### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# ╔═╡ fdf6853c-ddbf-4fd6-b4ca-c65b52f5b036
begin
	using CairoMakie
	using CSV
	using DataFrames
	using MixedModels
	using MixedModelsMakie
	CairoMakie.activate!(type="svg")
end

# ╔═╡ 7bb303da-e728-11eb-3cef-4f96ce335414
md"""
# MixedModels fits to data from Dorothea Pregla
"""

# ╔═╡ 9dfed156-b4f9-4b60-bfee-d0b4bdba2682
md"""
Dorothea provided the data in CSV format with missing data indicated by "NA".

First load the packages to be used.
"""

# ╔═╡ d0bf71cb-4f4e-4402-82b6-a85b1c84a090
md"""
Read the data from the .csv file and convert to a DataFrame.
"""

# ╔═╡ 112a2d45-642a-4156-abfc-ec7377ba637e
df = CSV.File("../../Dorothea_Pregla/SPL_decl.csv", missingstring="NA") |> DataFrame
# or CSV.read("../../Dorothea_Pregla/SPL_decl.csv", DataFrame; missingstring="NA")

# ╔═╡ 7f491d16-0dc4-4acf-86d8-c72ccd13836f
md"""
#### Description of the columns: (as given in the .rmd file)

- subj: subject number 
- item: number of the item (number of items: n=20)
- condition: a (canonical) and b (non-canonical), we did not use a latin square design, i.e., all participants saw both conditions of all items
- region: region in the sentence (0, 1, 2, 3, question)
  - 0: sentence onset ("hier")
  - 1: verb ("tröstet")
  - 2: NP1 ("der Tiger")
  - 3: adverb ("gerade")
  - question: NP2 + picture selection ("den Esel" + picture selection)
- subj_status: healthy control (HC) or individual with aphasia (IWA)
- sentence: the respective auditory presented sentence
- word: the respective word of the sentence
- rt: listening time for the respective region
- acc: picture selection accuracy
- age, sex, years of education: demographic data of the participant
- aphasia_type: Aachen aphasia test syndrome, NA for control participants
- digit_symbol_substitution: WAIS subtest, number of correct items in two minutes
- digit span, block span: WMS-R subtests, forward and backward raw scores and longest span
- picture span: working memory test, forward and backward raw scores and longest span
- lexdec: lexical decision task, mean reaction times in the task

The `subj` column is read as an integer.
Convert these values to strings.
I usually prepend the string with a character like `S` for subject and zero-pad the numbers so that sorting lexicographically is the same as sorting by numeric value.
"""

# ╔═╡ dabb1b1b-20cc-4644-a43b-2cae5a8d3222
df.subj = string.('S', lpad.(df.subj, ndigits(maximum(df.subj)), '0'));

# ╔═╡ b7cbf196-3071-45d8-8b5d-af25f981a553
describe(df)

# ╔═╡ ad91ad4a-c03a-4109-a445-75986c7a2164
md"""
### Initial model fit

In the .rmd file the contrasts for some of the variables are set by hand.
Here we will use a contrast specification as `EffectsCoding()` which produces -1/+1 coding for a two-level factor like :condition or :subj_status.

The initial model fit was for the subset of the data with `region == 2`.
"""

# ╔═╡ 4f21a265-7b53-4afc-bb6f-2442ef8a0540
m1 = fit(
	MixedModel,
	@formula(
		log(rt) ~
		1 + condition * subj_status +
		zerocorr(1 + condition * subj_status | item) +
		(1 + condition | subj)
	),
	filter(:region => ==("2"), df);
	contrasts = Dict(
		:subj => Grouping(),
		:item => Grouping(),
		:condition => EffectsCoding(),
		:subj_status => EffectsCoding(),
	),
	REML=true,
)

# ╔═╡ babe051a-40d1-48d2-ae28-8e6ed8e41af5
md"""
The REML criterion was used here to allow comparison with the `lmer` results.
The ML estimates are similar.
"""

# ╔═╡ 7cc1000d-fb72-4692-baca-a7001424e216
refit!(m1, REML=false)

# ╔═╡ 7f75d0e8-1cf4-4f82-ba81-6ff96de41315
md"""
Check that `condition`, `subj_status` and their interaction use the -1/+1 encoding.
"""

# ╔═╡ a09af6fd-d204-411f-b2ee-6712ce2b754d
Int.(m1.X')   # transpose of fixed-effects model matrix as integers (to save space)

# ╔═╡ 02cb5651-e0c9-4dec-9962-1191e4238674
md"""
The contrasts on `subj_status` and `condition` produce a +1/-1 coding and, if the data were balanced, these would give an `X'X` matrix which is diagonal.  (Even more, it would be a multiple of the identity, if you know what that expression means.)

