of a non-singular LMM in that paper. The present study served the purpose to estimate this parameter with a larger sample and a wider variety of experimental conditions. Therefore, the code in this script is largely the same as the one in `kwdyz.jl`. 
 
There will be another vignette modelling the additional experimental manipulations of target size and orientation of cue rectangle. This analysis was reported in the parsimonious mixed-model paper [(Bates et al., 2015)](https://arxiv.org/abs/1506.04967); they were also used in a paper of GAMMs [(Baayen et al., 2017)](https://doi.org/10.1016/j.jml.2016.11.006) Data and R scripts are also available in [R-package RePsychLing](https://github.com/dmbates/RePsychLing/tree/master/data/). Here we provide some of the corresponding analyses with _MixedModels.jl_ and a much wider variety of visualizations of LMM results. A _MixedModels.jl_-based analysis focusing on the complex experimental design and the analysis of a complex random-effect structure for this design is in script `kkl15_complex.jl`.

## Packages
"""

# ╔═╡ 539399d9-1b68-4d90-8e63-ff5f2674c494
md" ## Read data, compute and plot means"

# ╔═╡ 47e078b0-41ab-4186-8680-aff3a79ea3c7
begin
	dat = select(DataFrame(Arrow.Table("./data/kkl15.arrow")),
		:subj => (s -> categorical(string.('S', lpad.(s, 3, '0')))) => :Subj,
		:tar => categorical => :CTR,
		:rt)
	levels!(dat.CTR, ["val", "sod", "dos", "dod"])
	@transform!(dat,  :lrt = log(:rt))
	describe(dat)
end

# ╔═╡ 120fa224-f345-4c08-a6fa-f54e5efe7a39
md""" We recommend to code the levels/units of random factor / grouping variable not as a number, but as a string starting with a letter and of the same length for all levels/units. 

We also recommend to sort levels of factors into a meaningful order, that is overwrite the default alphabetic ordering. This is also a good place to choose alternative names for variables in the context of the present analysis.

The LMM analysis is based on log-transformed reaction times `lrt`, indicated by a _boxcox()_ check of model residuals. With the exception of diagnostic plots of model residuals, the analysis of untransformed reaction times did not lead to different results."""

# ╔═╡ 74d331c7-8574-4164-9ba6-1652c717d5e3
md"""
Comparative density plots of all response times by cue-target relation show the times for valid cues to be faster than for the other conditions.
"""

# ╔═╡ dd297971-1728-48d8-b73e-94d87555355e
data(dat) * 
mapping(
	:lrt => "log(Reaction time [ms])",	
	color= :CTR => renamer(
		"val" => "valid cue",   
		"sod" => "some obj/diff pos",
		"dos" =>  "diff obj/same pos", 
		"dod" => "diff obj/diff pos"
	) => "Cue-target relation",     
) * density() |> draw

# ╔═╡ 857a672f-9d1e-46da-aa90-5a0a48fdbf2e
md" An alternative visualization without overlap of the conditions can be accomplished with ridge plots."

# ╔═╡ 9191733b-0a81-4c82-8b64-4be285970e9e
md" **To be done** "

# ╔═╡ d10eeea1-12aa-4f22-b0fc-89c47016a09d
md" For the next set of plots we average the 86 subjects' data within the four experimental conditions. This table could be used as input for a repeated-measures ANOVA."

# ╔═╡ 56e0c598-680d-420b-9dbf-7362cba4d20e
md" For the next set of plots we average subjects' data within the four experimental conditions. This table could be used as input for a repeated-measures ANOVA.

Boxplots of the mean of log response time by subject under the different conditions show an outlier value under three of the four conditions; they are from the same subject."

# ╔═╡ 7795367d-5286-4311-baf5-9f69190f9cfa
dat_subj = combine(groupby(dat, [:Subj, :CTR]),
	:rt => length => :n, 
    :rt => mean => :rt_m,
    :lrt  => mean => :lrt_m
)

# ╔═╡ 90b45536-4397-418a-8bea-887a6d5bdff9
dat_cond = combine(groupby(dat_subj, [:CTR]),
	:n => length => :N,
    :lrt_m => mean => :lrt_M, 
    :lrt_m  => std => :lrt_SD, 
    :lrt_m => (x -> std(x)/sqrt(length(x))) => :lrt_SE,
)

