Bayesian Multilevel Models for Repeated Measures dаta A Conceptual and Practical Introduction in R

1. 1Represent each listener as a grouping factor with multiple observations per level: in the experiment, 15 listeners each respond to many stimuli, producing 4,170 rows in long format where each row is one listener's response to one stimulus word. Do not collapse to per-listener means.
2. 2Model two levels of variation explicitly: data-level (within-listener, trial-to-trial) and parameter-level (between-listener, systematic). A multilevel model in brms lets you estimate these independently rather than assuming all observations are exchangeable.
3. 3Add a random intercept for listener first to capture idiosyncratic average judgments (some listeners systematically judge speakers as taller, or systematically report more femaleness). This estimates between-listener variation in intercepts.
4. 4Add random slopes for each acoustic/categorical cue (e.g. VTL, f0, apparent age, apparent gender) grouped by listener so each listener can use each cue differently. This is the 'models with intercepts and slopes for each level of a grouping factor' structure from Chapter 9.
5. 5Estimate correlations between the random parameters using a multivariate normal distribution over the by-listener effects, and set hyperpriors on the standard deviations and correlation matrix so partial pooling can operate.
6. 6Rely on adaptive partial pooling rather than complete pooling (one estimate for all) or no pooling (independent per-listener fits); partial pooling shrinks noisy individual listener estimates toward the group mean, and you can inspect this via the shrinkage investigation.
7. 7Extract and inspect the random effects to see which listeners deviate and on which cues, then simulate data from the fitted parameters to check that the modeled between-listener spread reproduces the observed spread.

In the apparent-height and apparent-gender experiment, 15 listeners judged the same set of stimulus words, and the discussion explicitly reports 'between-listener variation in gender perception.' Consider two cues: voice pitch (f0) and resonance (VTL). One listener might treat low f0 as a strong signal of maleness while another weights VTL more heavily, and each may have a different baseline tendency to report 'male.' You model this with a by-listener random intercept (baseline maleness judgment) plus by-listener random slopes for f0 and VTL, allowing the correlation between them. Fitting this to the 4,170 observations, partial pooling pulls extreme individual slopes toward the group average when a listener contributed noisy or few consistent responses. The result separates the genuine cue effect from idiosyncratic listener behavior, so you don't mistake one listener's quirk for a population-level finding. The passages note listeners 'use acoustic information in idiosyncratic ways that are systematic within-listener, but which differ arbitrarily from each other between listeners' — exactly what random slopes capture.

• If you have more than one observation per listener, then you have repeated measures data and must model listener as a grouping factor — never treat rows as independent.
• If listeners differ mainly in average response level, then a random intercept suffices; if they differ in how strongly a cue drives their judgments, then add a random slope for that cue.
• If per-listener estimates are noisy or based on few trials, then prefer adaptive partial pooling over no-pooling so estimates borrow strength and shrink toward the group.
• If two random parameters (e.g. intercept and a slope) plausibly covary across listeners, then estimate their correlation via the multivariate normal rather than forcing independence.
• If a listener-level cue slope has values that are perfectly predictable from another (collinear) or the model becomes non-identifiable, then simplify the random-effects structure before adding more terms.

• Averaging each listener down to one number before analysis — the tell: your standard errors look implausibly small and effects seem 'too clean' because within-listener variation was discarded.
• Fitting only a random intercept when listeners actually differ in cue use — the tell: residuals show structured, listener-specific patterns against the acoustic predictors that the intercept can't absorb.
• Using complete pooling (ignoring listener) and calling an effect general — the tell: a result driven by one or two idiosyncratic listeners survives because their data is merged into the group.
• Using no-pooling (fully independent per-listener fits) with sparse data — the tell: wildly variable, extreme per-listener slopes that don't replicate on refit.
• Over-specifying a saturated random-effects structure the data can't support — the tell: convergence warnings, divergent transitions, or non-identifiable correlation estimates.

