From 907249c28b9a64cebb440efa9a0a000ea1a0032a Mon Sep 17 00:00:00 2001 From: Reinhold Kliegl Date: Fri, 28 Aug 2026 03:05:52 +0200 Subject: [PATCH 1/9] RK updates, including new example eyevoicespan with figures comparing observed, partial, fitted plots for four interactions in Pan et al. (2013; pyslk13). --- _quarto.yml | 4 + contrasts/contrasts_kwdyz11.qmd | 1 + examples/emotikon/fggk21.qmd | 57 +- .../eyevoicespan/Pan_etal.DevSci.2013.pdf | Bin 0 -> 531793 bytes examples/eyevoicespan/pylsk13.qmd | 503 ++++++++++++++++++ examples/eyevoicespan/pylsk13.rda | Bin 0 -> 1549 bytes .../eyevoicespan/pylsk13_interactions.qmd | 305 +++++++++++ examples/eyevoicespan/pylsk13_v3.R | 304 +++++++++++ examples/eyevoicespan/pylsk13_v4.R | 187 +++++++ examples/eyevoicespan/remef.v0.6.9.R | 226 ++++++++ examples/visual-attention/kkl15.qmd | 6 +- examples/visual-attention/kwdyz11.qmd | 7 +- fits/eyevoicespan_m00.json.zip | 3 + fits/eyevoicespan_m05.json.zip | 3 + fits/eyevoicespan_m09.json.zip | 3 + fits/eyevoicespan_m10.json.zip | 3 + references.bib | 12 + 17 files changed, 1608 insertions(+), 16 deletions(-) create mode 100644 examples/eyevoicespan/Pan_etal.DevSci.2013.pdf create mode 100644 examples/eyevoicespan/pylsk13.qmd create mode 100755 examples/eyevoicespan/pylsk13.rda create mode 100644 examples/eyevoicespan/pylsk13_interactions.qmd create mode 100644 examples/eyevoicespan/pylsk13_v3.R create mode 100644 examples/eyevoicespan/pylsk13_v4.R create mode 100644 examples/eyevoicespan/remef.v0.6.9.R create mode 100644 fits/eyevoicespan_m00.json.zip create mode 100644 fits/eyevoicespan_m05.json.zip create mode 100644 fits/eyevoicespan_m09.json.zip create mode 100644 fits/eyevoicespan_m10.json.zip diff --git a/_quarto.yml b/_quarto.yml index 54d0dab..0516852 100644 --- a/_quarto.yml +++ b/_quarto.yml @@ -110,6 +110,10 @@ website: contents: - examples/visual-attention/kwdyz11.qmd - examples/visual-attention/kkl15.qmd + - section: "Eye–Voice Span in Rapid Automatized Naming" + contents: + - examples/eyevoicespan/pylsk13.qmd + - examples/eyevoicespan/pylsk13_interactions.qmd - section: "Reference & Appendix" contents: - reference/useful_packages.qmd diff --git a/contrasts/contrasts_kwdyz11.qmd b/contrasts/contrasts_kwdyz11.qmd index 06bf306..f51b51b 100644 --- a/contrasts/contrasts_kwdyz11.qmd +++ b/contrasts/contrasts_kwdyz11.qmd @@ -38,6 +38,7 @@ progress = false ```{julia} #| echo: false using SMLP2026: fit_or_restore +using SMLP2026.RKUtils ``` # A word of caution {#sec-caution} diff --git a/examples/emotikon/fggk21.qmd b/examples/emotikon/fggk21.qmd index 3de604a..9c649b2 100644 --- a/examples/emotikon/fggk21.qmd +++ b/examples/emotikon/fggk21.qmd @@ -68,15 +68,10 @@ transform!(df, levels!(df.Sex, ["male", "female"]) recode!(df.Sex, "male" => "Boys", "female" => "Girls") levels!(df.Test, ["Run", "Star_r", "S20_r", "SLJ", "BPT"]) -recode!( - df.Test, - "Run" => "Endurance", - "Star_r" => "Coordination", - "S20_r" => "Speed", - "SLJ" => "PowerLOW", - "BPT" => "PowerUP", -) + describe(df) + +contrasts = Dict{Symbol,Any}(nm => SeqDiffCoding() for nm in (:Test, :Sex)) ``` ### Transformations @@ -92,6 +87,48 @@ select!(groupby(df, :Test), Not(:score), :score => zscore => :zScore) The preprocessing steps above are also packaged as `SMLP2026.fggk21_preprocessed()`, so that other pages (e.g. the [contrast-coding tutorial](../../contrasts/contrasts_fggk21.qmd)) can reuse them without repeating the code. ::: +## Time final LMM of paper + +**Warmup** + +```{julia} +#| eval: false +## final LMM +m_test = let + f_test = @formula zScore ~ 1 + Test*a1*Sex + (1 | School) + @time fit(MixedModel, f_test, df; contrasts, progress) +end +``` + +**Timing the full model with current MixedModels.jl** + +```{julia} +#| eval: false +## final LMM +m_osf = let + f = @formula zScore ~ 1 + Test*a1*Sex + + (1+Test+a1+Sex | School) + (1+Test | Child) + + zerocorr(1 + Test | Cohort) + fit(MixedModel, f, df; contrasts, progress) +end +``` + +Minimizing 4724 Time: 0:23:33 ( 0.30 s/it) + +**Timing the full model with new branch pa/gradient-fable** + +```{julia} +#Pkg.add MixedModels#pa/gradient-fable +m_osf2 = let + f = @formula zScore ~ 1 + Test*a1*Sex + + (1+Test+a1+Sex | School) + (1+Test | Child) + + zerocorr(1 + Test | Cohort) + fit(MixedModel, f, df; contrasts, progress, optimizer=:LD_LBFGS) +end +``` + +Minimizing 81 Time: 0:01:12 ( 0.90 s/it) + ## Extract a stratified subsample For the purpose of the tutorial, we extract a random sample of 1000 boys and 1000 girls. `Child`, `School`, and `Cohort` are grouping variables. @@ -659,10 +696,6 @@ issingular(m2) Depending on the random number generator seed, the model may or may not be supported in the alternative parameterization of scores. The fixed-effects profile is not affected (see the model comparisons below). -:::{.callout-caution} -RK: The order of RE terms is critical. In formula `f2` the `zerocorr()` term must be placed last as shown. If it is placed first, School-related and Child-related CPs are estimated/reported (?) as zero. This was not the case for formula `m1`. Thus, it appears to be related to the `0`-intercepts in School and Child terms. 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(2013)" +engine: julia +author: +- Reinhold Kliegl +- Jinger Pan +julia: + exeflags: ["--project", "--threads=auto"] +--- + +::: {.objectives title="Learning objectives"} +After working through this page you will be able to: + +- reproduce a covariate-based LMM analysis (`gaze duration` and `eye–voice span` as predictors of psychometric RAN) from a published study; +- complexify a fixed-effect structure with continuous-by-categorical interactions and prune it with likelihood-ratio tests; +- visualize higher-order interactions three ways — with *partial effects* (`MixedModelsExtras.partial_fitted`, the Julia analogue of R's `remef()`), with *marginal effects* (`Effects.jl`), and with model diagnostics (`MixedModelsMakie.jl`). +::: + +::: {.callout-note title="Before you start"} +**Prerequisites:** [Analysis of the sleepstudy data](../../lmm-intro/sleepstudy.qmd) for the modeling vocabulary; [Transformations and Effects](../../contrasts/transformation.qmd) for `Effects.jl`; [Creating multi-panel plots](../../visualization/AoGPlots.qmd) for the plotting stack. + +**Data used:** `pylsk13.rda`, distributed alongside this page (`examples/eyevoicespan/`). The original R script (`pylsk13_v4.R`) and the paper (`Pan_etal.DevSci.2013.pdf`) are in the same folder. +::: + +# Background + +@Pan2013 measured the eye movements of Chinese dyslexic and control children during +*rapid automatized naming* (RAN) of **digits** (alphanumeric) and **dice** surfaces +(symbolic). Both stimulus types require identical oral responses, which controls for +effects associated with speech production. + +The question addressed on this page is a psychometric one: how well do two eye-movement +measures obtained from the computerized RAN task — **gaze duration** (`gaze`, the summed +fixation time on an item) and the **eye–voice span** (`evs`, the distance in characters +between the currently fixated item and the item currently being named) — predict +naming speed (`ran`, seconds to name a card of items), and does that prediction differ +between the two `Condition`s (digit/dice) and the two `Group`s (control/dyslexic)? + +The analysis follows `pylsk13_v4.R`: + +1. **Setup** — read the data, check whether the response needs a transformation, center the covariates. +2. **Model building** — start from an additive covariate model, add the `Condition × Group` interaction, then the full `Condition × Group × evs × gaze` factorial, and prune it back with likelihood-ratio tests. +3. **Visualization** — partial-effect plots (Figures 1 and 2 of the paper), marginal-effect plots, and residual diagnostics. + +# Packages + +```{julia} +#| code-fold: true +#| output: false +using AlgebraOfGraphics +using AlgebraOfGraphics: density, linear +using BoxCox +using CairoMakie +using CategoricalArrays +using DataFrames +using Effects +using MixedModels +using MixedModelsMakie +using MixedModelsExtras # partial_fitted(): the Julia analogue of remef() +using RData # to read the .rda file +using Statistics +using StatsBase + +using SMLP2026: fit_or_restore + +const progress = false +set_aog_theme!() +``` + +# Read and prepare the data + +`pylsk13.rda` contains a single data frame `dat` with one row per child × condition +(56 children × 2 conditions = 112 rows). + +```{julia} +dat = DataFrame(load(joinpath("examples", "eyevoicespan", "pylsk13.rda"))["dat"]) +``` + +We follow the general recommendation to code the levels of grouping variables as +strings (here `S101`, `S102`, …), to give factors meaningful level names, and to fix +a sensible level order. `ran` is log-transformed (justified below) and the two +covariates are **centered** (not scaled) so that the intercept and the lower-order +terms are interpretable at the average `gaze` and `evs`. + +```{julia} +transform!(dat, + :subj => (x -> categorical(string.("S", x))) => :Subj, + :group => (x -> categorical(recode(x, 1 => "control", 2 => "dyslexic"))) => :Group, + :condition => (x -> categorical(recode(x, 1 => "digit", 2 => "dice"))) => :Condition, + :ran => ByRow(log) => :lran, +) +levels!(dat.Group, ["control", "dyslexic"]) +levels!(dat.Condition, ["digit", "dice"]) +dat.evs_c = dat.evs .- mean(dat.evs) +dat.gaze_c = dat.gaze .