# ╔═╡ ed4a011b-1773-4085-870e-5161ef3e501a
boxplot(
	dat_subj.CTR.refs,
	dat_subj.lrt_m;
	orientation=:horizontal,
	show_notch=true,
	axis=(; yticks=(
			1:4,
			[
				"valid cue",
				"same obj/diff pos",
				"diff obj/same pos",
				"diff obj/diff pos"
			]
		)
	),
	figure=(;resolution=(800, 300)),
)

# ╔═╡ ef659cc3-c948-49aa-9832-a8f69fd5cf5a
md"""
Mean of log reaction times for four cue-target relations. Targets appeared at (a) the cued position (valid) in a rectangle, (b) in the same rectangle cue, but at its other end, (c) on the second rectangle, but at a corresponding horizontal/vertical physical distance, or (d) at the other end of the second rectangle, that is $\sqrt{2}$ of horizontal/vertical distance diagonally across from the cue, that is also at larger physical distance compared to (c).

We remove the outlier subject and replot, but we model the data points in `dat` and check whether this subject appears as an outlier in the caterpillar plot of conditional modes.
"""

# ╔═╡ bf96e629-5bf3-4292-9572-0f47dff48608
dat_subj2 = @subset(dat_subj, :rt_m < 510);

# ╔═╡ 3fb2caa9-6873-42c9-8419-421d0cec2d16
boxplot(
	dat_subj2.CTR.refs,
	dat_subj2.lrt_m;
	orientation=:horizontal,
	show_notch=true,
	axis=(; yticks=(
			1:4,
			[
				"valid cue",
				"same obj/diff pos",
				"diff obj/same pos",
				"diff obj/diff pos"
			]
		)
	),
	figure=(;resolution=(800, 300)),
)

# ╔═╡ 4001cfa9-0fbe-40e3-b324-e0c1c26c6b8c
md" A better alternative to the boxplot is often a dotplot, because it also displays subjects' condition means."

# ╔═╡ 9f41d2bf-4c14-46db-9b65-f685afb19d2c
md" **To be done** "

# ╔═╡ 6fa62496-2432-4423-9e55-fd37b3f4f849
md"""
We can also look at correlations plots based on the four condition means. There are actually two correlation matrices which have correspondences in alternative parameterizatios of the LMM random-effec structure. One matrix is based on the four measures. If you think of the four measures as test scores, this matrix is the usual correlation matrix. The second matrix contains correlations between the Grand Mean (GM) and the three effects defined with the contrasts for the four levels of the condition factor in the next chunk. 

To this end, we

+ use the `unstack()` command to convert data from long to wide format,
+ compute the GM and the three experimental effects.
+ plot the correlation matrix for four measures/scores, and
+ plot the correlation matrix for GM and three effects

"""

# ╔═╡ f50e0fff-665b-4056-993c-b6dac881785b
begin
	dat_subj_w = unstack(dat_subj, :Subj, :CTR, :rt_m)
	@transform!(dat_subj_w,  :GM = (:val + :sod + :dos + :dod) ./4)
    @transform!(dat_subj_w,  :spatial =    :sod - :val)
	@transform!(dat_subj_w,  :object =     :dos - :sod)
	@transform!(dat_subj_w,  :attraction = :dod - :dos)
	describe(dat_subj_w)
end

# ╔═╡ a5226169-dd2e-4105-9569-98fd781332a4
@df dat_subj_w StatsPlots.corrplot(cols(2:5), grid = false, compact=false)

# ╔═╡ 1e740cc3-3037-4fa3-82d2-75b13b86a593
@df dat_subj_w StatsPlots.corrplot(cols(6:9), grid = false, compact=false)

# ╔═╡ 019a4876-e32d-41f4-9636-7efaea5e4929
md"**Note:** Two of the theoreticsally irrelevant within-subject effect correlations have a different sign than the corresponding, non-significant CPs in the LMM; they are negative here, numerically positive in the LMM. This occurs only very rarely in the case of ecological correlations. However, as they are not significant according to shortest coverage interval, it may not be that relevant either. It is the case both for effects based on log-transformed and raw reaction times."

