vader-sentiment-analysis

name	vader-sentiment-analysis
description	Use when scoring sentiment in social media text, informal writing, or user-generated content using VADER, tracking affective trajectories over time, performing multi-tiered sentiment analysis across titles and body text, or needing lexicon-based polarity scoring that preserves capitalization and emoticon signals

VADER Sentiment Analysis

Overview

VADER (Valence Aware Dictionary and sEntiment Reasoner) is a lexicon-and-rule-based sentiment tool optimized for social media and informal text. It produces four scores per text: positive, negative, neutral (proportions summing to 1.0), and a compound score normalized to [-1, +1]. The core principle: VADER reads sentiment signals that traditional NLP preprocessing destroys -- capitalization for emphasis, punctuation for intensity, emoticons for affect -- so preprocessing must preserve these signals, not strip them.

Compound score normalization formula:

S_compound = sum(V_i) / sqrt(sum(V_i)^2 + alpha)

Where V_i are the valence scores of each token after rule-based adjustments (negation, degree modifiers, capitalization boost, punctuation amplification), and alpha = 15 is the normalization constant. This bounds the score to [-1, +1] with diminishing sensitivity at extremes.

When to Use

• Scoring sentiment in social media posts, comments, reviews, or informal text
• Need a fast, deterministic, no-training-required sentiment baseline
• Tracking how sentiment changes over time across a corpus (longitudinal trajectory analysis)
• Multi-tiered analysis: scoring titles separately from body text to detect emphasis mismatches
• Establishing a sentiment baseline before applying more complex models (transformer-based, LLM-based)
• Corpus contains emoticons, slang, capitalized emphasis, exclamation marks

When NOT to use:

• Formal, technical, legal, or financial text (domain-specific vocabulary skews scores)
• Text in languages other than English (VADER's lexicon is English-only)
• When sarcasm, irony, or complex negation are prevalent (VADER misreads these systematically)
• When you need aspect-level sentiment (sentiment toward specific entities/features within text)
• As sole evidence of psychological or emotional state (VADER measures lexical valence, not emotion)

digraph vader_decision {
    rankdir=TB;
    "Informal/social\nmedia text?" [shape=diamond];
    "English language?" [shape=diamond];
    "Sarcasm/irony\nprevailing?" [shape=diamond];
    "Use VADER" [shape=box];
    "Do NOT use VADER\n(use transformer model)" [shape=box];
    "Do NOT use VADER\n(no multilingual support)" [shape=box];
    "Use VADER with\nsarcasm caveat in report" [shape=box];

    "Informal/social\nmedia text?" -> "English language?" [label="yes"];
    "Informal/social\nmedia text?" -> "Do NOT use VADER\n(use transformer model)" [label="no, formal text"];
    "English language?" -> "Sarcasm/irony\nprevailing?" [label="yes"];
    "English language?" -> "Do NOT use VADER\n(no multilingual support)" [label="no"];
    "Sarcasm/irony\nprevailing?" -> "Use VADER with\nsarcasm caveat in report" [label="yes, some"];
    "Sarcasm/irony\nprevailing?" -> "Use VADER" [label="no"];
}

Quick Reference

Parameter / Concept	Value	Notes
Compound score range	[-1.0, +1.0]	Normalized sum of valence; most commonly used metric
Positive threshold	compound >= 0.05	Default from Hutto & Gilbert (2014); validate for your corpus
Negative threshold	compound <= -0.05	Default; may need tightening for skewed corpora
Neutral band	-0.05 < compound < 0.05	Often the largest category; do NOT ignore it
pos/neg/neu scores	[0.0, 1.0] each, sum to 1.0	Proportions of text falling in each category
Alpha constant	15	Normalization denominator constant in compound formula
Capitalization boost	~0.733 added to valence	ALL CAPS words get intensity amplification
Exclamation amplification	+0.292 per ! (up to 4)	Increases magnitude without changing polarity
Negation window	3 words	"not" negates the next 3 sentiment-bearing tokens
Degree modifiers	~25 booster/dampener words	"very", "extremely" (boost); "barely", "somewhat" (dampen)
Minimum text length	3+ words recommended	Single words produce valid but low-confidence scores
Recommended corpus minimum	100+ texts for aggregates	Below 50, aggregate statistics are unreliable

Workflow

Copy this checklist and track progress:

VADER Sentiment Analysis Progress:
- [ ] Step 1: Validate corpus suitability for VADER
- [ ] Step 2: Preprocess text (VADER-safe: preserve sentiment signals)
- [ ] Step 3: Score at multiple tiers (title, body, combined)
- [ ] Step 4: Calibrate thresholds for this corpus
- [ ] Step 5: Compute aggregate sentiment distributions
- [ ] Step 6: Longitudinal windowing and trajectory analysis
- [ ] Step 7: Identify stabilization, volatility, and inflection patterns
- [ ] Step 8: Write findings to docs/analysis/07-vader-sentiment-analysis.md

Step 1: Validate Corpus Suitability

Before scoring, verify VADER is appropriate for this corpus.