- mean(dat.gaze) +describe(dat) +``` + +## Does the response need a transformation? + +The R script uses `MASS::boxcox()` to justify a log transform of `ran` (but not of +`gaze` or `evs`). The Julia equivalent fits a `BoxCoxTransformation` to a mixed model +of the untransformed response. + +```{julia} +m_ran = fit(MixedModel, + @formula(ran ~ 1 + Condition * Group + evs_c + gaze_c + (1 | Subj)), + dat; + contrasts=Dict(:Condition => DummyCoding(; base="digit"), + :Group => DummyCoding(; base="control")), + progress, +) +bc = fit(BoxCoxTransformation, m_ran; progress) +``` + +```{julia} +#| code-fold: true +#| fig-cap: "Box–Cox profile for the RAN response. The optimum is close to λ = 0, i.e. a log transform." +#| label: fig-boxcox +boxcoxplot(bc; conf_level=0.95) +``` + +The profile peaks near `λ = 0`, so `log(ran)` (= `lran`) is a reasonable choice and +matches the published analysis. + +## Condition and Group means + +```{julia} +cell_means = combine( + groupby(dat, [:Group, :Condition]), + :lran => mean => :lran_m, + :lran => (x -> std(x) / sqrt(length(x))) => :lran_se, + :evs => mean => :evs_m, + :gaze => mean => :gaze_m, + nrow => :n, +) +cell_means +``` + +```{julia} +#| code-fold: true +#| fig-cap: "Mean log(RAN) by Condition and Group. Naming dice is slower than naming digits in both groups, and the group difference is larger for digits." +#| label: fig-cellmeans +draw( + data(cell_means) * + mapping(:Condition, :lran_m => "log(RAN)"; color=:Group, group=:Group) * + visual(ScatterLines; markersize=16), +) +``` + +```{julia} +#| code-fold: true +#| fig-cap: "Comparative density of log(RAN) by Condition." +#| label: fig-density +draw( + data(dat) * + mapping(:lran => "log(RAN)"; color=:Condition) * + density(), +) +``` + +# Linear mixed models + +The two categorical predictors use treatment (dummy) contrasts with the same +reference levels as the published analysis (`digit` and `control`), so the +coefficients reproduce Table 3 of @Pan2013. + +::: {.callout-tip} +If the *intercept* should estimate the grand mean rather than the `digit`/`control` +cell — usually preferable in factorial designs — swap `DummyCoding` for +`EffectsCoding`. The omnibus tests below are unchanged; only the meaning of the +lower-order coefficients changes. +::: + +```{julia} +contrasts = Dict( + :Condition => DummyCoding(; base="digit"), + :Group => DummyCoding(; base="control"), +) +``` + +All models keep the maximal grouping structure supported by this design: a single +by-child random intercept (`(1 | Subj)`). With only two observations per child there +is no room for by-child random slopes. + +## Model building + +```{julia} +m00 = fit_or_restore("eyevoicespan_m00.json", MixedModel, + @formula(lran ~ 1 + Condition + Group + evs_c + gaze_c + (1 | Subj)), + dat; contrasts, progress) +``` + +```{julia} +m05 = fit_or_restore("eyevoicespan_m05.json", MixedModel, + @formula(lran ~ 1 + Condition * Group + evs_c + gaze_c + (1 | Subj)), + dat; contrasts, progress) +``` + +```{julia} +m10 = fit_or_restore("eyevoicespan_m10.json", MixedModel, + @formula(lran ~ 1 + Condition * Group * evs_c * gaze_c + (1 | Subj)), + dat; contrasts, progress) +``` + +`m10` is the full `Condition × Group × evs × gaze` factorial. The three highest-order +terms that involve the `evs × gaze` product are not significant, so we drop them: +the `Condition × Group × evs × gaze` four-way, the `Group × evs × gaze` three-way, +and the `Condition × evs × gaze` three-way. What remains (`m09`) is the model +whose coefficients correspond to Table 3 of @Pan2013. (The `z` statistics here differ +slightly from the published `t` values because of software differences — ML vs. REML, +contrast parameterization — but the substantive pattern is the same.) + +```{julia} +m09 = fit_or_restore("eyevoicespan_m09.json", MixedModel, + @formula(lran ~ 1 + Condition + Group + evs_c + gaze_c + + Condition & Group + Condition & evs_c + Condition & gaze_c + + Group & evs_c + Group & gaze_c + evs_c & gaze_c + + Condition & Group & evs_c + Condition & Group & gaze_c + + (1 | Subj)), + dat; contrasts, progress) +``` + +```{julia} +MixedModels.likelihoodratiotest(m00, m05, m09, m10) +``` + +Adding `Condition × Group` (`m05`) and the covariate interactions retained in `m09` +each improve the fit reliably; the extra terms in `m10` do not. `m09` is the +preferred model. + +## The preferred model + +```{julia} +VarCorr(m09) +``` + +```{julia} +m09 +``` + +The coefficients of interest: + +- **`evs_c` (−0.63)** — within `digit`/`control`, a larger eye–voice span predicts + *faster* (lower log) naming. +- **`Condition: dice & Group: dyslexic & evs_c` (−0.55, *p* ≈ .006)** — the three-way + interaction: the EVS benefit is distributed differently across cells (Figure 1 of the paper). +- **`evs_c & gaze_c` (−0.005, *p* ≈ .001)** — the two covariates interact. +- **`gaze_c` (+0.0036)** — longer gaze durations predict *slower* naming, as expected. + +# Diagnostics + +```{julia} +#| code-fold: true +#| fig-cap: "Residuals vs. fitted values for m09." +#| label: fig-resvsfitted +draw( + data((; f=fitted(m09), r=residuals(m09))) * + mapping(:f => "Fitted log(RAN)", :r => "Residual (m09)") * + visual(Scatter), +) +``` + +```{julia} +#| code-fold: true +#| fig-cap: "Normal quantile plot of the m09 residuals." +#| label: fig-qq +qqnorm(residuals(m09); qqline=:fitrobust) +``` + +```{julia} +#| code-fold: true +#| fig-cap: "Prediction intervals on the by-child random intercepts (m09)." +#| label: fig-caterpillar +caterpillar(m09, :Subj) +``` + +# Partial-effect plots (the `remef()` analogue) + +The R script visualizes the higher-order interactions with **partial effects** +computed by `remef()`: it takes the observed response, removes the contribution of +the nuisance terms (here everything involving `gaze` and the random intercept), and +keeps the terms of interest plus the residual. The result is an "adjusted" response +that isolates one slice of the model. + +`MixedModelsExtras.partial_fitted` is the Julia counterpart. It returns the fitted +values for a chosen set of coefficients; adding the residuals back reproduces +`remef(..., keep=TRUE)`. + +```{julia} +# keep every fixed effect that does NOT involve gaze; drop the by-child intercept +keep_evs = filter(c -> !occursin("gaze_c", c), coefnames(m09)) +# keep every fixed effect that does NOT involve evs; drop the by-child intercept +keep_gaze = filter(c -> !occursin("evs_c", c), coefnames(m09)) + +dp = select(dat, :Subj, :Group, :Condition, :evs, :gaze, :lran) +dp.partial_evs = + partial_fitted(m09, keep_evs, Dict(:Subj => String[]); mode=:include) .+ residuals(m09) +dp.partial_gaze = + partial_fitted(m09, keep_gaze, Dict(:Subj => String[]); mode=:include) .+ residuals(m09) +dp.cg = categorical(string.(dp.Condition, " / ", dp.Group)) +first(dp, 6) +``` + +For plotting we stack the observed response and each partial response into long +form, so that "observed vs. adjusted" becomes a facet column with a single shared +legend. + +```{julia} +stack_partial(col, label) = + insertcols!(select(dp, :evs, :gaze, :cg, col => :y), :kind => label) + +dp_evs = vcat(stack_partial(:lran, "observed"), stack_partial(:partial_evs, "adjusted")) +dp_gaze = vcat(stack_partial(:lran, "observed"), stack_partial(:partial_gaze, "adjusted")) +first(dp_evs, 4) +``` + +::: {.callout-note collapse="true" title="How the specification maps onto R's remef()"} +`remef(m09, fix = c(1, "condition:group:evs_c"), keep = TRUE, grouping = TRUE, ran = NULL)` +keeps the intercept, the three-way `condition:group:evs_c` term, **and** (because +`grouping = TRUE`) every lower-order term built from `condition`, `group`, and +`evs_c`; it removes everything involving `gaze_c` and all random effects. +`filter(c -> !occursin("gaze_c", c), coefnames(m09))` selects exactly that set of +fixed-effect coefficients, and `Dict(:Subj => String[])` drops the random intercept. +::: + +## Figure 1 — `Condition × Group × EVS` + +```{julia} +#| code-fold: true +#| fig-cap: "Left: observed log(RAN) vs. eye–voice span. Right: partial effect from m09 (gaze contribution and random intercept removed)." +#| label: fig-partial-evs +draw( + data(dp_evs) * + mapping( + :evs => "Eye–voice span", + :y => "log(RAN)"; + color=:cg => "Condition / Group", + col=:kind, + ) * + (visual(Scatter; alpha=0.5) + linear()); + facet=(; linkyaxes=:all), +) +``` + +The partial plot sharpens the pattern noted in the paper: the EVS benefit (negative +slope) is present for `digit` naming in the control group but is weak or absent in +the `dice / dyslexic` cell. + +## Figure 2 — `Condition × Group × Gaze` + +```{julia} +#| code-fold: true +#| fig-cap: "Left: observed log(RAN) vs. gaze duration. Right: partial effect from m09 (EVS contribution and random intercept removed)." +#| label: fig-partial-gaze +draw( + data(dp_gaze) * + mapping( + :gaze => "Gaze duration [ms]", + :y => "log(RAN)"; + color=:cg => "Condition / Group", + col=:kind, + ) * + (visual(Scatter; alpha=0.5) + linear()); + facet=(; linkyaxes=:all), +) +``` + +# Marginal-effect plots with `Effects.jl` + +`partial_fitted` adjusts *observed* data points. `Effects.jl` instead evaluates the +*model's prediction* on a regular grid, holding the variables that are not on the +grid at a typical value (the mean; for the centered covariates that is `0`). This is +the Julia analogue of R's `effects` / `emmeans`. + +## EVS effect by Condition and Group + +```{julia} +evsgrid = Dict( + :evs_c => range(extrema(dat.evs_c)...; length=50), + :Condition => levels(dat.Condition), + :Group => levels(dat.Group), +) +eff_evs = effects(evsgrid, m09) +eff_evs.evs = eff_evs.evs_c .+ mean(dat.evs) +eff_evs.cg = categorical(string.(eff_evs.Condition, " / ", eff_evs.Group)) +first(eff_evs, 6) +``` + +```{julia} +#| code-fold: true +#| fig-cap: "Model-predicted log(RAN) as a function of eye–voice span, with 95% confidence bands, by Condition and Group." +#| label: fig-effects-evs +draw( + data(eff_evs) * + mapping( + :evs => "Eye–voice span", + :lran => "log(RAN)"; + color=:cg => "Condition / Group", + lower=:lower, + upper=:upper, + ) * + visual(LinesFill), +) +``` + +## Gaze effect by Condition and Group + +```{julia} +#| code-fold: true +#| fig-cap: "Model-predicted log(RAN) as a function of gaze duration, with 95% confidence bands, by Condition and Group." +#| label: fig-effects-gaze +let + gazegrid = Dict( + :gaze_c => range(extrema(dat.gaze_c)...; length=50), + :Condition => levels(dat.Condition), + :Group => levels(dat.Group), + ) + eff_gaze = effects(gazegrid, m09) + eff_gaze.gaze = eff_gaze.gaze_c .+ mean(dat.gaze) + eff_gaze.cg = categorical(string.(eff_gaze.Condition, " / ", eff_gaze.Group)) + draw( + data(eff_gaze) * + mapping( + :gaze => "Gaze duration [ms]", + :lran => "log(RAN)"; + color=:cg => "Condition / Group", + lower=:lower, + upper=:upper, + ) * + visual(LinesFill), + ) +end +``` + +## `evs × gaze` interaction + +The reliable `evs_c & gaze_c` term means the gaze slope changes with EVS. We show it +by evaluating the model at three EVS levels (roughly the tertiles). + +```{julia} +#| code-fold: true +#| fig-cap: "The gaze-duration effect at small, medium, and large eye–voice span (model prediction, 95% bands)." +#| label: fig-effects-evsxgaze +let + qs = quantile(dat.evs, [1/6, 1/2, 5/6]) + grid = Dict( + :gaze_c => range(extrema(dat.gaze_c)...; length=50), + :evs_c => qs .- mean(dat.evs), + ) + eff = effects(grid, m09) + eff.gaze = eff.gaze_c .+ mean(dat.gaze) + eff.evs_level = categorical( + round.(eff.evs_c .+ mean(dat.evs); digits=2); + ) + draw( + data(eff) * + mapping( + :gaze => "Gaze duration [ms]", + :lran => "log(RAN)"; + color=:evs_level => "Eye–voice span", + lower=:lower, + upper=:upper, + ) * + visual(LinesFill), + ) +end +``` + +# See also + +- [Transformations and Effects](../../contrasts/transformation.qmd) — the `Effects.jl` workflow and Box–Cox transformations in more detail. +- [The Emotikon Project](../emotikon/fggk21.qmd) — model complexification and PCA of the random effects on a large dataset. +- R's [`remef`](https://github.com/hohenstein/remef) and the `partial_fitted` docstring in `MixedModelsExtras`. + +# References + +::: {#refs} +::: + +## Exercises + +1. **Contrast coding.