# ╔═╡ 317f7e3d-94ef-4a36-a45d-e08b5fe0cd20
md"""## Linear mixed model
"""

# ╔═╡ e827e62a-b458-46a7-a86c-b3c3392c3e6a
cntr1 = Dict(
    :CTR  => SeqDiffCoding(levels=["val", "sod", "dos", "dod"]),
 	)

# ╔═╡ bd24f002-3f17-4cea-b371-5a972956da11
begin	
	formula = @formula  lrt ~ 1 + CTR + (1 + CTR | Subj);
	m1 = fit(MixedModel, formula, dat, contrasts=cntr1)
end

# ╔═╡ 21ab3d31-c385-4520-a8c7-927d8d63f074
VarCorr(m1)

# ╔═╡ 51cab366-6b2d-4b27-a248-947a0e8032cb
issingular(m1)

# ╔═╡ 60a3548e-796c-4bdf-95c7-6fefbbb35cb9
MixedModels.PCA(m1)

# ╔═╡ 960f1f33-d24d-4aa8-a806-e948aeaa711d
md" We note that the critical correlation parameter between spatial (`sod`) and attraction (`dod`) is now estimated at .66 -- not that close to the 1.0 boundary that caused singularity in Kliegl et al. (2011; `kydwz11.jl`). However, the LMM based on log reaction times is still singular. Let's check for untransformed reaction times."  

# ╔═╡ dbc8c8fb-2ca0-4424-9dfa-458b21c96130
begin	
	formula_rt = @formula  rt ~ 1 + CTR + (1 + CTR | Subj);
	m1_rt = fit(MixedModel, formula_rt, dat, contrasts=cntr1)
	VarCorr(m1_rt)
end

# ╔═╡ d46d1bc3-baf5-4e93-8f4f-e3d400e5b0dd
issingular(m1_rt)

# ╔═╡ 37a7fbf7-68e7-419f-80fc-7c0ad0d30fa3
md"For untransformed reaction times, we the model is **not** singular."

# ╔═╡ 0ffa0a85-f197-47ce-8e22-4a7667ffd404
md""" ## Diagnostic plots of LMM residuals

Do model residuals meet LMM assumptions? Classic plots are 

+ Residual over fitted
+ Quantiles of model residuals over theoretical quantiles of normal distribution

### Residual-over-fitted plot

The slant in residuals show a lower and upper boundary of reaction times, that is we have have too few short and too few long residuals. Not ideal, but at least width of the residual band looks similar across the fitted values, that is there is no evidence for heteroskedasticity.
"""

# ╔═╡ e215a6c6-3499-4bd4-bdc5-c153ade0122a
scatter(fitted(m1), residuals(m1))

# ╔═╡ 2a00f1e4-f7a0-4b4f-941e-739c0af69a15
md" With many observations the scatterplot is not that informative. Contour plots or heatmaps may be an alternative. "

# ╔═╡ 2d5e62f0-170b-49a6-b9fd-cfb3ee06c59b
begin
	set_aog_theme!()
	df_rof = DataFrame(fitted = fitted(m1), resid=residuals(m1))
	data(df_rof) * mapping(:fitted, :resid) * density() |> draw
end

# ╔═╡ 89ffc792-7637-4e38-b80b-1b1406222fcd
md""" ### Q-Q plot

The plot of quantiles of model residuals over corresponding quantiles of the normal distribution should yield a straight line along the main diagonal. 
"""

# ╔═╡ bf4682ef-a098-4625-ab09-fdc381663916
qqnorm(m1)

# ╔═╡ dccc2e5b-76f1-4a0a-a622-3f76faf705b5
qqnorm(m1_rt)

# ╔═╡ 78828df6-37c6-4078-b238-ff99f01f4524
md""" ### Observed and theoretical normal distribution

The violation of expectation is again due to the fact that the distribution of residuals is narrower than expected from a normal distribution. We can see this in this plot. Overall, it does not look too bad.
"""

# ╔═╡ 1ea84110-ea5f-4eb1-9b56-54a35bff5099
begin
 n=nrow(dat)
 dat_rz = DataFrame(value=vcat(residuals(m1) ./ std(residuals(m1)), randn(n)), 
		            curve= vcat(fill.("residual", n), fill.("normal", n)))
 data(dat_rz) * mapping(:value, color=:curve) * density(bandwidth=.1) |> draw
end

# ╔═╡ 12e3d62f-0330-440d-9971-19d11c1993e0
md""" ## Conditional modes
### Caterpillar plot
"""

# ╔═╡ edbf6df5-bca3-4b5f-8c4c-a7c346899319
begin
	cm1 = ranefinfo(m1)[:Subj]
	caterpillar!(Figure(; resolution=(800,1000)), cm1; orderby=2)
end

# ╔═╡ f165a8e8-ec47-4262-956f-ab72d016afc1
md" When we order the conditional modes for GM, that is `(Intercept)`, the outlier subject _S113_ becomes visible; the associated experimental effects are not unusual."