• ▸Grouping factor: name the listener ID column (e.g. L) and confirm >1 row per level.
• ▸Observations per listener: record trials per listener to judge pooling need.
• ▸Random intercept: yes/no — do listeners differ in baseline judgment?
• ▸Cue slopes to vary by listener: list acoustic/categorical cues (e.g. VTL, f0, apparent age, apparent gender).
• ▸Correlation structure: state which by-listener parameters you allow to covary (multivariate normal).
• ▸Hyperpriors: specify priors on the by-listener SDs and correlation matrix.
• ▸Pooling choice: complete / no / adaptive partial (default: partial).
• ▸Diagnostic plan: how you will inspect random effects and shrinkage after fitting.
• ▸Simulation check: confirm you will simulate from parameters to validate between-listener spread.

1. 1Recognize that any two speakers 'sound' different in ways that go beyond fundamental frequency (f0) and vocal-tract length (VTL); treat this residual, systematic, per-speaker difference as its own source of variation to be modeled, not ignored.
2. 2Structure your data so every observation is tagged with its speaker source, since repeated measures from the same speaker produce non-independence at the parameter level (average behavior differs systematically between speakers).
3. 3Fit a Bayesian multilevel model that includes speaker random effects (random intercepts, and slopes where predictors vary within speaker), so between-speaker variation is estimated separately from data-level variation rather than being absorbed into error.
4. 4Include speaker random effects even when your fixed effects are f0 and VTL: the definition here is precisely the variation those two cues do not capture, so leaving speaker out misattributes idiosyncratic speaker differences to your predictors.
5. 5Use adaptive partial pooling for speaker terms so speakers with few observations are shrunk toward the group mean, stabilizing estimates while still letting genuinely distinct speakers stand apart (see the shrinkage discussion in Ch. 4.9).
6. 6Compare the model with speaker random effects against a version without them (as done in Section 12.2.8, 'Refitting the model without speaker random effects') to see how much apparent-characteristic judgments depend on speaker identity versus acoustics.
7. 7When speaker random effects are present, interpret listeners' apparent-height and apparent-gender judgments as associations conditioned on speaker, not as clean effects of the acoustic cues alone.

In the running perceptual experiment (Chapter 13), listeners judge apparent height and apparent gender from speech, and the stated acoustic cues are fundamental frequency (voice pitch) and vocal-tract length. Two speakers matched on f0 and VTL will still not sound identical, because idiosyncratic speaker differences persist beyond those two cues. The multinomial model of Chapter 12 therefore includes speaker random effects, and Section 12.2.8 refits the same model without them to expose the difference. The book also treats these as parameter-level variation: apparent judgments vary within a speaker (data level) but average judgments also vary systematically between speakers (upper level), analogous to reaction times that vary within a participant while mean reaction time varies between participants. Modeling both levels lets you say that a height judgment is partly driven by VTL and partly by that speaker's particular voice. If you drop the speaker term, that idiosyncratic variation leaks into your VTL and gender estimates, inflating apparent cue effects. Keeping the speaker random effect keeps the association attributable to acoustics honest.

• If multiple observations share the same speaker, then add a speaker random effect; independence is otherwise violated.
• If a predictor (e.g., stimulus condition) varies within speaker, then give it a random slope by speaker, not just a random intercept.
• If a speaker contributes few observations, then rely on partial pooling and shrink its estimate toward the group mean rather than trusting a no-pooling estimate.
• If removing the speaker random effect materially changes your fixed-effect estimates for f0/VTL, then the effect was partly speaker idiosyncrasy and you must report it as such.
• If you cannot randomly assign speakers, then argue equivalence of groups on other characteristics (dialect, background, education) before attributing differences to your predictor.

• Treating f0 and VTL as if they fully describe a voice; the tell is that residuals cluster by speaker, revealing structure the fixed effects missed.
• Fitting a single-level model to repeated-measures speaker data; the tell is overconfident, too-narrow intervals because non-independence is unmodeled.
• Dropping speaker random effects to 'simplify' and then reporting inflated acoustic effects; the tell is a large shift in estimates between the with- and without-speaker fits (as in 12.2.8).
• Confusing data-level within-speaker variation with parameter-level between-speaker variation and modeling only one; the tell is that either within- or between-speaker spread is systematically mis-estimated.
• Interpreting a speaker-conditioned association as a clean causal cue effect; the tell is claims like 'VTL causes taller judgments' with no acknowledgment that speaker identity co-varies.

