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Positioning Analysis Lab

Brand Strategy PCA + Simulation

Build perceptual maps from brand/product ratings, visualize competitive positioning, overlay customer preferences, and simulate market share impacts of repositioning strategies.

πŸ‘¨β€πŸ« Professor Mode: Guided Learning Experience

New to perceptual mapping? Enable Professor Mode for step-by-step guidance through creating and interpreting multidimensional scaling maps!

OVERVIEW & OBJECTIVE

Positioning analysis helps marketers understand how brands are perceived relative to competitors and customer preferences. This tool uses Principal Components Analysis (PCA) to reduce attribute ratings into interpretable dimensions, combined with preference mapping and market share simulation.

πŸ“Š Key Concepts & When to Use

πŸ“Š Best For

  • Brand positioning strategy
  • Competitive landscape mapping
  • New product opportunity finding
  • Segment-targeted repositioning

⚠️ Limitations

  • Requires interval-scale ratings
  • Assumes linear relationships
  • Dimension interpretation is subjective
  • 2D maps may oversimplify

🎯 Output

  • Visual perceptual map
  • Dimension interpretations
  • Competitive distance matrix
  • Market share simulations

πŸ“ˆ Marketing Advantage

Unlike focus groups, perceptual maps provide quantitative evidence of where your brand standsβ€”and where to move it for maximum impact.

πŸ“˜ The Math: How It Works

🎯 The Big Picture

You have ratings of brands on many attributes (e.g., "sporty", "luxurious", "affordable"). This tool finds the hidden dimensions that explain most of the variation in those ratings, then plots brands on those dimensions so you can see competitive positioning at a glance.

πŸ’‘
Analogy: Imagine 20 attributes are really just different ways of measuring 2-3 underlying concepts (like "premium-ness" and "performance"). PCA discovers those concepts automatically.

πŸ“Š Step-by-Step Process

  1. Center the data β€” Each attribute is centered (mean = 0) so we focus on differences between brands, not absolute rating levels.
    $$x'_{ij} = x_{ij} - \bar{x}_j$$
    xij = rating of brand i on attribute j xΜ„j = mean rating across all brands for attribute j x'ij = centered rating (deviation from attribute mean)

    Optional: Enable "Standardize" in Advanced Settings to also divide by standard deviation (z-scores). This gives all attributes equal weight regardless of variance.

  2. Compute covariance matrix β€” Measures how attributes vary together across brands. High covariance? They're measuring the same underlying dimension.
    $$C = \frac{1}{n-1}X'^TX'$$
    X' = matrix of centered ratings (brands Γ— attributes) X'T = transpose of X' (attributes Γ— brands) n = number of brands C = covariance matrix (attributes Γ— attributes)
  3. Extract eigenvalues & eigenvectors β€” Solve for the vectors that, when multiplied by C, only get scaled (not rotated). These become the new dimension axes.
    $$C \mathbf{v}_k = \lambda_k \mathbf{v}_k$$
    vk = eigenvector for dimension k (defines the axis direction) Ξ»k = eigenvalue for dimension k (variance explained by that axis) Eigenvalues sorted largest β†’ smallest; first eigenvector = Dimension I
  4. Project brands onto dimensions β€” Multiply each brand's centered ratings by the eigenvectors to get its coordinates on the new axes.
    $$\text{score}_{ik} = \sum_{j=1}^{p} x'_{ij} \cdot v_{jk}$$
    scoreik = brand i's coordinate on dimension k x'ij = brand i's centered rating on attribute j vjk = weight of attribute j in dimension k p = number of attributes

πŸ“ˆ Key Outputs Explained

Variance Explained
How much of the original attribute variation this dimension captures. If Dim I explains 60% and Dim II explains 25%, those two dimensions capture 85% of the information.
Attribute Loadings
Correlations between original attributes and the new dimensions. A loading of +0.85 means that attribute strongly defines the positive end of that dimension.
Brand Coordinates
Where each brand sits on each dimension. Positive = high on attributes that load positively; negative = high on attributes that load negatively.