# ╔═╡ 186c1a60-61d2-472c-8bdb-0a74728ea478
caterpillar!(Figure(; resolution=(800,1000)), cm1; orderby=1)

# ╔═╡ 7409472a-97a3-4790-83ed-e6760e4230fd
md"The catepillar plot also reveals that credibilty intervals are much shorter for subjects' Grand Means, shown in `(Intercept)`, than the subjects' experimental effects, because the latter are based on difference scores not means. Moreover, credibility intervals are shorter for the first spatial effect `sod` than the other two effects, because the spatial effect involves the valid condition which yielded three times as many trials than the other three conditions. Consequently, the spatial effect is more reliable. Unfortunately, due to differences in scaling of the x-axis of the panels this effect must be inferred. One option to reveal this difference is to reparameterize the LMM such model parameters estimate the conditional modes for the levels of condition rather than the contrast-based effects. This is accomplished by replacing the `1` in the random effect term with `0`, as shown next.
"

# ╔═╡ 9c8ee297-e4db-4c25-9ef6-1052050f3d43
begin	
	formula1L = @formula  rt ~ 1 + CTR + (0 + CTR | Subj);
	m1L = fit(MixedModel, formula1L, dat, contrasts=cntr1)
	VarCorr(m1L)
end

# ╔═╡ 94863fb5-a7e5-4eff-ad81-44a157a54e62
md" The caterpillar plot for levels shows the effect of the number of trials on credibility intervals; they are obviously much shorter for the valid condition. Note that this effect is not visible in a repeated-measure ANOVA with four condition means per subject as input." 

# ╔═╡ e8f21abc-6658-4d51-9a71-28eadec35065
begin
	cm1L = ranefinfo(m1L)[:Subj]
	caterpillar!(Figure(; resolution=(800,1000)), cm1L; orderby=1)
end

# ╔═╡ 2586e36d-36f7-480f-8848-5a4ace1f0b80
md"""### Shrinkage plot

#### Log-transformed reaction times (LMM `m1`)
"""

# ╔═╡ 06ba4e03-ecf1-492c-9c47-1dfa1ce2550a
shrinkageplot!(Figure(; resolution=(1000,1000)), m1)

# ╔═╡ aa38afc2-3eed-45f1-84d5-533861bd59ed
md"
Three of the CPs are imploded, but not the theoretically critical ones. These implosions did not occur (or were not as visible) for raw reaction times."

# ╔═╡ abda9d25-9308-4bf7-83cc-b5ad8ab30d19
md" #### Raw reaction times (LMM `m1_rt`)"

# ╔═╡ 1ce5ba11-d404-4611-ad2a-fa10796e7315
shrinkageplot!(Figure(; resolution=(1000,1000)), m1_rt)

# ╔═╡ e9b57232-8a63-45f9-938b-6c2e868d8a2e
md"The implosion is for three CP visualizations is not observed for raw reaction times. Interesting."

# ╔═╡ 19d5fc45-5547-4cef-abb9-19e6636aa162
md""" ## Parametric bootstrap

Here we 

+ generate a bootstrap sample
+ compute shortest covergage intervals for the LMM parameters
+ plot densities of bootstrapped parameter estimates for residual, fixed effects, variance components, and correlation parameters

### Generate a bootstrap sample

We generate 10,000 samples for the 15 model parameters (4 fixed effect, 4 VCs, 6 CPs, and 1 residual).
""" 

# ╔═╡ f840717c-8bd2-4358-a85f-df4b6eb0d8a8
begin
	samp = parametricbootstrap(rng, 10_000, m1) # use m1_rt for raw reaction times
	dat2 = DataFrame(samp.allpars)
	first(dat2, 10)
end

# ╔═╡ 63dc9d34-8c7c-4dd8-af62-8717e9e73946
nrow(dat2) # 10_000 estimates for each of 15 model parameters 

# ╔═╡ d600ea54-8848-4c2b-a364-b8dcc42a5491
md" ### Shortest coverage interval"

# ╔═╡ 8b158499-04f6-43a2-be6c-7ca5e28e0ce7
DataFrame(shortestcovint(samp))

# ╔═╡ c4d81087-18d7-4958-963c-d9dc304cb7ca
md"We can also visualize the shortest coverage intervals for fixed effects with the `ridgeplot()` command:"