• ▸Response variable: name the perceptual judgment (e.g., apparent height, apparent gender).
• ▸Acoustic fixed effects: list the cues modeled (f0, VTL) and how each is coded/centered.
• ▸Speaker ID column: confirm every row is tagged with its source speaker.
• ▸Random intercept by speaker: yes/no and justification.
• ▸Random slopes by speaker: which within-speaker predictors get them.
• ▸Pooling strategy: complete / no / partial — state which and why.
• ▸With-vs-without comparison: record fixed-effect estimates before and after removing speaker terms.
• ▸Interpretation note: state that effects are associations conditioned on speaker, not causes.
• ▸Group equivalence: note any non-random speaker assignment and controlled characteristics.

1. 1Isolate a voiced segment where the vocal folds vibrate periodically — a vowel or a sustained consonant like 'zzzzzz'. You can confirm phonation by pressing the front of the neck and feeling the larynx vibrate.
2. 2Measure the repetition rate of that periodic wave in cycles per second (Hertz). f0 is the number of times the sound wave repeats itself in a second; record it per vowel token (the passage's 'f0' column stores vowel fundamental frequency).
3. 3Store f0 as a continuous quantitative predictor per trial alongside the other acoustics (in the source data: 'vtl' for vocal-tract length, 'dur' for vowel duration), so it can enter models jointly rather than in isolation.
4. 4Map f0 to expected speaker attributes using the empirical direction: lower f0 -> longer/heavier folds -> larger, older, more likely male; higher f0 -> shorter folds -> smaller, younger. Use this to form pre-registered expectations before fitting.
5. 5Treat f0 as a probabilistic cue, not a deterministic one: it separates child from adult well (5-year-old vs 18-year-old) but poorly separates adults of similar age (18 vs 30), so scope your age claims accordingly.
6. 6Model apparent judgments (apparent height, apparent category, apparent gender) as functions of f0 plus VTL, and let listeners vary — the source pairs f0 with listener-specific and speaker random effects rather than a single population coefficient.
7. 7Interpret any f0 effect as association, not cause: an f0-judgment link established from perception data shows listeners use the cue, it does not prove f0 alone determines the trait.

The book's running experiment plays single words and asks 15 listeners to classify each speaker (boy/girl/man/woman) and estimate height in feet and inches (converted to cm). Each of 139 speakers contributes a vowel with a measured f0 in Hz and an estimated vocal-tract length. The stated logic: if a speaker with an f0 of 100 Hz is usually an adult male about 176 cm tall, then listeners familiar with that regularity should hear a stimulus near 100 Hz and identify the speaker as an adult male. So you predict that as measured f0 falls, apparent maleness, apparent adulthood, and apparent height all rise. You then test this by regressing the apparent-height and apparent-gender responses on f0 (and VTL), checking whether the coefficient runs in the expected low-f0-to-larger-older-male direction and whether it holds across individual listeners.

• If the segment is voiceless or aperiodic (a whistle-like harmonic is fine, a fan/waterfall-like noise is not), then do not report an f0 — there is no periodic vibration rate to measure.
• If you must distinguish a child from an adult, then f0 is a strong cue; if you must distinguish two adults of similar age, then treat f0 as weak and lean on other information.
• If f0 is low, then bias the guess toward older, taller, and male; if f0 is high, then bias toward younger, shorter, and female — but only as a likelihood, never a certainty.
• If you found an f0-to-judgment association, then state it as association plus world knowledge (folds grow with age, lengthen in male puberty) before implying the acoustic drives the percept.
• If listeners disagree systematically, then fit listener-specific terms rather than assuming one f0 effect applies to everyone.