Suitability checks:

Check	Pass Condition	Fail Action
Language	All or nearly all English	VADER cannot score non-English. Remove or flag non-English texts.
Register	Informal, conversational, social media	If formal/technical, document the limitation prominently. VADER was calibrated on tweets, not journals.
Text length	Average 10+ words per text unit	If most texts are 1-3 words, scores are valid but low-confidence. Flag in report.
Corpus size	50+ texts for aggregates, 100+ preferred	Below 50, do not compute aggregate distributions. Report individual scores only.
Sarcasm prevalence	Not the dominant mode	If corpus is heavily sarcastic (e.g., satire subreddits), VADER will systematically invert polarity. Document this.

If corpus fails suitability: Report the failure in the output document. Do not force VADER onto inappropriate text. State what was checked, what failed, and recommend alternatives (TextBlob, transformer models, manual annotation).

Step 2: Preprocess Text -- Preserve Sentiment Signals

CRITICAL: VADER's preprocessing requirements are the OPPOSITE of most NLP pipelines.

DO preserve (VADER uses these):

• CAPITALIZATION -- "GREAT" scores higher than "great" (intensity boost ~0.733)
• Punctuation -- "Good!!!" scores higher than "Good" (exclamation amplification)
• Emoticons/emoji -- :) has valence +2.2, :( has valence -2.2 in the lexicon
• Degree modifiers -- "very", "extremely", "barely" modify adjacent word valence
• Negation words -- "not", "never", "neither" flip polarity within a 3-word window
• Contractions -- "isn't", "won't", "can't" contain negation signals

DO remove (noise that does not carry sentiment):

• URLs (replace with empty string, not a token)
• User mentions/handles (@username)
• HTML entities and markup tags
• Hashtag symbols (remove # but KEEP the word: #amazing becomes amazing)
• Repeated whitespace (normalize to single spaces)

import re
from nltk.sentiment.vader import SentimentIntensityAnalyzer

def vader_safe_preprocess(text):
    """Clean text for VADER while preserving sentiment signals.
    DO NOT lowercase. DO NOT strip punctuation. DO NOT remove emoticons."""
    text = re.sub(r'https?://\S+|www\.\S+', '', text)  # Remove URLs
    text = re.sub(r'@\w+', '', text)                     # Remove @mentions
    text = re.sub(r'<[^>]+>', '', text)                   # Remove HTML tags
    text = re.sub(r'&\w+;', '', text)                     # Remove HTML entities
    text = re.sub(r'#(\w+)', r'\1', text)                 # Keep hashtag words
    text = re.sub(r'\s+', ' ', text).strip()              # Normalize whitespace
    return text

# WRONG: Do not do this
# text = text.lower()           # Destroys capitalization signals
# text = re.sub(r'[^\w\s]', '', text)  # Destroys emoticons and punctuation

Step 3: Score at Multiple Tiers

Score titles and body text separately. Titles carry concentrated sentiment (short, emphatic); body text carries diluted sentiment (longer, mixed). Combining them without separation loses this signal.

sia = SentimentIntensityAnalyzer()

def score_multi_tier(record):
    """Score title and body separately, then compute weighted combined."""
    title_text = vader_safe_preprocess(record.get('title', '') or '')
    body_text = vader_safe_preprocess(record.get('body', '') or '')

    title_scores = sia.polarity_scores(title_text) if title_text else None
    body_scores = sia.polarity_scores(body_text) if body_text else None