In this case, the `subj_status` factor is observational rather than a controlled experimental factor and the levels are unbalanced.
"""

# ╔═╡ 5b704af5-8cb2-4ce4-8efe-1c32beb3b137
combine(groupby(filter(:region => ==("2"), df), :subj_status), nrow)

# ╔═╡ 356893dd-b0b4-4ffe-a3f7-0d37b62c1cce
md"resulting in some off-diagonal non-zeros in `X'X`"

# ╔═╡ abbe119c-0746-4a3d-afd2-ff669892423a
m1.X'm1.X

# ╔═╡ 51e4a5c2-6a46-4de2-9763-00705fe508de
md"""
### Some diagnostic plots

Despite years of effort we do not have a definitive way of deciding on a suitable random-effects structure.
One way of examining the "estimates" of the random effects (technically these are the conditional means of the random effects given the observed data but informally we can think of them as estimates), is to compare these values, which have been "shrunk" toward the origin, to what we would get if we did not apply any shrinkage.
"""

# ╔═╡ e261b642-ed8e-4c00-9ec5-b037e82af0e2
shrinkageplot(m1)

# ╔═╡ f7f6d39b-3ca0-48fe-b85d-6feaab5edf54
md"""
This plot indicates that the random effect for subject is strong, because there is very little horizontal shrinkage, but the random effect for condition by subject is much less important.

For the random effects by item
"""

# ╔═╡ 4b036283-2529-4225-86fd-d88b2c9a45c0
shrinkageplot(m1, :item)

# ╔═╡ 141bf8da-1d3e-4ac0-aeb9-67cf0c298a0b
md"""
the "implosion" patterns in the panels on the right indicate again that the random effects for condition and for `subj_status` by item are not substantial.

We can also examine the precision of the distribution of the random effects with a "caterpillar" plot (so-called because it can look like a fuzzy caterpillar).
These are marginal 95% prediction intervals on individual random effects.

When the number of levels of the grouping factor is moderate we present this plot with one row for each of the levels.  For definiteness in the plot we order the rows by increasing mean of one of the random effects terms - the first one by default.
"""

# ╔═╡ 579ca400-dac1-4988-b662-6a74dfa74841
caterpillar(m1, :item)

# ╔═╡ 3c7a1106-1c4d-4c32-b22e-c44e532f3d8e
md"""
In this plot all the intervals, except for `8retest` and `7test` on `(Intercept)`, contain zero.
This is evidence that the random effects for `condition`, `subj_status`, and their interaction by item are not terribly important.

Because a likelihood-ratio test comparing this model to `m2` that has only simple, scalar random effects for `item` gives a p-value of 47%, we prefer the simpler model, `m2`.
"""

# ╔═╡ 96278a24-e281-4801-a1f8-7f2899913c0d
m2 = fit(
	MixedModel,
	@formula(
		log(rt) ~
		1 + condition * subj_status +
		(1 | item) +
		(1 + condition | subj)
	),
	filter(:region => ==("2"), df);
	contrasts = Dict(
		:subj => Grouping(),
		:item => Grouping(),
		:condition => EffectsCoding(),
		:subj_status => EffectsCoding(),
	),
)

# ╔═╡ 2fb51bbe-1d07-4535-8520-14c58c47478c
MixedModels.likelihoodratiotest(m2, m1)

# ╔═╡ e58f70f5-36b1-45f7-83fe-f861fa806ba3
md"""
When the number of levels of the grouping factor is larger, the rows and the axis annotations become messy and we revert to a quantile-quantile type of plot with the vertical axis defined by quantiles of the standard Gaussian (or "normal") distribution.
For these `qqcaterpillar` plots the ordering of the intervals is determined separately for each panel.
"""

# ╔═╡ 06a8bb39-e030-4f04-a4c7-6b0755137c19
qqcaterpillar(m2)

# ╔═╡ d3b25e36-c042-4510-b8da-01a13b610b40
md"""
This plot shows that the random effects for subject are substantial, reflecting what we saw in the shrinkage plot, and a few of the random effects for condition by subject  have prediction intervals that do not overlap zero.
"""

# ╔═╡ 0d531471-076f-4e07-a7a9-9f2005d583be
sum(leverage(m2))

# ╔═╡ 5e72ae53-c55c-4800-aa01-97d2ffde18b7
sum(leverage(m1))

# ╔═╡ 00000000-0000-0000-0000-000000000001
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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.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"
"""

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