Mix-Shift Decomposition

business analytics

slug: topic-map-business-analytics-mix-shift-decomposition

Vocabulary:

• mix_effect: Change in total due to shifts in the composition of segments (volume moving between segments)
• rate_effect: Change in total due to segments becoming more/less productive (intensity change within segments)
• volume_effect: Change in total due to overall size increase/decrease (scale change)
• decomposition: Breaking a total change into additive components that explain the change
• shift_share_analysis: Technique for decomposing economic changes into structural vs performance components
• compositional_change: When the makeup of the population changes (more high-value customers)
• intensity_change: When behavior within segments changes (existing customers spend more)
• interaction_effect: The combined effect of mix and rate changing simultaneously
• base_period: The starting timeframe for comparison
• comparison_period: The ending timeframe being analyzed
• constant_mix: Hypothetical scenario where segment composition doesn't change
• constant_rate: Hypothetical scenario where segment rates don't change

Concepts:

• three_way_decomposition: Total change = Volume effect + Mix effect + Rate effect (+ Interaction)
• counterfactual_analysis: "What would have happened if only mix changed but not rate?"
• attribution_problem: Assigning credit for change to different causal factors
• mathematical_exactness: Components must sum precisely to total observed change
• strategic_implications: Mix changes suggest market shifts; rate changes suggest operational improvements
• controllability: Rate effects often more controllable than mix effects
• waterfall_bridge: Visual representation showing how each effect contributes to total change
• hierarchical_decomposition: Can decompose at each cube level independently

Concepts_advanced:

• laspeyres_vs_paasche: Different index formulas for decomposition (base-weighted vs current-weighted)
• fisher_ideal_index: Geometric mean of Laspeyres and Paasche to eliminate bias
• interaction_term: The portion of change that can't be cleanly attributed to pure mix or pure rate
• nested_decomposition: Decompose mix effect further into sub-dimensions

Procedures:

• identify_time_periods: Determine base and comparison periods from compareBy dimension
• extract_frequencies: Get segment sizes (freq column) for both periods
• extract_rates: Get segment rates (measure.mean or similar) for both periods
• calculate_total_change: Compare grand totals between periods
• calculate_volume_effect: (total_freq_change) × (base_overall_rate)
• calculate_mix_effect: Hold rate constant, vary composition
• calculate_rate_effect: Hold composition constant, vary rates
• calculate_interaction_effect: The residual not explained by pure mix or pure rate
• validate_reconciliation: Ensure components sum to total change
• rank_contributors: Which segments contributed most to each effect

Procedures_detailed:

• mix_effect_calculation: Σ[(new_freq - old_freq) × old_rate]
• rate_effect_calculation: Σ[(new_rate - old_rate) × old_freq]
• interaction_effect_calculation: Σ[(new_freq - old_freq) × (new_rate - old_rate)]
• percentage_attribution: Express each effect as % of total change

Topics:

• revenue_variance_analysis
• margin_bridge_analysis
• productivity_decomposition
• market_share_shift_analysis
• customer_value_migration
• pricing_vs_volume_tradeoffs
• channel_mix_optimization
• product_portfolio_evolution
• workforce_productivity_analysis
• cost_driver_decomposition

Categories:

• variance_analysis
• causal_decomposition
• change_attribution
• strategic_analytics
• performance_diagnosis

Themes:

• understanding_why: Moving beyond "what changed" to "why it changed"
• actionable_insights: Mix effects suggest different actions than rate effects
• strategic_vs_operational: Mix often reflects strategy; rate reflects operations
• complexity_reduction: Simplifying messy change into understandable components

Trends:

• automated_commentary: AI-generated narratives explaining decomposition results
• real_time_decomposition: Continuous monitoring of mix vs rate effects
• predictive_decomposition: Forecasting future mix/rate scenarios
• multi_period_waterfalls: Chaining decompositions across many periods
• interactive_what_if: Adjusting mix or rate assumptions to model scenarios

Use_cases:

• retail: "Revenue up 10%: +15% from rate effect (higher prices), -5% from mix effect (shift to lower-price categories)"
• saas: "MRR grew $50K: +$60K rate effect (upsells), -$10K mix effect (more small customers)"
• manufacturing: "Output up 8%: +12% volume effect (more units), -4% mix effect (shift to simpler products)"
• banking: "Deposits increased $5M: +$8M rate effect (higher balances per customer), -$3M mix effect (lost high-value customers)"
• healthcare: "Costs up 20%: +5% volume (more patients), +10% mix (sicker patients), +5% rate (more expensive treatments)"
• media: "Ad revenue down -$2M: -$5M mix effect (shift to lower-CPM inventory), +$3M rate effect (pricing improvements)"
• ecommerce: "AOV up $15: +$20 mix effect (more premium purchases), -$5 rate effect (increased discounting)"
• hospitality: "RevPAR up 12%: +8% rate effect (higher room rates), +4% mix effect (more suite bookings)"