# ╔═╡ 3b4b8f63-44ba-4399-8d9e-31293f7d24c0
ridgeplot(samp, show_intercept=false)

# ╔═╡ ecf2d9c6-9e91-4bc7-adec-6b576bd6471f
md""" ### Comparative density plots of bootstrapped parameter estimates 

#### Residual 
"""

# ╔═╡ 06a66a4e-792f-4302-8530-75905c4d3922
data(@subset(dat2, :type == "σ" && :group == "residual")) * 
mapping(:value => "Residual") * density() |> draw

# ╔═╡ aa2531f8-3016-4f53-b4f5-68bfb293a192
md""" #### Fixed effects (w/o GM)

The shortest coverage interval for the `GM` ranges from 376 to 404 ms. To keep the plot range small we do not inlcude its density here.
"""


# ╔═╡ ce5cfe1a-7c90-41be-a489-fba2e25d4b3c
begin
	let 
	labels = [
		"CTR: sod" => "spatial effect",
		"CTR: dos" => "object effect",
		"CTR: dod" => "attraction effect",
	]
	data(@subset(dat2, :type == "β" && :names ≠ "(Intercept)")) * 
	mapping(:value => "Experimental effect size [ms]", 
	color=:names => renamer(labels) => "Experimental effects") * density() |> draw
	end
end

# ╔═╡ 5cf09fc4-7857-4a85-ada3-4980f3d1a571
md"The densitiies correspond nicely with the shortest coverage intervals."

# ╔═╡ 8ff68199-69ae-4290-872c-f64e8ccc0a24
begin
	let 
	labels = [
		"(Intercept)" => "GM",
		"CTR: sod" => "spatial effect",
		"CTR: dos" => "object effect",
		"CTR: dod" => "attraction effect",
	]
	data(@subset(dat2, :type == "σ" && :group == "Subj")) * 
	mapping(:value => "Standard deviations [ms]", 
	color=:names => renamer(labels) => "Variance components") * density() |> draw
	end
end

# ╔═╡ 20449205-de59-4f4f-b591-b6b7107772e9
md" The VC are all very nicely defined. "

# ╔═╡ 7e674218-3bf2-426e-b10b-579719d60a24
md"""
#### Correlation parameters (CPs)
"""

# ╔═╡ c0cc261d-3b48-4fc5-965f-c8b57dc7783c
begin
	let
	labels = [
		"(Intercept), CTR: sod" => "GM, spatial",
		"(Intercept), CTR: dos" => "GM, object",
		"CTR: sod, CTR: dos" => "spatial, object",
		"(Intercept), CTR: dod" => "GM, attraction",
		"CTR: sod, CTR: dod" => "spatial, attraction",
		"CTR: dos, CTR: dod" => "object, attraction"
		]
	data(@subset(dat2, :type == "ρ")) * 
	mapping(:value => "Correlation", color=:names => renamer(labels) => "Correlation parameters") *
	density() |> draw
	end
end

# ╔═╡ e449e136-62ec-4e85-8470-3fdb2d804ce7
md"""Three CPs stand out positively, the correlation between GM and the spatial effect, GM and attraction effect, and the correlation between spatial and attraction effects. The second CP was positive, but not significant in the first study. The third CP replicates a CP that was judged questionable in script `kwdyz11.jl`. 

The three remaining CPs are not well defined for log-transformed reaction times; they only fit noise and should be removed. It is also possible that fitting the complex experimental design (including target size and rectangle orientation) will lead to more acceptable estimates. The corresponding plot based on LMM `m1_rt` for raw reaction times still shows them with very wide distributions, but acceptable.
"""

# ╔═╡ aefcc7ad-58af-42ea-b0d7-d8e96b12104b
md" **That's it for now. Have fun!** "

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
AlgebraOfGraphics = "cbdf2221-f076-402e-a563-3d30da359d67"
Arrow = "69666777-d1a9-59fb-9406-91d4454c9d45"
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
CategoricalArrays = "324d7699-5711-5eae-9e2f-1d82baa6b597"
Chain = "8be319e6-bccf-4806-a6f7-6fae938471bc"
DataFrameMacros = "75880514-38bc-4a95-a458-c2aea5a3a702"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
MixedModels = "ff71e718-51f3-5ec2-a782-8ffcbfa3c316"
MixedModelsMakie = "b12ae82c-6730-437f-aff9-d2c38332a376"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"