πŸš€ What You Can Do With This

  • Identify competitive clusters β€” Brands near each other are perceived similarly (direct competitors)
  • Find whitespace β€” Empty areas on the map = potential positioning opportunities
  • Understand differentiation β€” Distance between brands shows how distinct they are in customers' minds
  • Guide repositioning β€” See which attributes you'd need to change to move toward a target position
  • Segment targeting β€” With preference data, see which customer segments prefer which positions

πŸ”¬ Technical Notes

This tool uses Principal Components Analysis (PCA) on brand-attribute ratings. The correlation matrix approach is equivalent to PCA on standardized data. Eigendecomposition uses Jacobi rotation for numerical stability. The scree plot and Kaiser criterion (eigenvalue > 1) guide dimension selection.

πŸ“ A note on terminology: Marketers often call positioning maps "MDS" (Multidimensional Scaling), but true MDS requires pairwise similarity data as input. When working with attribute ratings (like this tool), the correct term is PCA. The confusion arose because both methods produce similar-looking 2D mapsβ€”but the inputs and math differ. If someone says "let's do MDS" with attribute data, they almost certainly mean PCA.

MARKETING SCENARIOS

Load a pre-built marketing scenario with perceptual and preference data to explore positioning analysis without uploading your own files. Scenarios include beer brands, smartphone manufacturers, streaming services, and more.

DATA INPUTS

1. Perceptual Data (Required)

Required

Upload a CSV with brands as columns and attributes as rows. Each cell contains the average rating of that brand on that attribute (e.g., 1-7 scale).

Drag & Drop Perceptual Data CSV

Rows = attributes, Columns = brands. Include a header row with brand names.

No file uploaded.

2. Preference Data (Optional)

Optional

Upload customer preference ratings for each brand. This enables ideal point mapping, segment analysis, and market share simulation.

Include preference data for simulation

3. Customer Weights (Optional)

Optional

Upload customer-level usage rate or spending data to weight market share calculations. This makes simulations more realistic by accounting for heavy vs. light users.

Include customer weights for market share

4. Analysis Settings

?

πŸ“ Number of Dimensions

How many principal components (axes) to use for visualizing your positioning map.

Automatic: Uses 2D if first two dimensions explain β‰₯80% of variance; otherwise uses 3D for a more complete picture.
2 dimensions: Simpler, easier to interpret. Best when two clear factors dominate (e.g., Quality vs. Price).
3 dimensions: Captures more nuance but harder to visualize. Use when three distinct factors matter.

πŸ’‘ Start with Automatic. Switch to 3D if your scree plot shows a meaningful third dimension.
?

🎯 Focal Brand

Select one brand to get deeper competitive intelligence and positioning recommendations.

What you get: Nearest competitors, positioning gaps, attribute strengths/weaknesses, and repositioning opportunities.
No focal brand: General market overview without brand-specific recommendations.

πŸ’‘ Choose your own brand (or main competitor) to get actionable strategic insights.
βš™οΈ Advanced Settings
?

πŸ“ Standardize Attributes

Controls whether to convert all attribute ratings to z-scores (mean=0, std=1) before computing the positioning map.

OFF (default): Uses covariance matrix. Attributes with naturally higher variance will have more influence on brand positions. Preserves the "importance" implied by rating spread.
ON: Uses correlation matrix. All attributes contribute equally regardless of their rating variance. Good when mixing different scales.

πŸ’‘ Keep OFF unless your data mixes different scales (1-7 and 1-100) or you specifically want equal attribute weighting.