    # Weighted combination: title gets higher weight per-word
    # because titles are deliberately composed summaries
    combined = None
    if title_scores and body_scores:
        # Weight by inverse length (shorter = more concentrated sentiment)
        t_len = max(len(title_text.split()), 1)
        b_len = max(len(body_text.split()), 1)
        t_weight = 1.0 / t_len
        b_weight = 1.0 / b_len
        total_weight = t_weight + b_weight
        combined = {
            key: (title_scores[key] * t_weight + body_scores[key] * b_weight) / total_weight
            for key in ('neg', 'neu', 'pos', 'compound')
        }
    elif title_scores:
        combined = title_scores
    elif body_scores:
        combined = body_scores

    return {
        'title_compound': title_scores['compound'] if title_scores else None,
        'body_compound': body_scores['compound'] if body_scores else None,
        'combined_compound': combined['compound'] if combined else None,
        'title_scores': title_scores,
        'body_scores': body_scores,
    }

Tier mismatch detection: When title compound and body compound have opposite signs (one positive, one negative), flag the record as a "sentiment mismatch." These are often the most analytically interesting cases (e.g., sarcastic titles with earnest bodies, clickbait titles with nuanced content).

Step 4: Calibrate Thresholds

The default thresholds (0.05 / -0.05) were calibrated on a general social media corpus. Your corpus may need different cutoffs.

Calibration procedure:

1. Score the full corpus with default thresholds
2. Manually review 20-30 texts near each boundary (compound between -0.1 and 0.1)
3. Count misclassifications: texts labeled neutral that clearly have sentiment, or vice versa
4. Adjust thresholds to minimize boundary misclassification
5. Document the chosen thresholds and the calibration sample size

# Example: Tighter thresholds for a corpus with strong sentiment signals
POSITIVE_THRESHOLD = 0.10   # Raised from 0.05
NEGATIVE_THRESHOLD = -0.10  # Lowered from -0.05

def classify_sentiment(compound, pos_thresh=POSITIVE_THRESHOLD, neg_thresh=NEGATIVE_THRESHOLD):
    if compound >= pos_thresh:
        return 'positive'
    elif compound <= neg_thresh:
        return 'negative'
    else:
        return 'neutral'

If you skip calibration: Use the defaults (0.05 / -0.05) but document that thresholds were NOT validated for this corpus. This is acceptable for exploratory analysis, not for claims about sentiment distribution.

Step 5: Compute Aggregate Distributions

import pandas as pd
import numpy as np

def compute_aggregates(scores_df):
    """Compute corpus-level sentiment statistics."""
    compound = scores_df['combined_compound'].dropna()

    return {
        'total_scored': len(compound),
        'mean_compound': compound.mean(),
        'median_compound': compound.median(),
        'std_compound': compound.std(),
        'skewness': compound.skew(),
        'pct_positive': (compound >= POSITIVE_THRESHOLD).mean() * 100,
        'pct_negative': (compound <= NEGATIVE_THRESHOLD).mean() * 100,
        'pct_neutral': ((compound > NEGATIVE_THRESHOLD) & (compound < POSITIVE_THRESHOLD)).mean() * 100,
        'mean_positive_intensity': compound[compound >= POSITIVE_THRESHOLD].mean() if (compound >= POSITIVE_THRESHOLD).any() else None,
        'mean_negative_intensity': compound[compound <= NEGATIVE_THRESHOLD].mean() if (compound <= NEGATIVE_THRESHOLD).any() else None,
    }

Interpreting aggregate distributions:

• High neutral percentage (>60%): Normal for most corpora. Do NOT treat this as "VADER failed." Neutral is information, not absence of signal.
• Positive skew (mean > median): A few strongly positive texts pull the mean up. Report median as the more robust central tendency.
• Bimodal distribution: Corpus may contain two distinct populations (e.g., supportive vs. critical communities). Consider segmenting before aggregation.

Step 6: Longitudinal Windowing and Trajectory Analysis

To track sentiment over time, aggregate scores into temporal windows.

Window selection:

Corpus Timespan	Recommended Window	Min Texts per Window
Days to 1 week	Hourly	5+
1 week to 3 months	Daily	10+
3 months to 2 years	Weekly	20+
2+ years	Monthly	30+

def compute_temporal_trajectory(scores_df, date_column, window='W'):
    """Compute rolling sentiment trajectory.
    window: 'D' (daily), 'W' (weekly), 'M' (monthly), 'H' (hourly)"""
    df = scores_df.copy()
    df[date_column] = pd.to_datetime(df[date_column])
    df = df.set_index(date_column).sort_index()

    trajectory = df['combined_compound'].resample(window).agg([
        'mean', 'median', 'std', 'count'
    ]).rename(columns={
        'mean': 'sentiment_mean',
        'median': 'sentiment_median',
        'std': 'sentiment_volatility',
        'count': 'text_count',
    })

    # Drop windows with insufficient texts
    min_texts = 5
    trajectory = trajectory[trajectory['text_count'] >= min_texts]

    # Compute rolling smoothed trajectory (3-window moving average)
    trajectory['smoothed_mean'] = trajectory['sentiment_mean'].rolling(
        window=3, min_periods=2, center=True
    ).mean()

    return trajectory

If corpus lacks temporal metadata: Report that longitudinal analysis is not possible. Compute static aggregate distributions only. Do NOT fabricate temporal ordering from file position or row index.