• Equating f0 with pitch. The tell: reporting the perceived 'note' as if measured, when pitch is the internal auditory sensation and f0 is the measurable acoustic correlate (also weakly affected by loudness and spectral shape).
• Reading f0 as a size ruler. The tell: precise height claims from f0 alone, ignoring that VTL/resonance is the other main size cue and that folds are modifiable in range like a tightened guitar string.
• Overreaching on adult age. The tell: using f0 to sort a 30-year-old from an 18-year-old — the passage says it can't reliably do this.
• Confusing veridical and apparent. The tell: mixing the speaker's actual category (C_v/G_v/A_v) with the listener's reported category (C/G/A) when relating them to f0.
• Sliding from association to cause. The tell: writing that f0 'causes' a judgment from the statistical link alone rather than from combined empirical and physiological knowledge.

• ▸Segment ID: which voiced vowel/consonant token you measured
• ▸Voicing confirmed (Y/N): felt/observed periodic vibration, not noise
• ▸f0 (Hz): repetitions of the sound wave per second for this token
• ▸Speaker ID: link to the talker (1-139 style unique code)
• ▸VTL estimate (cm): resonance-based size cue to pair with f0
• ▸Expected direction: lower f0 -> older/taller/male; higher f0 -> younger/shorter/female
• ▸Apparent judgment recorded: category, height (cm), gender, age as reported
• ▸Age-scope flag: child-vs-adult (reliable) or adult-vs-adult (unreliable)
• ▸Claim wording check: 'association' not 'cause'; note world-knowledge basis

1. 1Record the target word (e.g. "heed") and extract the formant frequencies (resonant frequencies of the vocal tract) from the speech signal — these, not the fundamental frequency, carry the resonance information you need.
2. 2Convert the formant pattern into an estimate of effective vocal-tract length in centimeters, the physical space from the vocal folds to the lips, following the estimation procedure detailed in Chapter 13. Treat this centimeter value, not a raw acoustic number, as your resonance variable.
3. 3Anchor your scale: set the average adult male VTL to 15 cm as the reference point (as done for the Lee et al. 1999 data in Figure 1.1) so all other estimates are interpretable relative to it.
4. 4Separate the two acoustic cues explicitly — keep f0 (pitch, Hz) and VTL (resonance, cm) as distinct predictors, because they index different things: f0 tracks vocal-fold vibration rate, VTL tracks tract length.
5. 5Map VTL to the physical correlate you care about: lower resonance implies longer VTL, which predicts greater body length (height); because height grows from birth to adulthood, VTL predicts both height and age.
6. 6To manipulate perceived size experimentally, shift the spectral envelope (leaving f0 untouched) — a downward shift of 8% simulates roughly an 8% increase in speaker size and should 'sound bigger'.
7. 7Model apparent-height and apparent-category judgments against f0 and VTL together, and allow the use of VTL cues to interact with apparent age and apparent gender rather than assuming one fixed weighting across listeners.

In the book's experiment, 139 Michigan-English speakers each produced the word "heed" (recorded by Hillenbrand et al. 1995): 48 adult females, 45 adult males, 19 girls and 27 boys aged 10–12. Each speaker's f0 and estimated VTL were measured, showing substantial between-speaker variation. Every stimulus was then duplicated and its spectral envelope shifted down by 8%, simulating a speaker roughly 8% larger, giving 278 stimuli (139 × 2 resonance levels) while pitch was left unchanged. Fifteen American-English listeners each heard all 278 in randomized order (4,170 observations total) and judged apparent category (boy/girl/man/woman) and apparent height in feet and inches. Because lower resonance signals a longer vocal tract and a longer tract predicts a taller body, listeners should rate the envelope-shifted (lower-resonance) tokens as taller. The reference frame is the 15 cm average adult-male VTL set in Figure 1.1.

• If you want a measure of speaker size, use VTL (resonance/formants) rather than f0 — f0 mainly separates children from post-pubescent adults and fails to distinguish an 18-year-old from a 30-year-old.
• If resonance is lower, then infer a longer vocal tract in centimeters and expect a taller, likely older speaker.
• If you need to simulate a larger speaker without changing pitch, then shift the spectral envelope downward (e.g. 8%) and leave f0 alone.
• If comparing VTL estimates across speakers, then express them relative to the 15 cm adult-male anchor so values are interpretable.
• If a listener's height judgment must be modeled, then include apparent age and apparent gender as interacting factors, since VTL-cue use is category-dependent.