[compat]
AlgebraOfGraphics = "~0.5.4"
Arrow = "~2.1.0"
CairoMakie = "~0.6.5"
CategoricalArrays = "~0.10.1"
Chain = "~0.4.8"
DataFrameMacros = "~0.1.1"
DataFrames = "~1.2.2"
MixedModels = "~4.4.0"
MixedModelsMakie = "~0.3.10"
StatsBase = "~0.33.10"
StatsPlots = "~0.14.28"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.7.0-rc1"
manifest_format = "2.0"

[[deps.AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.0.1"

[[deps.AbstractTrees]]
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[[deps.Adapt]]
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git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
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[[deps.AlgebraOfGraphics]]
deps = ["Colors", "Dates", "FileIO", "GLM", "GeoInterface", "GeometryBasics", "GridLayoutBase", "KernelDensity", "Loess", "Makie", "PlotUtils", "PooledArrays", "RelocatableFolders", "StatsBase", "StructArrays", "Tables"]
git-tree-sha1 = "3746ac120f8b163dbd3bda0f36b6dec20c4f795a"
uuid = "cbdf2221-f076-402e-a563-3d30da359d67"
version = "0.5.4"

[[deps.Animations]]
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[[deps.ArgTools]]
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[[deps.Arpack]]
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[[deps.Arpack_jll]]
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git-tree-sha1 = "e214a9b9bd1b4e1b4f15b22c0994862b66af7ff7"
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[[deps.ArrayInterface]]
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[[deps.Arrow]]
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git-tree-sha1 = "c70e6a9dc363040d6ff31c8ccbadafc1103ff9c8"
uuid = "69666777-d1a9-59fb-9406-91d4454c9d45"
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[[deps.ArrowTypes]]
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[[deps.Artifacts]]
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[[deps.Automa]]
deps = ["Printf", "ScanByte", "TranscodingStreams"]
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[[deps.AxisAlgorithms]]
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[[deps.Base64]]
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[[deps.BenchmarkTools]]
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[[deps.BitIntegers]]
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[[deps.Bzip2_jll]]
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[[deps.CEnum]]
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[[deps.Cairo]]
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[[deps.CairoMakie]]
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[[deps.Cairo_jll]]
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git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
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[[deps.CategoricalArrays]]
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[[deps.Chain]]
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[[deps.ChainRulesCore]]
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[[deps.Clustering]]
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[[deps.CodecBzip2]]
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git-tree-sha1 = "2e62a725210ce3c3c2e1a3080190e7ca491f18d7"
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[[deps.CodecLz4]]
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[[deps.CodecZlib]]
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[[deps.CodecZstd]]
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[[deps.ColorBrewer]]
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[[deps.ColorSchemes]]
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[[deps.ColorTypes]]
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[[deps.ColorVectorSpace]]
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[[deps.Colors]]
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[[deps.Compat]]
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[[deps.CompilerSupportLibraries_jll]]
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[[deps.ContextVariablesX]]
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[[deps.Contour]]
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[[deps.Crayons]]
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[[deps.DataAPI]]
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[[deps.DataFrameMacros]]
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deps = ["ColorTypes", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "OrderedCollections", "PkgVersion", "ProgressMeter"]
git-tree-sha1 = "945b8d87c5e8d5e34e6207ee15edb9d11ae44716"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.4.3"

[[deps.TimeZones]]
deps = ["Dates", "Future", "LazyArtifacts", "Mocking", "Pkg", "Printf", "RecipesBase", "Serialization", "Unicode"]
git-tree-sha1 = "6c9040665b2da00d30143261aea22c7427aada1c"
uuid = "f269a46b-ccf7-5d73-abea-4c690281aa53"
version = "1.5.7"

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[deps.URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.18.0+4"

[[deps.Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "80661f59d28714632132c73779f8becc19a113f2"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.4"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[deps.isoband_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "a1ac99674715995a536bbce674b068ec1b7d893d"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.2+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
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# ╠═1ce5ba11-d404-4611-ad2a-fa10796e7315
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# ╠═f840717c-8bd2-4358-a85f-df4b6eb0d8a8
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# ╠═7e674218-3bf2-426e-b10b-579719d60a24
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# ╟─aefcc7ad-58af-42ea-b0d7-d8e96b12104b
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