** Refit `m09` with `EffectsCoding` for `Condition` and `Group`. Which coefficients change, which stay the same, and what does the intercept estimate now? + +::: {.callout-note collapse="true" title="Solution"} +The omnibus likelihood-ratio tests, `VarCorr`, the residual standard deviation, and the fitted values are all unchanged — the model space is the same. The intercept now estimates the grand mean (the unweighted average over the four `Condition × Group` cells) instead of the `digit`/`control` cell, and every lower-order `Condition`/`Group` coefficient becomes a deviation from that grand mean rather than a simple difference from a reference level. The highest-order interaction coefficient is unchanged up to a scale factor. +::: + +2. **Partial vs. marginal.** @fig-partial-evs (partial effects) and @fig-effects-evs (marginal effects) both show the EVS slopes by cell. What does each one add that the other does not? + +::: {.callout-note collapse="true" title="Solution"} +The partial-effect plot keeps the residuals, so it shows the *scatter* of individual observations around the adjusted regression line — useful for spotting influential points and for judging how much of the variance the term actually explains. The marginal-effect plot shows the model's prediction with a proper confidence band and no leftover noise from other terms, which makes the *estimated* slopes and their uncertainty directly comparable across cells. Use partial effects to inspect the data given the model; use marginal effects to communicate the model. +::: + +3. **Why center?** The covariates were centered before fitting. What would change in the `m09` coefficient table if `evs` and `gaze` entered on their raw scales, and would any of the omnibus tests change? + +::: {.callout-note collapse="true" title="Solution"} +Only the interpretation of the lower-order terms shifts. With raw covariates, `Condition: dice` would estimate the digit-vs-dice difference at `evs = 0` and `gaze = 0` — an extrapolation far outside the data — inflating its standard error and making it hard to interpret. The intercept would likewise refer to `evs = gaze = 0`. The higher-order interaction coefficients, the variance components, the fitted values, and every likelihood-ratio test are invariant to centering. +::: + +--- + +*This page was rendered from git revision {{< git-rev short=true >}} using Quarto {{< version >}} and Julia {{< julia-version >}}.* diff --git a/examples/eyevoicespan/pylsk13.rda b/examples/eyevoicespan/pylsk13.rda new file mode 100755 index 0000000000000000000000000000000000000000..3835513def06117179ad999421d1ac4784778629 GIT binary patch literal 1549 zcmV+o2J-nIiwFP!000002JP7SZxm%12k@QQtwJM$k!biqi~*tLY`b)~$Ch~$MTmg0 zm4s3%y7T}P+OlmqiU=yia0L>ZD2NG%F{lZ|kSJhG5F~O61O*ik3iO~Y^rDbxuzqKs z@3X@G2OgVzIy>(>^S;k}%)9S2@7esc#Qa2$$76f!zTm}IpN&73$LHydqqjI*g};yD zYcJ>n6;MK@G>c}_9D1GR(mX1oa;l*D6roD0q8eI4Z_rYDla|qPdYj&%6||C$&`~-@ z$LR$9Kqu)Gouza1GyOup(s{Z-7wI>;M3hdDU@#d-1L1?UTBh(ALRL1&Yx7q zosl5plge=oal8U-XJ{$=P2*?1IzD5^$@Lj*XNdU$){}8GnqV?l%5^zxS89>O85*z= zpH0Tk`4p1)J%6vKop?0Y!C1h)!+H|Wno`qJprp=E92e(KQg{rcnh%qurgr{>;mk2tWR04d;Xd9 zjqSs63LJvNa0jqAw7!H>$j4e|&44dh|6S=L8|$Anj{So@rH!@FS_B7K=V@Nw0~zok z+tCll-8i~^g*~5*{i*dFwCQ^4bjx$(v_*$M(P@@-!)cd!<21|q;9TDroe$0}nGeoQ zdG4G}9$T5-DeHyPBI}xSOV$VHrabRXhg)p-!Pt41Jl9UUJg3ebnUAr0TA6;8=}j!J zf%SGVy+hWmSe&iLqx0NpVmp3fekbc~;IW(O9qb2fhnC;CGuj}ho^flu&GI}sUCeKn z_0GA?{?c~-!F)aMV!zyAy;@EK`%UY+!g093_SdyU*FC3^^z-rpEEAGG{>mV1qH>HRuBI_^52ml$sy$EA(!YhwHtS>I)j({;8} z<2cJW&&cmaY@9k7R|m`0algTS)^XH%9Geeu?a=wt7B>&If7#4qfEhK&a()Todf7JK6HMEM>Qv7|3N#Eo2dOcr9TCcuu>U*TV zH|qIvT1_kBL}&(0BR$WhsgzFzG@bOiLJHDLr1^%l9=%TU3*x*?T8_q%M|z#+Pb7^a zz8q~A$I-V#Jg`OhPE)b)ZW6vK;k_XeLc%wl!t@nQq-Dapm#zt)pK_>=@E#L(x9}RO z6!zC5;fV0n(u>00M*D@=Ct|Ny-%$mP7v9H&HJDQA1)Dhq8pRT_E@W2#&))D{!Z)G;R literal 0 HcmV?d00001 diff --git a/examples/eyevoicespan/pylsk13_interactions.qmd b/examples/eyevoicespan/pylsk13_interactions.qmd new file mode 100644 index 0000000..eb88bcb --- /dev/null +++ b/examples/eyevoicespan/pylsk13_interactions.qmd @@ -0,0 +1,305 @@ +--- +title: "Interactions Three Ways: Observed, Partial, and Predicted (Pan et al., 2013)" +engine: julia +author: +- Reinhold Kliegl +- Jinger Pan +julia: + exeflags: ["--project", "--threads=auto"] +--- + +::: {.objectives title="Learning objectives"} +After working through this page you will be able to: + +- distinguish three complementary views of a model term — the **observed** relationship, the **partial-effect** view (`remef` / `MixedModelsExtras.partial_fitted`), and the **predicted** (marginal) view (`Effects.jl`); +- read each of the significant interactions in `m09` off a consistent three-panel figure; +- explain *why* an interaction that is invisible in the raw data can be obvious in the partial-effect plot. +::: + +::: {.callout-note title="Before you start"} +**Prerequisite:** [Eye–Voice Span in Rapid Automatized Naming](pylsk13.qmd) — this page reuses its preferred model `m09` and its cached fit. Read that page first for the background, the data, and the model-building steps. + +**Data used:** `pylsk13.rda` (`examples/eyevoicespan/`). +::: + +# Why three panels? + +Model `m09` from the [companion page](pylsk13.qmd) has four reliable interaction +terms. Each one describes how the slope of one predictor changes with another, but a +raw scatterplot rarely shows that directly: the other twelve terms in the model, the +by-child random intercept, and the residual noise are all superimposed on it. + +Three views pull the term apart: + +| View | What it shows | How it is computed | +|---|---|---| +| **Observed** | `log(RAN)` against the predictor, split by the moderator, with an ordinary least-squares line per group | nothing removed — the raw data | +| **Partial** | the same, after subtracting every model term *except* the target interaction and its lower-order relatives, and the random intercept | `partial_fitted(m09, keep; mode=:include) .+ residuals(m09)` — the Julia analogue of R's `remef(..., keep=TRUE, grouping=TRUE, ran=NULL)` | +| **Predicted** | the model's fitted mean on a regular grid, with a 95% confidence band, holding the other predictors at typical values | `Effects.effects(grid, m09)` | + +The **observed** panel is honest about scatter but confounded. The **partial** panel +keeps the residual scatter (so you can still judge influence and fit) while removing +the confounds. The **predicted** panel removes the scatter too and adds proper +inferential uncertainty, but it *averages over* the predictors that are not on the +grid — so it can look weaker than the partial view when a moderator you have +collapsed also interacts with the x-axis variable. + +# Setup + +```{julia} +#| code-fold: true +#| output: false +using AlgebraOfGraphics +using AlgebraOfGraphics: linear +using CairoMakie +using CategoricalArrays +using DataFrames +using Effects +using MixedModels +using MixedModelsExtras +using RData +using Statistics +using StatsBase + +using SMLP2026: fit_or_restore + +const progress = false +set_aog_theme!() +``` + +```{julia} +#| code-fold: true +dat = DataFrame(load(joinpath("examples", "eyevoicespan", "pylsk13.rda"))["dat"]) +transform!(dat, + :subj => (x -> categorical(string.("S", x))) => :Subj, + :group => (x -> categorical(recode(x, 1 => "control", 2 => "dyslexic"))) => :Group, + :condition => (x -> categorical(recode(x, 1 => "digit", 2 => "dice"))) => :Condition, + :ran => ByRow(log) => :lran, +) +levels!(dat.Group, ["control", "dyslexic"]) +levels!(dat.Condition, ["digit", "dice"]) +dat.evs_c = dat.evs .- mean(dat.evs) +dat.gaze_c = dat.gaze .- mean(dat.gaze) + +contrasts = Dict( + :Condition => DummyCoding(; base="digit"), + :Group => DummyCoding(; base="control"), +) +m09 = fit_or_restore("eyevoicespan_m09.json", MixedModel, + @formula(lran ~ 1 + Condition + Group + evs_c + gaze_c + + Condition & Group + Condition & evs_c + Condition & gaze_c + + Group & evs_c + Group & gaze_c + evs_c & gaze_c + + Condition & Group & evs_c + Condition & Group & gaze_c + + (1 | Subj)), + dat; contrasts, progress) +``` + +The four interaction terms and their coefficients: + +```{julia} +#| code-fold: true +let + targets = ["Condition: dice & evs_c", "Group: dyslexic & evs_c", "evs_c & gaze_c", + "Condition: dice & Group: dyslexic & evs_c"] + filter(:Name => in(targets), DataFrame(coeftable(m09))) +end +``` + +All four are reliable: `Condition & evs_c` (*p* ≈ .002), `Group & evs_c` (*p* ≈ .001), +`evs_c & gaze_c` (*p* ≈ .001), and the three-way `Condition & Group & evs_c` +(*p* ≈ .006). + +# Partial responses + +`partial(keep)` returns the observed response with every term *not* in `keep` +removed, plus the by-child random intercept removed — exactly what +`remef(m09, fix = keep, keep = TRUE, grouping = TRUE, ran = NULL)` produces in R. +`grouping = TRUE` means "also keep every lower-order term built from the same +variables", which here we spell out explicitly in each `keep` vector. + +```{julia} +partial(keep) = partial_fitted(m09, keep, Dict(:Subj => String[]); mode=:include) .+ residuals(m09) + +keep_C_evs = ["(Intercept)", "Condition: dice", "evs_c", "Condition: dice & evs_c"] +keep_G_evs = ["(Intercept)", "Group: dyslexic", "evs_c", "Group: dyslexic & evs_c"] +keep_evs_gz = ["(Intercept)", "evs_c", "gaze_c", "evs_c & gaze_c"] +keep_CG_evs = filter(c -> !occursin("gaze_c", c), coefnames(m09)) # everything without gaze + +dp = select(dat, :Subj, :Condition, :Group, :evs, :gaze, :evs_c, :gaze_c, :lran) +dp.pf_C_evs = partial(keep_C_evs) +dp.pf_G_evs = partial(keep_G_evs) +dp.pf_evs_gz = partial(keep_evs_gz) +dp.pf_CG_evs = partial(keep_CG_evs) +dp.cg = categorical(string.(dp.Condition, " / ", dp.Group)) + +# tertiles of eye–voice span, for the EVS × Gaze figure +cut = quantile(dat.evs, [1/3, 2/3]) +evsgrp(x) = x ≤ cut[1] ? "low" : x ≤ cut[2] ? "mid" : "high" +dp.evs_grp = categorical(evsgrp.(dp.evs); levels=["low", "mid", "high"]) +tert_med = [median(dat.evs[evsgrp.(dat.evs) .== g]) for g in ["low", "mid", "high"]] +first(dp, 6) +``` + +# The three-panel helper + +```{julia} +#| code-fold: true +""" + three_panel(; obs_df, xcol, xlab, obs_y, par_y, pred_df, color, colorlab, title) + +One figure row: observed | partial | predicted, sharing the y-axis, with one +shared colour legend. `pred_df` must carry `:yhat`, `:lower`, `:upper` and the +same `color` column as `obs_df`. +""" +function three_panel(; obs_df, xcol, xlab, obs_y, par_y, pred_df, color, colorlab, title) + fig = Figure(; size=(1050, 380)) + ylims = (nothing, nothing, 2.0, 4.0) + pobs = data(obs_df) * mapping(xcol => xlab, obs_y => "log(RAN)"; color=color => colorlab) * + (visual(Scatter; alpha=0.35) + linear()) + ppar = data(obs_df) * mapping(xcol => xlab, par_y => "adjusted log(RAN)"; color=color => colorlab) * + (visual(Scatter; alpha=0.35) + linear()) + ppred = data(pred_df) * mapping(xcol => xlab, :yhat => "predicted log(RAN)"; + color=color => colorlab, lower=:lower, upper=:upper) * + visual(LinesFill) + g = draw!