Step 7: Identify Stabilization, Volatility, and Inflection Patterns

Pattern definitions:

Pattern	Detection Method	Interpretation
Stabilization	Volatility (std) decreasing over 3+ consecutive windows	Sentiment is converging; opinions are settling
Volatility spike	Window std > 2x the corpus-wide median std	Mixed reactions within the window; polarizing content or event
Positive inflection	3+ consecutive windows of increasing smoothed mean	Upward sentiment shift
Negative inflection	3+ consecutive windows of decreasing smoothed mean	Downward sentiment shift
Sentiment plateau	Smoothed mean varies < 0.05 over 5+ windows	Stable affective state; no significant change
Polarity reversal	Smoothed mean crosses zero	Shift from net-positive to net-negative or vice versa

def detect_patterns(trajectory):
    """Detect sentiment trajectory patterns."""
    patterns = []
    sm = trajectory['smoothed_mean'].values
    vol = trajectory['sentiment_volatility'].values
    median_vol = np.nanmedian(vol)

    for i in range(2, len(sm)):
        # Volatility spikes
        if vol[i] > 2 * median_vol:
            patterns.append({
                'type': 'volatility_spike',
                'window_index': i,
                'volatility': vol[i],
                'threshold': 2 * median_vol,
            })

        # Positive inflection (3 consecutive increases)
        if i >= 2 and sm[i] > sm[i-1] > sm[i-2]:
            patterns.append({
                'type': 'positive_inflection',
                'window_index': i,
                'values': [sm[i-2], sm[i-1], sm[i]],
            })

        # Negative inflection (3 consecutive decreases)
        if i >= 2 and sm[i] < sm[i-1] < sm[i-2]:
            patterns.append({
                'type': 'negative_inflection',
                'window_index': i,
                'values': [sm[i-2], sm[i-1], sm[i]],
            })

        # Polarity reversal
        if i >= 1 and sm[i] * sm[i-1] < 0:
            patterns.append({
                'type': 'polarity_reversal',
                'window_index': i,
                'from_value': sm[i-1],
                'to_value': sm[i],
            })

    return patterns

Step 8: Write Report

Write all findings to docs/analysis/07-vader-sentiment-analysis.md.

Report Output Template

The final report MUST be written to docs/analysis/07-vader-sentiment-analysis.md with this structure:

# VADER Sentiment Analysis

## Methodology
- **Tool:** VADER (Valence Aware Dictionary and sEntiment Reasoner) via NLTK
- **Corpus:** [N texts scored, average text length, date range if temporal]
- **Preprocessing:** VADER-safe (preserved capitalization, punctuation, emoticons; removed URLs, mentions, HTML)
- **Tiers scored:** [title / body / combined -- list which were available]
- **Thresholds:** positive >= [X], negative <= [Y] [calibrated / default]
- **Temporal window:** [window size, minimum texts per window] (if longitudinal)

## Corpus Suitability Assessment
- Language: [English / mixed -- percentage]
- Register: [informal / formal / mixed]
- Average text length: [N words]
- Sarcasm/irony prevalence: [low / moderate / high -- impact on reliability]
- **Overall suitability:** [suitable / suitable with caveats / unsuitable]

## Aggregate Sentiment Distribution

| Metric | Value |
|--------|-------|
| Texts scored | [N] |
| Mean compound | [X.XXX] |
| Median compound | [X.XXX] |
| Std deviation | [X.XXX] |
| Skewness | [X.XXX] |
| % Positive | [X.X%] |
| % Negative | [X.X%] |
| % Neutral | [X.X%] |
| Mean positive intensity | [X.XXX] |
| Mean negative intensity | [X.XXX] |

## Multi-Tier Analysis

### Title Sentiment
[Distribution statistics for titles]

### Body Sentiment
[Distribution statistics for body text]

### Tier Comparison
- Correlation between title and body compound: [r = X.XX]
- Sentiment mismatch count: [N texts with opposite-sign title vs. body]
- [Interpretation of mismatches]