• Confusing pitch with resonance: attributing size to f0. The tell — you predict a helium-voiced speaker sounds higher-pitched, when in fact helium raises resonance (short-VTL effect) while pitch stays put.
• Treating VTL as an acoustic number rather than a physical estimate. The tell — you report it in Hz or arbitrary units instead of centimeters of tract length.
• Omitting the male-VTL anchor. The tell — your VTL values can't be compared across speakers or to Figure 1.1 because there's no 15 cm reference.
• Letting the spectral-envelope shift bleed into f0. The tell — your 'size' manipulation also changes perceived pitch, so you can't attribute the effect to resonance alone (the Alvin/Chipmunks trick changed both by speeding playback).
• Assuming a single fixed VTL-to-height mapping for all speakers and listeners. The tell — your model ignores age-dependent and gender-dependent use of VTL cues and misfits children versus adults.

• ▸Stimulus word: the recorded token analyzed (e.g. "heed").
• ▸Measured formants: resonant frequencies extracted from the signal.
• ▸Estimated VTL (cm): tract length derived from formants per Chapter 13 method.
• ▸Male anchor check: confirm scale set so avg adult-male VTL = 15 cm.
• ▸f0 (Hz): fundamental frequency, kept separate as the pitch cue.
• ▸Envelope shift applied: percentage down-shift and simulated size change (e.g. −8% ≈ +8% size).
• ▸Predicted height/age: inference from VTL (lower resonance → longer tract → taller/older).
• ▸Speaker category factors: apparent age and gender to interact with VTL cue use.
• ▸Notes on cue confounds: confirm f0 held constant during any resonance manipulation.

1. 1Record the two judgments listeners make per trial as separate variables: the four-way apparent category (b/g/m/w) in column C, then decompose it into apparent age (A: a=adult, c=child) and apparent gender (G: f/m). Apparent age is the child-vs-adult split of that category.
2. 2Keep apparent age distinct from veridical age (A_v). The moderator you care about is what the listener perceived (A), not the ground truth (A_v), because the claim is about how listeners *interpret* cues, not about accuracy.
3. 3Include the vocal-tract-length estimate (vtl, in cm) and f0 (in Hz) as acoustic predictors, since these are the cues whose interpretation apparent age is supposed to moderate.
4. 4Model apparent height (height, cm) as the outcome and enter an interaction term between VTL and apparent age, so the slope relating VTL to judged height is allowed to differ for child-categorized vs adult-categorized voices.
5. 5Add speaker and listener random effects (S has 139 levels, L has 15) so idiosyncratic per-listener cue use and per-speaker offsets do not masquerade as an age effect.
6. 6Also test apparent gender (G) as a second moderator of the VTL→height relationship, and test apparent age as a moderator of gender perception, since these perceived categories feed back on each other.
7. 7Read the interaction coefficients, not just the main effects: a reliable VTL-by-apparent-age term is the evidence that the child/adult categorization changes how the resonance cue is converted into a height estimate.

In the book's single experiment, 15 listeners each responded to all 278 stimuli (139 speakers × 2 resonance levels), giving 4,170 rows in exp_data_all, each row one listener's response to one word. On every trial the listener picked one of 'boy 10–12', 'girl 10–12', 'man 18+', or 'woman 18+' (stored as C, then split into A and G) and estimated the speaker's height in feet and inches, later converted to centimeters (height). The resonance manipulation shifts implied vocal-tract length up or down — the same trick used to make 'Alvin and the Chipmunks' sound small, but run in reverse — while leaving f0 unchanged, so VTL can be probed independently of pitch. Because low resonances and low f0 are expected to signal taller and older speakers, you fit apparent height on vtl and f0 with an interaction between vtl and apparent age (A). If the VTL slope is steeper when the voice was categorized as a child than when categorized as an adult, apparent age is acting as the moderator: the same resonance cue is read differently depending on the child/adult judgment. The book frames exactly this in §13.4.1, 'Age-dependent use of VTL cues on apparent height'.