(fig[1, 1], pobs; axis=(; limits=ylims, title="Observed")) + draw!(fig[1, 2], ppar; axis=(; limits=ylims, title="Partial (remef)")) + draw!(fig[1, 3], ppred; axis=(; limits=ylims, title="Predicted (Effects)")) + legend!(fig[1, 4], g) + Label(fig[0, 1:4], title; fontsize=16, font=:bold) + return fig +end +``` + +# (1) Condition × EVS + +```{julia} +#| code-fold: true +#| fig-cap: "The eye–voice-span slope by naming Condition. Observed: both slopes negative. Partial: only `digit` retains a slope once Group and gaze are removed. Predicted: same pattern, averaged over Group (hence weaker) and with model uncertainty." +#| label: fig-c-evs +let + grid = Dict(:evs_c => range(extrema(dat.evs_c)...; length=50), :Condition => levels(dat.Condition)) + e = effects(grid, m09) + rename!(e, :lran => :yhat) + e.evs = e.evs_c .+ mean(dat.evs) + three_panel(; obs_df=dp, xcol=:evs, xlab="Eye–voice span", obs_y=:lran, par_y=:pf_C_evs, + pred_df=e, color=:Condition, colorlab="Condition", title="Condition × EVS") +end +``` + +A larger eye–voice span goes with faster naming, and the partial panel shows this +benefit is carried almost entirely by **digit** naming: once the (also reliable) +`Group × EVS` term and everything involving gaze are stripped out, the `dice` slope +is essentially flat. The predicted panel collapses over Group, so its `digit`/`dice` +lines separate less — the interaction is real but the *marginal* prediction dilutes it. + +# (2) Group × EVS + +```{julia} +#| code-fold: true +#| fig-cap: "The eye–voice-span slope by Group. The EVS benefit is concentrated in the control children." +#| label: fig-g-evs +let + grid = Dict(:evs_c => range(extrema(dat.evs_c)...; length=50), :Group => levels(dat.Group)) + e = effects(grid, m09) + rename!(e, :lran => :yhat) + e.evs = e.evs_c .+ mean(dat.evs) + three_panel(; obs_df=dp, xcol=:evs, xlab="Eye–voice span", obs_y=:lran, par_y=:pf_G_evs, + pred_df=e, color=:Group, colorlab="Group", title="Group × EVS") +end +``` + +The partial panel isolates the mirror-image of Figure 1: the steep negative EVS slope +belongs to the **control** group, while the dyslexic slope is shallow. Substantively, +a wide eye–voice span — reading ahead of the voice — pays off more for the children +who are already fluent. + +# (3) EVS × Gaze + +```{julia} +#| code-fold: true +#| fig-cap: "The gaze-duration slope at low, mid, and high eye–voice span (tertiles). Observed: the three slopes are nearly identical. Partial and Predicted: the gaze slope is steeper when the eye–voice span is short." +#| label: fig-evs-gaze +let + grid = Dict(:gaze_c => range(extrema(dat.gaze_c)...; length=50), + :evs_c => tert_med .- mean(dat.evs)) + e = effects(grid, m09) + rename!(e, :lran => :yhat) + e.gaze = e.gaze_c .+ mean(dat.gaze) + pts = tert_med .- mean(dat.evs) + e.evs_grp = categorical(["low", "mid", "high"][[findmin(abs.(pts .- v))[2] for v in e.evs_c]]; + levels=["low", "mid", "high"]) + three_panel(; obs_df=dp, xcol=:gaze, xlab="Gaze duration [ms]", obs_y=:lran, par_y=:pf_evs_gz, + pred_df=e, color=:evs_grp, colorlab="EVS tertile", title="EVS × Gaze") +end +``` + +This is the clearest demonstration of what the partial view buys you. In the raw data +the gaze-duration slope looks the same at every eye–voice span. After removing the +`Condition`, `Group`, and random-intercept contributions, a fan opens up: longer gaze +durations cost more (steeper positive slope) when the reader is *not* looking far +ahead. The predicted panel confirms the crossing pattern with confidence bands. + +# (4) Condition × Group × EVS + +```{julia} +#| code-fold: true +#| fig-cap: "The three-way interaction (Figure 1 of Pan et al., 2013). The negative EVS slope is specific to the digit / control cell." +#| label: fig-cg-evs +let + grid = Dict(:evs_c => range(extrema(dat.evs_c)...; length=50), + :Condition => levels(dat.Condition), :Group => levels(dat.Group)) + e = effects(grid, m09) + rename!(e, :lran => :yhat) + e.evs = e.evs_c .+ mean(dat.evs) + e.cg = categorical(string.(e.Condition, " / ", e.Group)) + three_panel(; obs_df=dp, xcol=:evs, xlab="Eye–voice span", obs_y=:lran, par_y=:pf_CG_evs, + pred_df=e, color=:cg, colorlab="Condition / Group", title="Condition × Group × EVS") +end +``` + +Putting `Condition` and `Group` back together: the partial panel shows three flat +cells and one steeply declining one — **digit naming in control children**. The EVS +benefit found in Figures 1 and 2 is not additive; it is a property of that single +cell. Because the three-way grid here retains *all* the non-gaze structure, the +predicted panel now agrees closely with the partial panel — nothing has been averaged +away. + +# Takeaways + +- Read an interaction from the **partial** panel: it removes the confounds that hide + the term in raw data while keeping the scatter that tells you how well it is + determined. +- Use the **predicted** panel for inference (confidence bands) and for communicating a + clean model summary — but remember it averages over whatever you left off the grid. +- When the partial and predicted panels *disagree* (Figures 1–3) it is usually because + a collapsed moderator also interacts with the x-axis variable; when they *agree* + (Figure 4) the grid already contains everything that matters. + +# References + +::: {#refs} +::: + +## Exercises + +1. **Keep the random intercept.** Recompute `pf_CG_evs` with `Dict(:Subj => ["(Intercept)"])` instead of `Dict(:Subj => String[])`. What changes in the partial panel, and which R `remef` argument does this correspond to? + +::: {.callout-note collapse="true" title="Solution"} +Each point moves vertically by that child's estimated random intercept (± ~0.1 on the log scale), so the within-cell scatter grows and the cells separate a little more by their child composition. It corresponds to `remef(..., ran = list("(Intercept)"))` (keep the by-subject intercept) rather than `ran = NULL`. +::: + +2. **Effects grid resolution.** In Figure 3 the predicted lines are evaluated at three EVS values (the tertile medians). Replace them with five quantiles. Does the qualitative "fan" conclusion change? What is the cost? + +::: {.callout-note collapse="true" title="Solution"} +The conclusion is unchanged — the gaze slope still decreases monotonically as EVS grows. The cost is only visual: five overlapping bands are harder to read than three, and the extreme quantiles are supported by fewer observations, so their bands are wider. +::: + +3. **A non-significant term.** Build a three-panel figure for `Condition × gaze_c` (*p* ≈ .16 in `m09`). What do you expect the partial panel to look like, and why is that the right null result to show learners? + +::: {.callout-note collapse="true" title="Solution"} +The two partial slopes should be nearly parallel — the interaction coefficient is small and uncertain. Showing it next to the significant interactions makes the point that the partial-effect plot is not a device for manufacturing patterns: when the term is null, the plot looks null. +::: + +--- + +*This page was rendered from git revision {{< git-rev short=true >}} using Quarto {{< version >}} and Julia {{< julia-version >}}.* diff --git a/examples/eyevoicespan/pylsk13_v3.R b/examples/eyevoicespan/pylsk13_v3.R new file mode 100644 index 0000000..25b46b9 --- /dev/null +++ b/examples/eyevoicespan/pylsk13_v3.R @@ -0,0 +1,304 @@ +# Predicting psychometric digit-RAN and dice-RAN with gaze duration and +# eye-voice span (EVS) from computerized assessment of digit-RAN and dice-RAN +# in Chinese control and dyslexic children. These results are reported in: + +# Pan et al. (2013). Eye–voice span during rapid automatized naming of digits +# and dice in Chinese normal and dyslexic children. Developmental Science. + +# June 2013, Reinhold Kliegl & Jinger Pan +# 7 & 14 December 2016, Reinhold Kliegl + +library(ggplot2) +library(grid) +library(reshape2) +library(plyr) +library(MASS) +library(lme4) +library("LMERConvenienceFunctions" ) +library(gtools) +library(latticeExtra) + +library(RePsychLing) + +source("remef.v0.6.9.R") + +RKstats <- function(x) c(N=length(x), M=mean(x), SD=sd(x), SE=sd(x)/sqrt(length(x)) ) + +vplayout <- function(x, y) { +viewport(layout.pos.row = x, layout.pos.col = y) +} + +theme_set(theme_bw()) + +# OVERVIEW +# Part 1: Setup +# Part 2: Preliminary analyses +# Part 3: Main LMM analyses: Using gaze and EVS as covariates +# Part 4: Figures of paper -- including some new figures (3-group visualisation) + +# PART 1: SETUP + +load("pylsk13.rda") + +data <- dat +data$Subj <- factor(data$subj) +data$Group <- factor(data$group, labels=c("control", "dyslexic")) +data$Condition <- factor(data$condition, labels=c("digit", "dice")) + + +# Check distributions of continuous variables +boxcox(ran ~ subj*condition, data=data) +boxcox(gaze ~ subj*condition, data=data) +boxcox(evs ~ subj*condition, data=data) + +# Justifies log-transform of ran, not of gaze and evs +data$lran <- log(data$ran) + +# Center covariates +data$gaze.c <- scale(data$gaze,scale=FALSE,center=TRUE) +data$evs.c <- scale(data$evs,scale=FALSE,center=TRUE) + +# PART 2: PRELIMINARY ANALYSES + +# Overall and within-group correlations +data_w <- cbind(data[data$Condition=="digit", ], + data[data$Condition=="dice", ])[ , c(9:10, 4, 19, 6, 21, 5, 20)] +names(data_w) <- c("Subj", "Group", "g_ran", "c_ran", "g_evs", "c_evs", "g_gaze", "c_gaze") +options(digits=2) + +# Psychometric RAN (pmRAN) +M_RAN <- ddply(data, c("Group", "Condition"), with, each(RKstats) (lran) ) +# Note: SEs only valid for between-subject comparisons (Group) + +ggplot(data=M_RAN, aes(x=Group, y=M, group=Condition, shape=Condition)) + + geom_line() + geom_point() + + scale_y_continuous("log(RAN)") + + geom_errorbar(aes(ymax=M+2*SE, ymin=M-2*SE, width=0.03)) + + coord_cartesian(ylim=c(2,4)) + +r1 <- lmer(lran ~ group*condition + (1 | subj), REML=FALSE, data=data) +print(summary(r1), cor=FALSE) + +r1b <- lmer(lran ~ group*condition + (1 + condition || subj), REML=FALSE, data=data) +print(summary(r1b), cor=FALSE) +summary(rePCA(r1b)) + +anova(r1, r1b) # not significant + +## max model not possible +#r1c <- lmer(lran ~ group*condition + (1 + condition | subj), REML=FALSE, data=data, +# control=lmerControl(check.nobs.vs.nRE = "ignore")) +#print(summary(r1c), cor=FALSE) + + +# Gaze -- replicates pattern for pmRAN +M_gaze <- ddply(data, c("Group", "Condition"), with, each(RKstats) (gaze) ) +# Note: SEs only valid for between-subject comparisons (Group) + +qplot(data=M_gaze, x=Group, y=M, group=Condition, + shape=Condition, geom=c("line", "point"), ylab="Gaze duration (ms)") + + geom_errorbar(aes(max=M+2*SE, min=M-2*SE, width=0.03)) + +g1 <- lmer(gaze ~ group*condition + (1 | subj), REML=FALSE, data=data) +print(summary(g1), cor=FALSE) + +g1b <- lmer(gaze ~ group*condition + (1 + condition || subj), REML=FALSE, data=data) +print(summary(g1b), cor=FALSE) +summary(rePCA(g1b)) + +anova(g1, g1b) + +# So if we include gaze as covariate for pmRAN +r1 <- lmer(lran ~ group*condition + (1 | subj), data=data, REML=FALSE) +r2 <- lmer(lran ~ group*condition+gaze + (1 | subj), data=data, REML=FALSE) +print(summary(r2), cor=FALSE) + +r2a <- lmer(lran ~ (group+condition+gaze.c)^2 + (1 | subj), data=data, REML=FALSE) +print(summary(r2a), cor=FALSE) + +r2b <- lmer(lran ~ (group+condition+gaze.c)^3 + (1 | subj), data=data, REML=FALSE) +print(summary(r2b), cor=FALSE) + +anova(r1, r2, r2a, r2b) + +# Add variance components for within-subject effects +r3a <- lmer(lran ~ group*condition+gaze.c + (1 + condition || subj), data=data, REML=FALSE) +print(summary(r3a), cor=FALSE) +summary(rePCA(r3a)) +anova(r2, r3a) + +r3b <- lmer(lran ~ group*condition+gaze.c + (1 + gaze.c || subj), data=data, REML=FALSE) +print(summary(r3b), cor=FALSE) +summary(rePCA(r3b)) +anova(r2, r3b) + +# r2 looks like best model + +# Three main effects (group, condition, gaze.c), plus significant group * condition interaction +r2 <- lmer(lran ~ group*condition+gaze.c + (1 | subj), REML=FALSE, data=data) +print(summary(r2)) + +# EVS -- replicates pattern for pmRAN +M_EVS <- ddply(data, c("Group", "Condition"), with, each(RKstats) (evs)) +# Note: SEs only valid for between-subject comparisons (Group) + +qplot(data=M_EVS, x=Group, y=M, group=Condition, shape=Condition, geom=c("line", "point"), ylab="Eye-voice span (char)") + + geom_errorbar(aes(max=M+1*SE, min=M-1*SE, width=0.03)) + +e1 <- lmer(evs ~ group*condition + (1 | subj), REML=FALSE, data=data) +print(summary(e1), cor=FALSE) + +# So if we include evs as covariate for pmRAN, +data$evs.c <- scale(data$evs,scale=FALSE,center=TRUE) + +r3 <- lmer(lran ~ group*condition+evs.c + (1 | subj), data=data, REML=FALSE) +r3a <- lmer(lran ~ (group+condition+evs.c)^2 + (1 | subj), data=data, REML=FALSE) +r3b <- lmer(lran ~ (group+condition+evs.c)^3 + (1 | subj), data=data, REML=FALSE) + +anova(r1, r3, r3a, r3b) # evs.c is significant covariate +# Three main effects (group, condition, evs.c), plus significant condition*group interaction + +# PART 3: Main LMM analyses: Using gaze and EVS as covariates + +m00 <- lmer(lran ~ condition+group+evs.c+gaze.c + (1 | subj), data=data, REML=FALSE) +print(summary(m00), cor=FALSE) + +# Minimum model given previous results +m05 <- lmer(lran ~ condition*group+evs.c+gaze.c + (1 | subj), data=data, REML=FALSE) +print(summary(m05), cor=FALSE) + +# Full factorial +m10 <- lmer(lran ~ condition*group*evs.c*gaze.c + (1 | subj), data=data, REML=FALSE) +print(summary(m10), cor=FALSE) + +# Remove 3 non-significant higher-order interactions involving evs.c:gaze.c +m09 <- lmer(lran ~ condition*group*evs.c*gaze.c - condition:group:evs.c:gaze.c + - group:evs.c:gaze.c - condition:gaze.c:evs.c + + (1 | subj), data=data, REML=FALSE) +print(summary(m09), corr=FALSE) +anova(m00, m05, m09, m10) +# Best model; reported in Table 3 + +# Check effect of log-transformation +m09b <- lmer(ran ~ condition*group*evs.c*gaze.c - condition:group:evs.c:gaze.c + - group:evs.c:gaze.c - condition:gaze.c:evs.c + + (1 | subj), data=data, REML=FALSE) +print(summary(m09b), corr=FALSE) + +# Check residuals +qqmath(resid(m09)) + +qplot(x=fitted(m09), y=resid(m09), geom="point", + xlab="Fitted values", ylab="Standardized residuals") + + geom_hline(yintercept=0) + + geom_density2d(size=1) + +# ... for log-transformed values +qqmath(resid(m09b)) +qplot(x=fitted(m09b), y=resid(m09), geom="point", + xlab="Fitted values", ylab="Standardized residuals") + + geom_hline(yintercept=0) + + geom_density2d(size=1) + +# PART 4: Figures -- unadjusted and partial plots (model m09) of interactions + + +# Figure 1: Condition x Group x EVS (t=-2.5) + +# Unadjusted observed scores +p1 <- qplot(data=data, y=lran, x=evs, group=Condition:Group, color=Condition:Group, + geom=c("point", "smooth"), method=lm, + xlab = "Eye-voice span", ylab="log(RAN)", ylim=c(2, 4)) + + theme(legend.position = "none", panel.background=element_rect(fill = "white")) +p1 + +# -- evs for dice better predictor for dyslexic, +# -- evs for digits better predictor for control + +# Partial effects +data$CndGrpEVS.m09 <- remef(m09, keep=TRUE, grouping=TRUE, fix = c(1, "condition:group:evs.c"), + ran = NULL, plot=FALSE) + +p2 <- + ggplot(data=data, aes(y=CndGrpEVS.m09, x=evs, + group=Condition:Group, color=Condition:Group)) + + geom_point() + + geom_smooth(method="lm") + + scale_x_continuous("Eye-voice span") + + scale_y_continuous("Adjusted log(RAN)") + + coord_cartesian(ylim=c(2,4)) + + theme(legend.position = c(.30, .20), + legend.text = element_text(size=8), + panel.background=element_rect(fill = "white")) +p2 + +# -- evs only predictor for control in digit-RAN! + +grid.newpage() # Figure 1 +pushViewport(viewport(layout = grid.layout(1,2))) +print(p1, vp=vplayout(1,1)) +print(p2, vp=vplayout(1,2)) + + +# Figure 2: EVSgroup x GAZE + +# Partial effect for Condition x Group x GD +data$CndGrpGAZE.m09 <- + remef(m09, keep=TRUE, grouping=TRUE, fix = c(1, "condition:group:gaze.c"), ran = NULL) + +p3 <- + ggplot(data=data, aes(y=CndGrpGAZE.m09, x=gaze, + group=Condition:Group, color=Condition:Group)) + + geom_point() + + geom_smooth(method="lm") + + scale_x_continuous("Gaze duration") + + scale_y_continuous("Adjusted log(RAN)") + + coord_cartesian(ylim=c(2,4)) + + theme(legend.position = c(.75, .25), panel.background=element_rect(fill = "white")) +p3 + +# -- dice control slope looks different, but this difference is not strong enough? + +# Partial effect for EVS x GD, visualized for small and large EVS groups + +# ... form two EVS groups +idEVS <- ddply(data, "Subj", with, each(M=mean)(evs)) +idEVS$EVSgroup.2 <- quantcut(idEVS$M, seq(0, 1, by=1/2), label=c("small", "large")) +data1 <- merge(data, idEVS, by="Subj") + +data1$EVS_GAZE.m09 <- remef(m09, keep=TRUE, grouping=TRUE, fix = c(1, "evs.c:gaze.c"), ran = NULL, plot=FALSE) + +p4 <- qplot(data=data1, y=EVS_GAZE.m09, x=gaze, group=EVSgroup.2, color=EVSgroup.2, geom=c("point", "smooth"), method=lm, + xlab = "Gaze duration", ylab="Adjusted log(RAN)", ylim=c(2, 4)) + scale_colour_hue("EVS group") + + theme(legend.position = c(.75, .25),panel.background=element_rect(fill = "white")) + +p4b <- qplot(data=data1, y=lran, x=gaze, group=EVSgroup.2, color=EVSgroup.2, geom=c("point", "smooth"), method=lm, + xlab = "Gaze duration", ylab="log(RAN)", ylim=c(2, 4)) + scale_colour_hue("EVS group") + + theme(legend.position = c(.75, .25),panel.background=element_rect(fill = "white")) + +grid.newpage() # Figure 2 +pushViewport(viewport(layout = grid.layout(1,2))) +print(p4b, vp=vplayout(1,1)) +print(p4, vp=vplayout(1,2)) + +# Partial effect for EVS x GD, visualized for small, medium, and large EVS groups + +# ... form three EVS groups +idEVS2 <- ddply(data, "Subj", with, each(M=mean)(evs)) +idEVS2$EVSgroup.3 <- quantcut(idEVS2$M, seq(0, 1, by=1/3), label=c("small", "medium", "large")) +data2 <- merge(data1, idEVS2, by="Subj") + +# ... ... partial efffects +p5 <- qplot(data=data2, y=EVS_GAZE.m09, x=gaze, group=EVSgroup.3, color=EVSgroup.3, geom=c("point", "smooth"), method=lm, + xlab = "Gaze duration", ylab="Adjusted log(RAN)", ylim=c(2, 4)) + scale_colour_hue("EVS group") + + theme(legend.position = c(.75, .25),panel.background=element_rect(fill = "white")) + +# ... ... zero-order relations +p5b <- qplot(data=data2, y=lran, x=gaze, group=EVSgroup.3, color=EVSgroup.3, geom=c("point", "smooth"), method=lm, + xlab = "Gaze duration", ylab="log(RAN)", ylim=c(2, 4)) + scale_colour_hue("EVS group") + + theme(legend.position = c(.75, .25),panel.background=element_rect(fill = "white")) + +grid.newpage() # New Figure (Dec 2016) +pushViewport(viewport(layout = grid.layout(1,2))) +print(p5b, vp=vplayout(1,1)) +print(p5, vp=vplayout(1,2)) diff --git a/examples/eyevoicespan/pylsk13_v4.R b/examples/eyevoicespan/pylsk13_v4.R new file mode 100644 index 0000000..a00b49d --- /dev/null +++ b/examples/eyevoicespan/pylsk13_v4.R @@ -0,0 +1,187 @@ +# Predicting psychometric digit-RAN and dice-RAN with gaze duration and +# eye-voice span (EVS) from computerized assessment of digit-RAN and dice-RAN +# in Chinese control and dyslexic children. These results are reported in: + +# Pan et al. (2013). Eye–voice span during rapid automatized naming of digits +# and dice in Chinese normal and dyslexic children. Developmental Science. + +# June 2013, Reinhold Kliegl & Jinger Pan +# 7 & 14 December 2016, Reinhold Kliegl + +library(ggplot2) +library(grid) +library(reshape2) +library(plyr) +library(MASS) +library(lme4) +library("LMERConvenienceFunctions" ) +library(gtools) +library(latticeExtra) + +library(RePsychLing) + +source("remef.v0.6.9.R") + +RKstats <- function(x) c(N=length(x), M=mean(x), SD=sd(x), SE=sd(x)/sqrt(length(x)) ) + +vplayout <- function(x, y) { +viewport(layout.pos.row = x, layout.pos.col = y) +} + +theme_set(theme_bw()) + +# OVERVIEW +# Part 1: Setup +# Part 2: Preliminary analyses +# Part 3: Main LMM analyses: Using gaze and EVS as covariates +# Part 4: Figures of paper -- including some new figures (3-group visualisation) + +# PART 1: SETUP + +load("pylsk13.rda") + +data <- dat +data$Subj <- factor(data$subj) +data$Group <- factor(data$group, labels=c("control", "dyslexic")) +data$Condition <- factor(data$condition, labels=c("digit", "dice")) + + +# Check distributions of continuous variables +boxcox(ran ~ subj*condition, data=data) +boxcox(gaze ~ subj*condition, data=data) +boxcox(evs ~ subj*condition, data=data) + +# Justifies log-transform of ran, not of gaze and evs +data$lran <- log(data$ran) + +# Center covariates +data$gaze_c <- scale(data$gaze,scale=FALSE,center=TRUE) +data$evs_c <- scale(data$evs,scale=FALSE,center=TRUE) + +# PART 2: Preliminary analysis: + +# PART 3: Main LMM analyses: Using gaze and EVS as covariates + +m00 <- lmer(lran ~ condition+group+evs_c+gaze_c + (1 | subj), data=data, REML=FALSE) +print(summary(m00), cor=FALSE) + +# Minimum model given previous results +m05 <- lmer(lran ~ condition*group+evs_c+gaze_c + (1 | subj), data=data, REML=FALSE) +print(summary(m05), cor=FALSE) + +# Full factorial +m10 <- lmer(lran ~ condition*group*evs_c*gaze_c + (1 | subj), data=data, REML=FALSE) +print(summary(m10), cor=FALSE) + +# Remove 3 non-significant higher-order interactions involving evs_c:gaze_c +m09 <- lmer(lran ~ condition*group*evs_c*gaze_c - condition:group:evs_c:gaze_c + - group:evs_c:gaze_c - condition:gaze_c:evs_c + + (1 | subj), data=data, REML=FALSE) +print(summary(m09), corr=FALSE) +anova(m00, m05, m09, m10) +# Best model; reported in Table 3 + +# Check effect of log-transformation +m09b <- lmer(ran ~ condition*group*evs_c*gaze_c - condition:group:evs_c:gaze_c + - group:evs_c:gaze_c - condition:gaze_c:evs_c + + (1 | subj), data=data, REML=FALSE) +print(summary(m09b), corr=FALSE) + +# Check residuals +qqmath(resid(m09)) + +qplot(x=fitted(m09), y=resid(m09), geom="point", + xlab="Fitted values", ylab="Standardized residuals") + + geom_hline(yintercept=0) + + geom_density2d(size=1) + +# ... for log-transformed values +qqmath(resid(m09b)) +qplot(x=fitted(m09b), y=resid(m09), geom="point", + xlab="Fitted values", ylab="Standardized residuals") + + geom_hline(yintercept=0) + + geom_density2d(linewidth=1) + +# PART 4: Figures -- unadjusted and partial plots (model m09) of interactions + + +# Figure 1: Condition x Group x EVS (t=-2.5) + +## Unadjusted observed scores +p1 <- + ggplot(data=data, aes(y=lran, x=evs, group=Condition:Group, color=Condition:Group)) + + geom_point() + geom_smooth(method="lm") + + scale_x_continuous("Eye-voice span") + + scale_y_continuous("log(RAN)") + + coord_cartesian(ylim=c(2,4)) + + theme(legend.position = "none", + panel.background=element_rect(fill = "white")) +p1 + +# -- evs for dice better predictor for dyslexic, +# -- evs for digits better predictor for control + +## Partial effects +data$CndGrpEVS.m09 <- + remef(m09, keep=TRUE, grouping=TRUE, fix = c(1, "condition:group:evs_c"), + ran = NULL, plot=FALSE) + +p2 <- + ggplot(data=data, aes(y=CndGrpEVS.m09, x=evs, + group=Condition:Group, color=Condition:Group)) + + geom_point() + + geom_smooth(method="lm") + + scale_x_continuous("Eye-voice span") + + scale_y_continuous("Adjusted log(RAN)") + + coord_cartesian(ylim=c(2,4)) + + theme(legend.position = c(.30, .20), + legend.text = element_text(size=8), + panel.background=element_rect(fill = "white")) +p2 + +## Combine in two-panel figure + +grid.newpage() # Figure 1 +pushViewport(viewport(layout = grid.layout(1,2))) +print(p1, vp=vplayout(1,1)) +print(p2, vp=vplayout(1,2)) + +#-- evs only predictor for control in digit-RAN! + +# Figure 2: EVSgroup x GAZE + +## Unadjusted observed scores +p3 <- + ggplot(data=data, aes(y=lran, x=gaze, + group=Condition:Group, color=Condition:Group)) + + geom_point() + + geom_smooth(method="lm") + + scale_x_continuous("Gaze duration") + + scale_y_continuous("log(RAN)") + + coord_cartesian(ylim=c(2,4)) + + theme(legend.position = "none") +p3 + +## Partial effect for Condition x Group x GD +data$CndGrpGAZE.m09 <- + remef(m09, keep=TRUE, grouping=TRUE, fix = c(1, "condition:group:gaze_c"), ran = NULL) + +p4 <- + ggplot(data=data, aes(y=CndGrpGAZE.m09, x=gaze, + group=Condition:Group, color=Condition:Group)) + + geom_point() + + geom_smooth(method="lm") + + scale_x_continuous("Gaze duration") + + scale_y_continuous("Adjusted log(RAN)") + + coord_cartesian(ylim=c(2,4)) + + theme(legend.position = c(.75, .25), + panel.background=element_rect(fill = "white")) +p4 + +## Combine in two-panel figure + +grid.newpage() # Figure 2 +pushViewport(viewport(layout = grid.layout(1,2))) +print(p3, vp=vplayout(1,1)) +print(p4, vp=vplayout(1,2)) + diff --git a/examples/eyevoicespan/remef.v0.6.9.R b/examples/eyevoicespan/remef.v0.6.9.R new file mode 100644 index 0000000..b79baa1 --- /dev/null +++ b/examples/eyevoicespan/remef.v0.6.9.R @@ -0,0 +1,226 @@ +############################################################# +### function remef (REMove EFfects) +# remove random factors variance and fixed effects from the dependent variable of an LMM analysis + +# by Sven Hohenstein, Reinhold Kliegl, 2011, 2012, 2013 + +# v0.6.9, July 2013 + +## VERSION HISTORY: +# changes to last version (v0.6.8, June 2013): +# - function now works with glmerMod models created with glmer +# v0.6.7, December 2012: +# - function now uses the new lme4 function for 'lmerMod' objects +# (lme4Eigen is no longer used) +# - the plot parameter is deprecated +# - minor code changes +# v0.6.6, February 2012: +# - the argument "all" (string) for the parameter 'ran' +# selects all random effects +# v0.6.5, February 2012: +# - the function now works with objects created by the library +# lme4Eigen too +# changes to last version (v0.6.2, August 2011): +# - former parameter 'link' is now called 'family' +# - family parameter is specified as object (not string), +# like, e.g., in lmer() +# - functions are called from the correct package +# - new parameter 'plot': if TRUE, a plot of the uncorrected +# and corrected dependent variable is displayed +# v0.6.2 August 2011 +# - a bug occuring when NULL was part of the random effects list +# was removed +# v0.6, June 2011 +# - a bug was removed +# v0.54, June 2011: +# - new parameter 'link' specifying the logit link function; either +# "identity" or "logit" +# - redundant entries are removed from the vectors in the list 'ran' +# v0.54, June 2011: +# - Fixed effects (in the vector 'fix') can be integers or strings +# (e.g., c(2:4, "Effect1", 6, "Effect2") ) +# v0.52, May 2011 +# - Correction: If grouping was TRUE and a specified fixed main effect of a +# factor was not present in any interaction, the function failed +# v0.51, May 2011: +# - parameter 'grouping' also works if keep = FALSE, if grouping is TRUE, +# the effect and all adssociated ones of higher order are chosen to be +# removed +# v0.5, May 2011: +# - new boolean parameter: 'grouping'; if both keep and grouping are TRUE, +# the effects in fix and all subeffects are chosen to be kept +# Note: In the present version, if keep is FALSE, grouping will be ignored +# v0.4a, May 2011: +# - if keep is TRUE, the to be kept effects are not removed from the +# dependent variable but are actually added to the residuals +# - more efficient processing and less operations (if keep is set properly) +# v0.4, April 2011: +# - new parameter 'keep' allows the remove the effects not specified +# - more efficient processing +# v0.32, April 2011: +# - Correction: If random effects of random factors with order numbers < 1 +# were specified, the output was not correct. +# v0.3a, April 2011: +# changes to last version (v0.3): +# - more efficient processing +# v0.3, April 2011: +# changes to last version (v0.2): +# - now it is possible to remove all random effects (even random slopes) +# - the parameter 'ran' must be a list of vectors +# - switched order position of parameters 'fix' and 'ran' +# v0.2, February 2011: +# changes to last version (v0.1): +# - Correction: If just one fixed effect was specified, the function failed. +# Now it is possible to specify a single number as parameter 'fix' + + +## INPUT: +# model: an object of class 'mer' (lme4 packge), 'lmerMod' (lme4Eigen package) +# ran: list of vectors of natural numbers according to random effects of the model; +# the maximum length of this list is the number of random factors; +# each list member includes the numbers of the random effects (of the current random factor) +# (e.g., list(1:2, NULL, c(1, 3)) ) +# default value: NULL (no random-factor related variance is removed) +# fix: vector of natural numbers or strings according to fixed effects of the model +# (e.g., c(2:4, 6, 8:10), c("Effect1", "Effect2"), or c(2:4, "Effect1", 6, "Effect2")) +# Vectors can consist of both integers and strings (R will transform all intergers to +# strings if at least one string is entered); +# redundant values will be ignored (one effect can't be removed more than once) +# default value: NULL (no fixed effects are removed) +# keep: logical value; if TRUE, the specified effects are not removed but kept +# (and all other effects are removed) +# grouping: logical value; if FALSE the specified effects in fix are used; +# if TRUE, effects are grouped: +# - if keep=TRUE, the specified effect (and all effects associated with the +# variables) as well as all effects of lower order consisting solitary of +# a subset of the variables of the specified effet are kept +# (e.g., if the interaction A:B:C is specified, the following effects are +# chosen: A:B:C, A:B, A:C, B:C, A, B, and C) +# - if keep=FALSE, the specified effect (and all effects associated with the +# variables) as well as all effects of higher order consisting of +# all variables of the specified effet (and other variables) are removed +# (e.g., if the interaction A:B:C is specified, the following effects are +# chosen: A:B:C and A:B:C:x) +# family: a family object including a link function; +# either "identity" (default) or "logit" link function; this must be the +# link function which was used for generating the model; +# - gaussian(link = "identity") is the right option for most purposes, e.g. Gaussian +# distributions; the dependent variable is not transformed +# - binomial(link = "logit") is used for binomial dependent variables; the output vector +# will contain probabilities which can be rounded to obtain data in the +# original metric (zeroes and ones); note that even if keep=FALSE, the +# base for the calculation are not the input values but the residuals + +## OUTPUT: a numerical vector + +## How does it work? +# Random factor variance and fixed effects are removed from the dependent variable of an LMM analysis. +# The order of effects in the fixed-effects input vector is the same as in the model output. +# The returned vector includes the dependent variable corrected by the specified effects. +# Note. The currect version of this function works for the "identity" and "logit" model link functions +# only. + +remef <- function(model, fix = NULL, ran = NULL, keep = FALSE, grouping = FALSE, family = gaussian(link = "identity"), plot = FALSE) { + # name of link function + mclass <- class(model) + sup_classes <- c("mer", "lmerMod", "glmerMod") # supported object classes + if (!mclass %in% c(sup_classes)) stop("This class is not supported yet.") + fixef.fnc <- lme4::fixef + ranef.fnc <- lme4::ranef + moma <- model.matrix(model) + # model matrix + if (is.function(family)) family <- family() + link <- family$link + if (!