## Longitudinal Trajectory (if temporal data available)

### Trajectory Summary
[Table: window, mean, median, volatility, text count]

### Detected Patterns
- Volatility spikes: [N detected, windows where they occurred]
- Positive inflections: [N detected, windows]
- Negative inflections: [N detected, windows]
- Polarity reversals: [N detected, windows]
- Stabilization periods: [windows]
- Plateau periods: [windows]

### Trajectory Interpretation
[Narrative synthesis of the affective trajectory -- what the patterns mean in context]

## Limitations and Caveats
- VADER is lexicon-based and does not understand context, sarcasm, or irony
- Compound scores are NOT probabilities -- they are normalized valence sums
- [Corpus-specific limitations identified in Step 1]
- [Threshold calibration status -- calibrated or default]
- [Any texts excluded and why]
- Results should be cross-validated with a second method (transformer model, manual review) before drawing conclusions

## References
- Hutto, C.J. & Gilbert, E.E. (2014). VADER: A Parsimonious Rule-based Model for Sentiment Analysis of Social Media Text. ICWSM.
- [Additional references as applicable]

Good Patterns

• Preserve capitalization and punctuation before VADER scoring -- these are sentiment signals, not noise
• Score titles and body text separately -- titles carry concentrated, intentional sentiment; bodies carry diluted, complex sentiment
• Calibrate thresholds on your corpus -- the defaults (0.05) were for a general social media dataset, not yours
• Report neutral percentages -- high neutral rates are normal and informative, not a failure
• Use temporal windowing for longitudinal analysis -- raw per-text scores over time are noisy; windowed aggregates reveal trajectory
• Document the compound score formula -- readers need to understand that compound is a normalized sum, not a probability
• Cross-validate with a second method -- VADER as baseline, transformer or manual review as validation

Anti-Patterns

Anti-Pattern	Why It Fails	Instead
Lowercasing text before VADER	Destroys capitalization intensity boost (~0.733 per ALL CAPS word)	Pass original-case text to VADER
Stripping punctuation before VADER	Destroys exclamation amplification (+0.292 per !)	Remove only non-sentiment punctuation (URLs, HTML)
Using default thresholds without validation	0.05 was calibrated on general tweets; your corpus may have different neutral bands	Manually review 20-30 boundary cases; adjust thresholds
Ignoring neutral scores	Neutral is often 40-70% of a corpus; ignoring it misrepresents the distribution	Report neutral percentage and interpret it as genuine signal
Treating compound as probability	Compound is a normalized valence sum, not P(positive). 0.85 does not mean 85% likely positive	Describe compound as "sentiment intensity" not "sentiment probability"
Applying VADER to formal/technical text without caveat	VADER was calibrated on informal text; technical jargon gets arbitrary scores	Document the domain mismatch; supplement with domain-tuned tools
Averaging compound scores without windowing	Raw chronological averages are noisy and misleading	Aggregate into temporal windows with minimum text counts
Claiming VADER detects emotion or psychological state	VADER measures lexical valence, not internal states	Use "sentiment polarity" and "valence intensity," never "emotion" or "feeling"
Ignoring sarcasm/irony limitations	"Oh great, another update that breaks everything" scores positive	Flag sarcasm-prone content; note systematic misclassification risk

Boundaries

This skill SHOULD produce:

• Multi-tiered sentiment scores (title, body, combined compound)
• Calibrated threshold classifications (positive / negative / neutral)
• Aggregate distribution statistics with neutral percentage
• Longitudinal sentiment trajectory with temporal windowing (if timestamps available)
• Pattern detection: stabilization, volatility, inflection, plateau, polarity reversal
• Written report at docs/analysis/07-vader-sentiment-analysis.md

This skill should NOT:

• Claim VADER captures nuanced emotion, sarcasm, or irony (it does not)
• Use compound scores as sole evidence of psychological or emotional state
• Apply VADER to non-English text without flagging the limitation
• Skip preprocessing validation (a single text.lower() upstream destroys the analysis)
• Treat a single threshold set as universally valid across corpora
• Ignore the neutral category or treat it as "no data"
• Draw causal conclusions from sentiment trajectories (correlation in time is not causation)