• If the research question is about how cues are *interpreted*, then use apparent age (A) as the predictor; if it is about listener accuracy, then compare A against veridical A_v.
• If a VTL-by-apparent-age interaction term is reliably non-zero, then treat apparent age as a genuine moderator and report separate VTL slopes per category rather than a single pooled slope.
• If f0 is low and the voice is categorized as adult, then weight it toward maleness as well as tallness; for a child-categorized voice, do not read low f0 as a maleness cue (the maleness link is post-pubescent).
• If you expect adultness to raise judged height, then remember the boy-to-man height gap is larger than the girl-to-woman gap, so the age effect on height should interact with apparent gender too.
• If between-listener differences look large, then keep listener random effects (and possibly listener-specific slopes) so idiosyncratic-but-systematic cue use is separated from the population-level age moderation.

• Substituting veridical age (A_v) for apparent age (A) in the model — the tell is that your 'moderator' effect shrinks or vanishes because listeners are often inaccurate, so the perceived category and the true category diverge.
• Fitting only main effects of VTL and apparent age and concluding age 'has an effect' — the tell is you never estimated the interaction, so you cannot say the cue is *interpreted* differently, only that categories differ on average height.
• Letting f0 and resonance covary in the stimuli — here they are decoupled (resonance changed, pitch untouched); if you don't preserve that separation you cannot attribute a moderating effect to VTL specifically.
• Ignoring listener random effects and reading a population slope as universal — the tell is that a few listeners with idiosyncratic cue use drive the apparent-age interaction.
• Treating apparent gender and apparent age as independent — the tell is contradictory results, since the book shows apparent age affects perceived femaleness and gender affects the height read-off, so omitting one biases the other.

• ▸Outcome: name the DV (apparent height in cm, column height) and its units.
• ▸Moderator: apparent age A coded a=adult / c=child (perceived, not A_v).
• ▸Primary cue: VTL estimate (vtl, cm) — the resonance-based cue being interpreted.
• ▸Secondary cue: f0 (Hz) — pitch cue; note it is unaffected by the resonance manipulation.
• ▸Interaction term: VTL × apparent age — write the coefficient and its interval here.
• ▸Second moderator check: apparent gender G (f/m) and its interaction with VTL/age.
• ▸Random effects: speaker S (139 levels) and listener L (15 levels) — confirm both included.
• ▸Slope-by-category readout: VTL→height slope for child voices vs adult voices.
• ▸Conclusion line: is apparent age a reliable moderator? (yes/no + which cue it reshapes)

1. 1Collect the categorical gender response as a binary judgment per trial: code G as 'f' (female) or 'm' (male) — do not conflate it with veridical gender (G_v) or with the four-way speaker category (C: b/g/m/w), which you can collapse into G separately.
2. 2Because apparent gender is binary, model it with logistic regression; keep the four-category response (C) available so you can derive both apparent gender (m/w → male; b/g... note here b/w vs collapse) and apparent age (a/c) from the same category judgment.
3. 3Enter apparent gender as a predictor (moderator), not just an outcome: interact it with acoustic cues (f0, vtl) when predicting apparent height, since the passages state acoustic information may be 'used differently based on the apparent category of the speaker.'
4. 4Test the effect of apparent age on the perception of femaleness — include apparent age (A: adult/child) as a predictor of gender judgments, because post-pubescent f0 lowering is the acoustic basis for maleness only in adults.
5. 5Add listener random effects to capture between-listener variation in gender perception; refit without them to check how much of the gender signal is idiosyncratic versus systematic across the 15 listeners.
6. 6After fitting on gross cues (f0, vtl), inspect residual structure to check whether gender perception goes 'beyond gross acoustic cues' — if f0 and vtl alone don't account for the judgments, note the shortfall rather than forcing a cue-only story.
7. 7Report apparent gender's downstream effect on height: quantify how judging a voice as male shifts the apparent-height estimate, since maleness is expected to associate with taller-sounding speakers, especially for older speakers.