(link %in% c("identity", "logit"))) stop("Unknown link function specified.") + if (keep || link == "logit") { + #DV <- lme4::residuals(model) # use residuals as base and add effects + DV <- residuals(model) + } else { + # use actual data as base and remove effects (this is not possible with the logit link function) + DV <- model@frame[ , 1] + } + fix <- unique(fix) # remove redundant values + if (any(is.character(fix))) { # strings were entered as fixed effects + suppressWarnings( fix.num <- as.numeric(fix) ) + # fix.num, numerical fix vector + ef.names.idx <- is.na(fix.num) + # logical vector indicating the positions of effect names in the fix vector + for (ef in fix[ef.names.idx]) { + if(!any(ef == names(fixef.fnc(model)))) stop(paste("The fixed effect", ef, "is not present in the model.")) + # stops the function if any fixed effect string is not present in the model + } + fix.num[ef.names.idx] <- which( names(fixef.fnc(model)) %in% fix[ef.names.idx] ) + fix <- unique(fix.num) + } + if (grouping & length(fix) > 0) { + new.fix <- NULL # help variable for the construction of a new 'fix' vector + for (ef in fix) { # choose the specified effects and all lower-order/higher-order effects of the relevant variables + # var.str <- attr(lme4::model.matrix(model), "assign") + var.str <- attr(moma, "assign") + # var.str, structure of the variables + if (!var.str[ef]) { # the specified effect is the intercept + new.fix <- unique(c(new.fix, ef)) + } else { # the specified effect is NOT the intercept + var.mat <- attr(terms(model), "factors") + # var.mat, variable matrix + ef.order <- attr(terms(model), "order") + # ef.order, order of effects (0: intercept, 1: main effect, 2: two-factor interaction, etc.) + if (keep) { # choose specified effect an all associated ones of lower order + ass.ef <- which( var.str %in% which( colSums( matrix( var.mat[ var.mat[ , var.str[ef] ] == 1, ] , ncol = length(ef.order)) ) == ef.order ) ) + # ass.ef, effects associated with the input effect (integer(s)) + } else { # choose specified effect an all associated ones of higher order + ass.ef <- which( var.str %in% which( colSums( matrix( var.mat[ var.mat[ , var.str[ef] ] == 1, ] , ncol = length(ef.order)) ) == ef.order[var.str[ef]] ) ) + } + new.fix <- unique(c(new.fix, ass.ef)) + } + } + fix <- new.fix + } + if (!keep && link == "logit") { # keep effects! + fix <- setdiff(seq_along(fixef.fnc(model)), fix) + } + # remove random factor variance + if (identical(ran, "all")) { + ran <- lapply(ranef(model), seq_along) + } + if (length(ran) > 0) { + rf_before.end.at <- -1 + # for (rf in 1 : length(ran)) { + for (rf in seq_along(ranef.fnc(model))) { # rf, random factor + if (rf > length(ran)) { # non-specified random factors + if (!keep && link == "logit") { # keep effects! + ran[[rf]] <- seq.int(ncol(ranef.fnc(model)[[rf]])) + } else { + ran[[rf]] <- NULL + } + } else { + if(!is.null(ran[[rf]])) ran[[rf]] <- unique(ran[[rf]]) + if (!keep && link == "logit") { # keep effects! + ran[[rf]] <- setdiff(seq.int(ncol(ranef.fnc(model)[[rf]])), ran[[rf]]) + } + } + n.rf.levels <- nrow(ranef.fnc(model)[[rf]]) + # n.rf.levels, number of random-factor levels + for (re in ran[[rf]]) { # re, random effect (e.g., intercept, slope) + idx.re <- ( ((re - 1) * n.rf.levels + 1) : (re * n.rf.levels) ) + (rf_before.end.at + 1) + #idx.re, numbers of lines of the (transpose) random effect matrix for the currect random effect + if (mclass == "lmerMod") re.matrix <- model@pp$Zt else re.matrix <- model@Zt + DV <- DV + sign((keep || link == "logit") - 0.5) * ( as.vector( ranef.fnc(model)[[rf]][ , re] %*% re.matrix[idx.re, ] ) ) + # Note. re.matrix is the transpose sparse random-effect matrix (class dgCMatrix) + # Note. sign(keep - 0.5) is +1 if keep==TRUE and -1 otherwise + } + rf_before.end.at <- rf_before.end.at + prod(dim(ranef.fnc(model)[[rf]])) + # at which line of the random-effect matrix did the current random effect end? + } + } + # remove fixed effects + DV <- DV + sign((keep || link == "logit") - 0.5) * ( matrix(moma[ , fix], nrow = length(DV)) %*% fixef.fnc(model)[fix] ) + if (link == "logit") DV <- ( 1 / (1 + exp(- DV)) ) + # if DV is rounded, zeros and ones will result + if (plot) { + warning("The 'plot' parameter is deprecated.") + } + return(as.vector(DV)) +} + +############################################################# diff --git a/examples/visual-attention/kkl15.qmd b/examples/visual-attention/kkl15.qmd index ba7bc5f..d07d4d3 100644 --- a/examples/visual-attention/kkl15.qmd +++ b/examples/visual-attention/kkl15.qmd @@ -32,7 +32,7 @@ We specify three contrasts for the four-level factor CTR that are derived from s This comparison is of interest because a few years after the publication of @Kliegl2011, 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. -Here we also include two additional experimental manipulations of target size and orientation of cue rectangle. A similar analysis was reported in the parsimonious mixed-model paper [@Bates2015]; it was also used in a paper of GAMEMs [@Baayen2017]. Data and R scripts of those analyses are also available in [R-package RePsychLing](https://github.com/dmbates/RePsychLing/tree/master/data/). +Here we also include two additional experimental manipulations of target size and orientation of cue rectangle. A similar analysis was reported in the parsimonious mixed-model paper [@Bates2015]; it was also used in a paper of GAMMs [@Baayen2017]. Data and R scripts of those analyses are also available in [R-package RePsychLing](https://github.com/dmbates/RePsychLing/tree/master/data/). The analysis is based on reaction times `rt` to maintain compatibility with @Kliegl2011. @@ -40,7 +40,7 @@ In this vignette we focus on the reduction of model complexity. And we start wit “Neither the [maximal] nor the [minimal] linear mixed models are appropriate for most repeated measures analysis. Using the [maximal] model is generally wasteful and costly in terms of statiscal power for testing hypotheses. On the other hand, the [minimal] model fails to account for nontrivial correlation among repeated measurements. This results in inflated [T]ype I error rates when non-negligible correlation does in fact exist. We can usually find middle ground, a covariance model that adequately accounts for correlation but is more parsimonious than the [maximal] model. Doing so allows us full control over [T]ype I error rates without needlessly sacrificing power.” -Stroup, W. W. (2012, p. 185). _Generalized linear mixed models: Modern concepts, methods and applica?ons._ CRC Press, Boca Raton. +Stroup, W. W. (2012, p. 185). _Generalized linear mixed models: Modern concepts, methods and applications._ CRC Press, Boca Raton. # Packages @@ -68,6 +68,8 @@ progress = isinteractive() ```{julia} #| echo: false using SMLP2026: fit_or_restore, bootstrap_or_restore + +using SMLP2026.RKUtils ``` # Read data, compute and plot means diff --git a/examples/visual-attention/kwdyz11.qmd b/examples/visual-attention/kwdyz11.qmd index 735a9c2..7181486 100644 --- a/examples/visual-attention/kwdyz11.qmd +++ b/examples/visual-attention/kwdyz11.qmd @@ -59,8 +59,11 @@ using MixedModels using MixedModelsMakie using Random using MixedModelsDatasets: dataset -using SMLP2026: fit_or_restore + using StatsBase + +using SMLP2026: fit_or_restore, bootstrap_or_restore +using SMLP2026.RKUtils ``` # Read data, compute and plot densities and means @@ -163,7 +166,7 @@ contrasts = Dict( ) m1 = let form = @formula(log(rt) ~ 1 + CTR + (1 + CTR | Subj)) - fit_or_restore("kwdyz11_m1.json", MixedModel, form, dat; contrasts) + fit_or_restore("kwdyz11_m1.json", MixedModel, form, dat; contrasts, REML=true) end ``` diff --git a/fits/eyevoicespan_m00.json.zip b/fits/eyevoicespan_m00.json.zip new file mode 100644 index 0000000..b0453cd --- /dev/null +++ b/fits/eyevoicespan_m00.json.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:02618ff85db9afa15e436cc41dbd2e2babeacdb61904993d15b89003fcdb61ab +size 646 diff --git a/fits/eyevoicespan_m05.json.zip b/fits/eyevoicespan_m05.json.zip new file mode 100644 index 0000000..fa162b6 --- /dev/null +++ b/fits/eyevoicespan_m05.json.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a49a374ece734172ebd0650b4b93ef87604ebb38121c058cbb1f4d4756d1773e +size 640 diff --git a/fits/eyevoicespan_m09.json.zip b/fits/eyevoicespan_m09.json.zip new file mode 100644 index 0000000..ea0c5ce --- /dev/null +++ b/fits/eyevoicespan_m09.json.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a9f4d85839984d1b6d6f83fe280998f8a962718b43ad3883bd816c92fe7dd5b6 +size 664 diff --git a/fits/eyevoicespan_m10.json.zip b/fits/eyevoicespan_m10.json.zip new file mode 100644 index 0000000..db4a59f --- /dev/null +++ b/fits/eyevoicespan_m10.json.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4ddbbf0840639d0e3b8e6ffa969028522df983eea9dd9beb2eb0e1d809fb86ff +size 616 diff --git a/references.bib b/references.bib index 293b87d..1fe078d 100644 --- a/references.bib +++ b/references.bib @@ -80,6 +80,18 @@ @Article{Kliegl2011 publisher = {Frontiers Media {SA}}, } +@Article{Pan2013, + author = {Jinger Pan and Ming Yan and Jochen Laubrock and Hua Shu and Reinhold Kliegl}, + journal = {Developmental Science}, + title = {Eye--voice span during rapid automatized naming of digits and dice in {Chinese} normal and dyslexic children}, + year = {2013}, + volume = {16}, + number = {6}, + pages = {967--979}, + doi = {10.1111/desc.12075}, + publisher = {Wiley}, +} + @Misc{Bates2015, author = {Bates, Douglas and Kliegl, Reinhold and Vasishth, Shravan and Baayen, Harald}, title = {Parsimonious Mixed Models}, From 666a84f5985a4ccdc4ce9929c6ceae9c265327ae Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 08:58:38 +0000 Subject: [PATCH 2/9] remove timing detritus --- examples/emotikon/fggk21.qmd | 42 ------------------------------------ 1 file changed, 42 deletions(-) diff --git a/examples/emotikon/fggk21.qmd b/examples/emotikon/fggk21.qmd index 9c649b2..9e86e6b 100644 --- a/examples/emotikon/fggk21.qmd +++ b/examples/emotikon/fggk21.qmd @@ -87,48 +87,6 @@ select!(groupby(df, :Test), Not(:score), :score => zscore => :zScore) The preprocessing steps above are also packaged as `SMLP2026.fggk21_preprocessed()`, so that other pages (e.g. the [contrast-coding tutorial](../../contrasts/contrasts_fggk21.qmd)) can reuse them without repeating the code. ::: -## Time final LMM of paper - -**Warmup** - -```{julia} -#| eval: false -## final LMM -m_test = let - f_test = @formula zScore ~ 1 + Test*a1*Sex + (1 | School) - @time fit(MixedModel, f_test, df; contrasts, progress) -end -``` - -**Timing the full model with current MixedModels.jl** - -```{julia} -#| eval: false -## final LMM -m_osf = let - f = @formula zScore ~ 1 + Test*a1*Sex + - (1+Test+a1+Sex | School) + (1+Test | Child) + - zerocorr(1 + Test | Cohort) - fit(MixedModel, f, df; contrasts, progress) -end -``` - -Minimizing 4724 Time: 0:23:33 ( 0.30 s/it) - -**Timing the full model with new branch pa/gradient-fable** - -```{julia} -#Pkg.add MixedModels#pa/gradient-fable -m_osf2 = let - f = @formula zScore ~ 1 + Test*a1*Sex + - (1+Test+a1+Sex | School) + (1+Test | Child) + - zerocorr(1 + Test | Cohort) - fit(MixedModel, f, df; contrasts, progress, optimizer=:LD_LBFGS) -end -``` - -Minimizing 81 Time: 0:01:12 ( 0.90 s/it) - ## Extract a stratified subsample For the purpose of the tutorial, we extract a random sample of 1000 boys and 1000 girls. `Child`, `School`, and `Cohort` are grouping variables. From 2f31bc6fa8ba6a17efb125d818770867160f5f7b Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 09:04:33 +0000 Subject: [PATCH 3/9] Update examples/emotikon/fggk21.qmd --- examples/emotikon/fggk21.qmd | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/examples/emotikon/fggk21.qmd b/examples/emotikon/fggk21.qmd index 9e86e6b..fe95470 100644 --- a/examples/emotikon/fggk21.qmd +++ b/examples/emotikon/fggk21.qmd @@ -68,7 +68,14 @@ transform!