PERCEPTUAL MAP

🏷️ Brands ?
🏷️ Brand Positions
Each dot represents a brand's perceived position based on customer ratings. Brands closer together are seen as more similar; brands far apart are perceived as distinct alternatives.
πŸ“ From Your Data
Loading insights...
πŸ“Š Attributes ?
πŸ“Š Attribute Vectors
Arrows showing which direction each attribute increases. Brands positioned toward an arrow's tip are rated higher on that attribute. Longer arrows explain more of the perceptual variance.
πŸ“ From Your Data
Loading insights...
πŸ”΅ Competitive Zones ?
πŸ”΅ Voronoi Competitive Zones
Voronoi tessellation showing each brand's "territory"β€”the region of the map where that brand is the closest option. Larger zones indicate less direct competition; smaller zones mean crowded positioning.
πŸ“ From Your Data
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✨ Entry Opportunities ?
✨ Market Entry Opportunities
Positions where a new entrant would capture the most market share, calculated using your preference model. Unlike simple "whitespace," these account for actual customer demandβ€”showing where segment preferences are underserved.
πŸ“ˆ Simulated Entry Analysis
Loading insights...
🎯 Click a brand for details β€’ Drag to simulate repositioning

πŸ” Key Discoveries

πŸ’‘

Run the analysis to discover insights about your competitive landscape.

🎚️ Dimension Explorer ORIGINAL ℹ️

Interactively explore what each dimension means. Click any brand chip to see details. Each row's height and variance bar show that dimension's explanatory power.

Loading... Dimension I Loading...
0% variance
Loading... Dimension II Loading...
0% variance

COMPETITIVE INTELLIGENCE

πŸ—ΊοΈ Competitive Distance Matrix ℹ️

This heatmap shows perceptual distances between all brand pairs. Dark blue = very similar (direct competitors), Light/white = very different (differentiated positioning).

πŸ“Š Brand Profile Comparison ORIGINAL

Select up to 3 brands to compare their attribute profiles side-by-side. The radar chart reveals where brands excel and where they're vulnerable.

πŸ“ˆ Attribute Importance ℹ️

Which attributes most differentiate brands in customers' minds? Longer bars = greater differentiation power. Hover over ℹ️ for details.

DIMENSION INTERPRETATION

Each dimension represents an underlying perceptual theme. Attributes with high positive or negative loadings define what the dimension means.

Dimension Variance Positive End (High) Negative End (Low) Interpretation
Run analysis to see dimension interpretations.

Brand Coordinates ORIGINAL

These coordinates define each brand's position on the perceptual map. Brands with similar coordinates are perceived similarly by customers. Use these values to identify direct competitors (close positions) and differentiated brands (distant positions).

Brand Dimension I Dimension II Dimension III
Run analysis to see brand coordinates.

Attribute Loadings

Attribute loadings show how strongly each attribute correlates with each dimension. High positive loadings (green) indicate the attribute increases along that dimension; high negative loadings (red) indicate the attribute decreases. Attributes near zero have little influence on that dimension.

View full attribute loading table
Attribute Dimension I Dimension II Dimension III
Run analysis to see attribute loadings.

SUMMARY REPORTS

APA-Style Report

After you run the positioning analysis, this panel will provide a formal statistical summary suitable for academic reports, including variance explained, dimensionality, and key findings.

Managerial Interpretation

This panel translates the positioning analysis into plain-language strategic insights, highlighting competitive positioning, segment opportunities, and recommended actions.

DIAGNOSTICS & ASSUMPTIONS

Diagnostics & assumptions

Key Assumptions

  • Linear relationships: PCA assumes that brand-attribute relationships are linear. Non-linear perceptions may require alternative techniques.
  • Interval-scale data: Perceptual ratings should be measured on interval scales (e.g., 1-7 Likert). Ordinal data may violate assumptions.
  • Adequate sample: Preference data should include enough customers per segment for stable ideal point estimates (typically 30+ per segment).

Interpretation Cautions

  • Perceptual maps show relative positionsβ€”absolute scale depends on input data normalization.
  • Dimension interpretations are subjective and should be validated with qualitative research.
  • Market share simulations assume current competitive dynamics remain stable.

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