In the book's experiment, 15 listeners each responded to all 278 stimuli (139 speakers × 2 resonance levels), for 4,170 observations. On every trial the listener picked one of four categories — boy, girl, man, or woman — which the analysis collapses into apparent gender G (f/m) and apparent age A (a/c). The stimuli were resonance-scaled: level 'b' raised resonance frequencies to sound bigger (a reverse of the Alvin-and-the-Chipmunks manipulation) while leaving pitch untouched, so vtl and f0 vary somewhat independently as gender cues. When analyzing apparent gender, the book models the probability of a 'female' response as a function of f0 and vtl, then examines the effect of apparent age on femaleness — because lower f0 signals maleness mainly for post-pubescent speakers. It also models between-listener variation and asks whether the judgments require information beyond the gross cues of pitch and resonance. Finally, apparent gender feeds back into the apparent-height model as a moderator, testing whether judging a voice male raises the estimated height.

• If the speaker is judged adult, then treat low f0 as strong evidence of maleness; if judged child, then downweight f0 as a gender cue because pre-pubescent vocal folds haven't diverged by sex.
• If you want gender both as outcome and as a moderator, then keep the raw four-way category (C) and derive G and A from it rather than asking gender directly.
• If listeners diverge widely in their gender responses to the same voice, then keep listener random effects; if divergence is negligible after refitting without them, then report the pooled effect.
• If f0 and vtl leave systematic error in the gender predictions, then conclude perception goes beyond gross acoustic cues and flag it rather than adding noise terms.
• If you are modeling apparent height, then include apparent gender as a predictor, because maleness is expected to raise apparent height, especially for older speakers.

• Using veridical gender (G_v) where apparent gender (G) belongs — the tell is that acoustic cues predict the outcome almost perfectly, because you've smuggled the true category in.
• Treating gender judgments as pure output and never as a moderator — the tell is a height model where f0/vtl effects don't change across male/female judgments even though the design lets them.
• Applying the low-f0-means-male rule to child stimuli — the tell is inflated maleness predictions for boys/girls whose vocal folds haven't yet diverged by sex.
• Pooling all 15 listeners without random effects — the tell is a tidy population gender curve that hides systematic within-listener, arbitrary-between-listener differences.
• Assuming pitch and resonance fully explain gender perception — the tell is unexplained systematic residuals that the passages attribute to cues 'beyond gross acoustic cues.'

• ▸Response variable: record apparent gender as G = f or m, derived from the four-way category C.
• ▸Distinguish veridical: log G_v separately; never substitute it for G in the model.
• ▸Acoustic predictors: list f0 (Hz) and vtl (cm) as the gross cues entered.
• ▸Age moderator: include A (a/c) and its interaction with f0 to test age-dependent maleness.
• ▸Listener term: specify random effect for L (1–15) to capture between-listener variation.
• ▸Refit check: note the model version fit without listener random effects for comparison.
• ▸Moderator role: state where apparent gender enters the apparent-height model as a predictor.
• ▸Residual check: record whether f0+vtl leave systematic error (beyond-gross-cues flag).
• ▸Research question tie-back: name which gender question (femaleness-by-age, listener variation, or beyond-cues) each term answers.

1. 1Record apparent height as a continuous outcome in centimeters. Listeners in this experiment estimated height in feet and inches; convert each response to cm before analysis so the outcome variable (`height`) is a floating-point number.
2. 2Assemble the two acoustic predictors that drive the estimate: vocal-tract length (`vtl`, in cm, estimated from speech per Chapter 13) and fundamental frequency (`f0`, in Hz). Lower resonance implies a longer vocal tract, and there is a strong positive relationship between vocal-tract length and body height across the human population, so VTL is your primary size cue.
3. 3Include the listener's own perceptual categorizations as predictors, not just veridical facts: apparent age (`A`: a/c) and apparent gender (`G`: f/m). These are the categories the listener reported, and they mediate how acoustics get mapped to height.
4. 4Model VTL's effect on apparent height as conditional on apparent age. Expect listeners to weight VTL cues differently when they judge a speaker to be a child versus an adult (the age-dependent use of VTL cues on apparent height).
5. 5Add an apparent-gender term: expect apparent maleness to be associated with taller estimates, especially for speakers judged older. Encode the man/boy gap as larger than the woman/girl gap when reasoning about adultness effects.
6. 6Fit a Bayesian multilevel regression (brms/Stan) with by-listener random effects, because with 15 listeners each responding to all 278 stimuli (4,170 total observations), listeners use acoustic information in idiosyncratic ways that are systematic within-listener but differ between listeners.
7. 7Keep the data in long format: one row per trial (listener × stimulus). With 139 speakers × 2 resonance levels = 278 stimuli and 15 listeners, confirm you have 4,170 rows before fitting.