(df, levels!(df.Sex, ["male", "female"]) recode!(df.Sex, "male" => "Boys", "female" => "Girls") levels!(df.Test, ["Run", "Star_r", "S20_r", "SLJ", "BPT"]) - +recode!( + df.Test, + "Run" => "Endurance", + "Star_r" => "Coordination", + "S20_r" => "Speed", + "SLJ" => "PowerLOW", + "BPT" => "PowerUP", +) describe(df) contrasts = Dict{Symbol,Any}(nm => SeqDiffCoding() for nm in (:Test, :Sex)) From 78dbe2807e671174462536b70ccb72764ea58984 Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 09:05:03 +0000 Subject: [PATCH 4/9] remove alt contrasts --- examples/emotikon/fggk21.qmd | 2 -- 1 file changed, 2 deletions(-) diff --git a/examples/emotikon/fggk21.qmd b/examples/emotikon/fggk21.qmd index fe95470..41a9e0d 100644 --- a/examples/emotikon/fggk21.qmd +++ b/examples/emotikon/fggk21.qmd @@ -77,8 +77,6 @@ recode!( "BPT" => "PowerUP", ) describe(df) - -contrasts = Dict{Symbol,Any}(nm => SeqDiffCoding() for nm in (:Test, :Sex)) ``` ### Transformations From 2feba7fc1f29028f86599020eee04af0d8526605 Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 11:33:11 +0200 Subject: [PATCH 5/9] move chonky files to LFS --- .gitattributes | 2 ++ .../eyevoicespan/Pan_etal.DevSci.2013.pdf | Bin 531793 -> 131 bytes examples/eyevoicespan/pylsk13.rda | Bin 1549 -> 129 bytes 3 files changed, 2 insertions(+) diff --git a/.gitattributes b/.gitattributes index 03d92dd..db95ba5 100644 --- a/.gitattributes +++ b/.gitattributes @@ -3,3 +3,5 @@ *.RDs filter=lfs diff=lfs merge=lfs -text *.RDS 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zcmWN{yAi`63;@vHQ?NkHA0cmJKm_iR;ES+}OdnUTc^7@TkB?|`9=u8U?DO%eyxz7m zt$Dm9AC%>#m(h#hwi_Qdf)c4j6OytzZD2NG%F{lZ|kSJhG5F~O61O*ik3iO~Y^rDbxuzqKs z@3X@G2OgVzIy>(>^S;k}%)9S2@7esc#Qa2$$76f!zTm}IpN&73$LHydqqjI*g};yD zYcJ>n6;MK@G>c}_9D1GR(mX1oa;l*D6roD0q8eI4Z_rYDla|qPdYj&%6||C$&`~-@ z$LR$9Kqu)Gouza1GyOup(s{Z-7wI>;M3hdDU@#d-1L1?UTBh(ALRL1&Yx7q zosl5plge=oal8U-XJ{$=P2*?1IzD5^$@Lj*XNdU$){}8GnqV?l%5^zxS89>O85*z= zpH0Tk`4p1)J%6vKop?0Y!C1h)!+H|Wno`qJprp=E92e(KQg{rcnh%qurgr{>;mk2tWR04d;Xd9 zjqSs63LJvNa0jqAw7!H>$j4e|&44dh|6S=L8|$Anj{So@rH!@FS_B7K=V@Nw0~zok z+tCll-8i~^g*~5*{i*dFwCQ^4bjx$(v_*$M(P@@-!)cd!<21|q;9TDroe$0}nGeoQ zdG4G}9$T5-DeHyPBI}xSOV$VHrabRXhg)p-!Pt41Jl9UUJg3ebnUAr0TA6;8=}j!J zf%SGVy+hWmSe&iLqx0NpVmp3fekbc~;IW(O9qb2fhnC;CGuj}ho^flu&GI}sUCeKn z_0GA?{?c~-!F)aMV!zyAy;@EK`%UY+!g093_SdyU*FC3^^z-rpEEAGG{>mV1qH>HRuBI_^52ml$sy$EA(!YhwHtS>I)j({;8} z<2cJW&&cmaY@9k7R|m`0algTS)^XH%9Geeu?a=wt7B>&If7#4qfEhK&a()Todf7JK6HMEM>Qv7|3N#Eo2dOcr9TCcuu>U*TV zH|qIvT1_kBL}&(0BR$WhsgzFzG@bOiLJHDLr1^%l9=%TU3*x*?T8_q%M|z#+Pb7^a zz8q~A$I-V#Jg`OhPE)b)ZW6vK;k_XeLc%wl!t@nQq-Dapm#zt)pK_>=@E#L(x9}RO z6!zC5;fV0n(u>00M*D@=Ct|Ny-%$mP7v9H&HJDQA1)Dhq8pRT_E@W2#&))D{!Z)G;R From 8ae01e819560c2464d5970ab865240eae9b06e5d Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 11:49:56 +0200 Subject: [PATCH 6/9] fix some paths --- examples/eyevoicespan/pylsk13.qmd | 2 +- examples/eyevoicespan/pylsk13_interactions.qmd | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/eyevoicespan/pylsk13.qmd b/examples/eyevoicespan/pylsk13.qmd index fe70fa7..4b208aa 100644 --- a/examples/eyevoicespan/pylsk13.qmd +++ b/examples/eyevoicespan/pylsk13.qmd @@ -73,7 +73,7 @@ set_aog_theme!() (56 children × 2 conditions = 112 rows). ```{julia} -dat = DataFrame(load(joinpath("examples", "eyevoicespan", "pylsk13.rda"))["dat"]) +dat = DataFrame(load(joinpath(@__DIR__, "pylsk13.rda"))["dat"]) ``` We follow the general recommendation to code the levels of grouping variables as diff --git a/examples/eyevoicespan/pylsk13_interactions.qmd b/examples/eyevoicespan/pylsk13_interactions.qmd index eb88bcb..842c668 100644 --- a/examples/eyevoicespan/pylsk13_interactions.qmd +++ b/examples/eyevoicespan/pylsk13_interactions.qmd @@ -69,7 +69,7 @@ set_aog_theme!() ```{julia} #| code-fold: true -dat = DataFrame(load(joinpath("examples", "eyevoicespan", "pylsk13.rda"))["dat"]) +dat = DataFrame(load(joinpath(@__DIR__, "pylsk13.rda"))["dat"]) transform!(dat, :subj => (x -> categorical(string.("S", x))) => :Subj, :group => (x -> categorical(recode(x, 1 => "control", 2 => "dyslexic"))) => :Group, From 02f1dfba5909f3347e40f6df546cd3415f6fcb09 Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 12:09:41 +0200 Subject: [PATCH 7/9] no more LinesFill --- examples/eyevoicespan/pylsk13.qmd | 36 +++++++------------ .../eyevoicespan/pylsk13_interactions.qmd | 6 ++-- 2 files changed, 16 insertions(+), 26 deletions(-) diff --git a/examples/eyevoicespan/pylsk13.qmd b/examples/eyevoicespan/pylsk13.qmd index 4b208aa..31903a8 100644 --- a/examples/eyevoicespan/pylsk13.qmd +++ b/examples/eyevoicespan/pylsk13.qmd @@ -395,13 +395,12 @@ draw( data(eff_evs) * mapping( :evs => "Eye–voice span", - :lran => "log(RAN)"; color=:cg => "Condition / Group", - lower=:lower, - upper=:upper, - ) * - visual(LinesFill), -) + ) * ( + mapping(:lran => "log(RAN)") * visual(Lines) + + mapping(:lower, :upper) * visual(Band; alpha=0.3) + ) + ) ``` ## Gaze effect by Condition and Group @@ -421,15 +420,10 @@ let eff_gaze.cg = categorical(string.(eff_gaze.Condition, " / ", eff_gaze.Group)) draw( data(eff_gaze) * - mapping( - :gaze => "Gaze duration [ms]", - :lran => "log(RAN)"; - color=:cg => "Condition / Group", - lower=:lower, - upper=:upper, - ) * - visual(LinesFill), - ) + mapping(:gaze => "Gaze duration [ms]";) * ( + mapping(:lran => "log(RAN)") * visual(Lines) + + mapping(:lower, :upper) * visual(Band; alpha=0.3) + )) end ``` @@ -455,14 +449,10 @@ let ) draw( data(eff) * - mapping( - :gaze => "Gaze duration [ms]", - :lran => "log(RAN)"; - color=:evs_level => "Eye–voice span", - lower=:lower, - upper=:upper, - ) * - visual(LinesFill), + mapping(:gaze => "Gaze duration [ms]"; + color=:evs_level => "Eye–voice span") * + (mapping(:lran => "log(RAN)") * visual(Lines) + + mapping(:lower, :upper) * visual(Band; alpha=0.3)) ) end ``` diff --git a/examples/eyevoicespan/pylsk13_interactions.qmd b/examples/eyevoicespan/pylsk13_interactions.qmd index 842c668..908b538 100644 --- a/examples/eyevoicespan/pylsk13_interactions.qmd +++ b/examples/eyevoicespan/pylsk13_interactions.qmd @@ -158,9 +158,9 @@ function three_panel(; obs_df, xcol, xlab, obs_y, par_y, pred_df, color, colorla (visual(Scatter; alpha=0.35) + linear()) ppar = data(obs_df) * mapping(xcol => xlab, par_y => "adjusted log(RAN)"; color=color => colorlab) * (visual(Scatter; alpha=0.35) + linear()) - ppred = data(pred_df) * mapping(xcol => xlab, :yhat => "predicted log(RAN)"; - color=color => colorlab, lower=:lower, upper=:upper) * - visual(LinesFill) + ppred = data(pred_df) * mapping(xcol => xlab, color=color => colorlab) * + (mapping(:yhat => "predicted log(RAN)") * visual(Lines) + + mapping(:lower, :upper) * visual(Band; alpha=0.3)) g = draw!(fig[1, 1], pobs; axis=(; limits=ylims, title="Observed")) draw!(fig[1, 2], ppar; axis=(; limits=ylims, title="Partial (remef)")) draw!(fig[1, 3], ppred; axis=(; limits=ylims, title="Predicted (Effects)")) From 3ec9f21ca91adf73b74754fe20f1478935d05642 Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 12:33:08 +0200 Subject: [PATCH 8/9] oops --- examples/eyevoicespan/pylsk13.qmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/eyevoicespan/pylsk13.qmd b/examples/eyevoicespan/pylsk13.qmd index 31903a8..44e6903 100644 --- a/examples/eyevoicespan/pylsk13.qmd +++ b/examples/eyevoicespan/pylsk13.qmd @@ -420,7 +420,7 @@ let eff_gaze.cg = categorical(string.(eff_gaze.Condition, " / ", eff_gaze.Group)) draw( data(eff_gaze) * - mapping(:gaze => "Gaze duration [ms]";) * ( + mapping(:gaze => "Gaze duration [ms]"; color=:cg => "Condition / Group") * ( mapping(:lran => "log(RAN)") * visual(Lines) + mapping(:lower, :upper) * visual(Band; alpha=0.3) )) From bbf0c124098512f9fc69a2f057e9d5f220d0effd Mon Sep 17 00:00:00 2001 From: Phillip Alday Date: Fri, 28 Aug 2026 12:33:18 +0200 Subject: [PATCH 9/9] fix level --- examples/eyevoicespan/pylsk13_interactions.qmd | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/examples/eyevoicespan/pylsk13_interactions.qmd b/examples/eyevoicespan/pylsk13_interactions.qmd index 908b538..91447a8 100644 --- a/examples/eyevoicespan/pylsk13_interactions.qmd +++ b/examples/eyevoicespan/pylsk13_interactions.qmd @@ -35,7 +35,7 @@ Three views pull the term apart: |---|---|---| | **Observed** | `log(RAN)` against the predictor, split by the moderator, with an ordinary least-squares line per group | nothing removed — the raw data | | **Partial** | the same, after subtracting every model term *except* the target interaction and its lower-order relatives, and the random intercept | `partial_fitted(m09, keep; mode=:include) .+ residuals(m09)` — the Julia analogue of R's `remef(..., keep=TRUE, grouping=TRUE, ran=NULL)` | -| **Predicted** | the model's fitted mean on a regular grid, with a 95% confidence band, holding the other predictors at typical values | `Effects.effects(grid, m09)` | +| **Predicted** | the model's fitted mean on a regular grid, with a 95% confidence band, holding the other predictors at typical values | `Effects.effects(grid, m09; level=0.95)` | The **observed** panel is honest about scatter but confounded. The **partial** panel keeps the residual scatter (so you can still judge influence and fit) while removing @@ -178,7 +178,7 @@ end #| label: fig-c-evs let grid = Dict(:evs_c => range(extrema(dat.evs_c)...; length=50), :Condition => levels(dat.Condition)) - e = effects(grid, m09) + e = effects(grid, m09; level=0.95) rename!(e, :lran => :yhat) e.evs = e.evs_c .+ mean(dat.evs) three_panel(; obs_df=dp, xcol=:evs, xlab="Eye–voice span", obs_y=:lran, par_y=:pf_C_evs, @@ -200,7 +200,7 @@ lines separate less — the interaction is real but the *marginal* prediction di #| label: fig-g-evs let grid = Dict(:evs_c => range(extrema(dat.evs_c)...; length=50), :Group => levels(dat.Group)) - e = effects(grid, m09) + e = effects(grid, m09; level=0.95) rename!(e, :lran => :yhat) e.evs = e.evs_c .+ mean(dat.evs) three_panel(; obs_df=dp, xcol=:evs, xlab="Eye–voice span", obs_y=:lran, par_y=:pf_G_evs, @@ -222,7 +222,7 @@ who are already fluent. let grid = Dict(:gaze_c => range(extrema(dat.gaze_c)...; length=50), :evs_c => tert_med .- mean(dat.evs)) - e = effects(grid, m09) + e = effects(grid, m09; level=0.95) rename!(e, :lran => :yhat) e.gaze = e.gaze_c .+ mean(dat.gaze) pts = tert_med .- mean(dat.evs) @@ -248,7 +248,7 @@ ahead. The predicted panel confirms the crossing pattern with confidence bands. let grid = Dict(:evs_c => range(extrema(dat.evs_c)...; length=50), :Condition => levels(dat.Condition), :Group => levels(dat.Group)) - e = effects(grid, m09) + e = effects(grid, m09; level=0.95) rename!(e, :lran => :yhat) e.evs = e.evs_c .+ mean(dat.evs) e.cg = categorical(string.(e.Condition, " / ", e.Group))

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