Insufficient Data Handling

digraph insufficient_data {
    rankdir=TB;
    node [shape=diamond, style=filled, fillcolor="#f0f0f0"];

    start [label="Corpus size?", shape=diamond];
    tiny [label="< 30 texts", shape=box, fillcolor="#ffcccc"];
    small [label="30-49 texts", shape=box, fillcolor="#fff3cc"];
    adequate [label="50-99 texts", shape=box, fillcolor="#ffffcc"];
    good [label="100+ texts", shape=box, fillcolor="#ccffcc"];

    start -> tiny [label="< 30"];
    start -> small [label="30-49"];
    start -> adequate [label="50-99"];
    start -> good [label="100+"];

    tiny_action [label="Score individually.\nDo NOT compute aggregates.\nReport individual scores only.", shape=box, fillcolor="#ffcccc"];
    small_action [label="Compute aggregates\nwith LOW CONFIDENCE flag.\nSkip longitudinal analysis.", shape=box, fillcolor="#fff3cc"];
    adequate_action [label="Full aggregates.\nLongitudinal only if 5+\ntexts per window.", shape=box, fillcolor="#ffffcc"];
    good_action [label="Full analysis pipeline.\nAll features available.", shape=box, fillcolor="#ccffcc"];

    tiny -> tiny_action;
    small -> small_action;
    adequate -> adequate_action;
    good -> good_action;
}

Condition	Action
Corpus < 30 texts	Score individual texts. Do NOT compute aggregate distributions (mean, std, percentages are not meaningful). Report individual scores in a table.
Corpus 30-49 texts	Compute aggregates but flag every statistic as "low confidence, N < 50." Skip longitudinal trajectory analysis.
Corpus 50-99 texts	Full aggregate analysis. Longitudinal analysis only if at least 5 texts fall in each temporal window.
Corpus 100+ texts	Full analysis pipeline including longitudinal trajectory, pattern detection, and tier comparison.
Most texts are 1-3 words	VADER will produce scores, but they reflect single-word lexicon lookups, not sentence-level analysis. Flag: "scores reflect individual word valence, not compositional sentiment."
No temporal metadata	Skip Steps 6-7 entirely. Report static aggregates only. Document that longitudinal analysis was not possible.
>60% neutral scores	This is NORMAL, not a failure. Report the neutral percentage. Analyze the distribution of the non-neutral minority. Consider whether the neutral band is too wide (calibrate thresholds).
All scores near zero	The corpus may genuinely lack strong sentiment (factual/informational content). Document this finding. Do not widen thresholds to manufacture sentiment.
Tier data missing (no titles, or no body)	Score available tiers only. Do not fabricate missing tiers. Note which tiers were unavailable in the report.

Common Mistakes

Mistake	Fix
Running text.lower() before VADER	Remove lowercasing from preprocessing. VADER needs original case.
Reporting only positive/negative percentages	Always include neutral percentage. It is usually the largest category.
Using compound score as a probability	Describe it as "normalized valence intensity" in reports. Never use "likelihood" or "probability."
Skipping threshold calibration	Review 20-30 boundary texts manually. Adjust if misclassification rate > 20%.
Ignoring title/body differences	Score separately. Titles are short and emphatic; bodies are long and mixed.
Aggregating without temporal windowing	Raw chronological scores are too noisy. Use windowed aggregation with minimum text counts.
Claiming VADER "detected anger/joy/fear"	VADER detects positive/negative/neutral valence, not discrete emotions. Use valence vocabulary.
Not documenting VADER version/library	Report whether using vaderSentiment package or nltk.sentiment.vader. Lexicons differ slightly.
Applying to sarcastic corpus without caveat	VADER reads "Oh great, another failure" as positive. Flag sarcasm risk in limitations.
Computing trajectory on < 5 texts per window	Aggregate statistics on tiny windows are noise. Enforce minimum text counts per window.

References

• VADER: A Parsimonious Rule-based Model for Sentiment Analysis of Social Media Text (Hutto & Gilbert, 2014) -- Original VADER paper with lexicon construction and validation methodology
• vaderSentiment GitHub Repository -- Official Python implementation with 7,500+ lexical features
• NLTK VADER Module -- NLTK implementation reference
• Tracking Sentiment by Time Series Analysis (ACM SIGIR 2016) -- Sentiment velocity and acceleration for temporal tracking
• Longitudinal Sentiment Analysis with Conversation Textual Data (Fudan J. Humanities, 2024) -- Growth curve models for longitudinal textual sentiment
• Analysis of Customer Reviews with Improved VADER (J. Big Data, 2023) -- Domain-specific VADER lexicon extensions