Load `exp_data_all` from the bmmb package with `data(exp_data_all)` and `head(exp_data_all)`. Each row is one listener's response to one word: columns include `L` (listener 1–15), `height` (e.g. 165.6 cm, the apparent height), `vtl` (estimated vocal-tract length in cm), `f0` (vowel fundamental frequency in Hz), plus the listener's judgments `A` (apparent age) and `G` (apparent gender), and the veridical `C_v`, `A_v`, `G_v`. Because resonance was manipulated at two levels (`R` = a for actual, b for the 'big' modification made in the manner of Alvin and the Chipmunks but in reverse, without touching pitch), the same speaker appears twice with different implied VTL. You model `height` as a function of `vtl` and `f0`, allowing the VTL slope to differ by apparent age and adding an apparent-gender term, with by-listener random effects. The result lets you show that apparent taller estimates track lower resonance (longer VTL) and that this VTL weighting is age-dependent, and that apparently male speakers are judged taller, especially when judged to be adults.

• If the listener judged the speaker an adult rather than a child, then expect a stronger VTL-to-height slope and interpret the resonance cue as the dominant size signal.
• If a voice has lower resonance (longer estimated VTL), then predict a taller apparent height; if lower f0 co-occurs, then also expect apparent older and, for post-pubescent voices, apparent male.
• If the speaker is judged male, then shift the apparent-height estimate upward relative to a female judgment, and widen that shift for speakers judged older.
• If you have repeated measures from the same 15 listeners, then include by-listener random effects rather than pooling all responses, because listeners differ arbitrarily in cue use.
• If you want the physical size cue, then use estimated vocal-tract length in centimeters rather than a raw acoustic resonance measure, since VTL is the physical correlate that maps onto body height.

• Treating apparent height as if it tracks veridical height. The tell: you use `C_v`/`A_v` instead of the listener's reported `A`/`G`/`C`, and you ignore that listeners are often inaccurate but consistent in their errors.
• Modeling VTL's effect as a single fixed slope. The tell: your model can't reproduce the age-dependent use of VTL cues, and residuals split by apparent age.
• Confounding pitch and resonance in the size manipulation. The tell: you assume the 'big' resonance level changed f0 — it did not; the manipulation altered resonance only, mimicking a longer vocal tract.
• Ignoring between-listener idiosyncrasy by pooling all 4,170 observations into a single-level model. The tell: underestimated uncertainty and a fit that misses systematic within-listener patterns.
• Forgetting the unit conversion. The tell: implausible height magnitudes because responses were collected in feet and inches but analyzed as if already in centimeters.

• ▸Outcome: apparent height in cm (confirm feet/inches were converted)
• ▸Primary acoustic cue: estimated vocal-tract length `vtl` (cm)
• ▸Secondary acoustic cue: fundamental frequency `f0` (Hz)
• ▸Apparent age predictor `A` (a/c) — set as moderator of the VTL slope
• ▸Apparent gender predictor `G` (f/m) — expected positive shift for male, larger when adult
• ▸Random effects grouping: listener `L` (1–15) — include by-listener terms
• ▸Data structure check: long format, 4,170 rows = 15 listeners × 278 stimuli
• ▸Resonance condition `R` (a=actual, b=big) — verify pitch unchanged across levels
• ▸Research aim: quantify how acoustics map to apparent height and how apparent category modulates that mapping