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Metrics Guide

Self-Complexity Measurement Specification (v2.2)

A profile-based framework for quantifying identity structure. Living specification — cite the version you used.

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Overview

Everythingist Research Dashboard — Revised May 2026.

This document specifies all self-complexity metrics implemented in the Research Dashboard, including:

  • Legacy metrics (Scott, 1969; applied by Linville, 1985, 1987)
  • Component metrics (Rafaeli-Mor et al., 1999)
  • Composite metric (Sakaki, 2004)
  • Spatial/AST metrics (reconstructed from Schleicher & McConnell, 2005)
  • Connectivity and network metrics (novel)
  • Novel SSM extensions that formalize identity as a geometric-network system

Self-complexity is theoretically defined as a function of (1) the number of self-aspects and (2) the degree of independence vs. overlap among those aspects (Linville, 1985, 1987).

Version history (v2.2 and v1.0 changes)

Changes from v2.1

ChangeDetail
Primitives flaggedItem #6 (Aspect Centroid) and item #17's primitive #16 (per-attribute Bridge Load) now carry an explicit "computational primitive — not stored as a standalone field in scMetrics" footer. Reduces ambiguity for readers comparing the body's numbered concepts against the dashboard's stored fields.
K* ↔ validAspectCountCross-document notation note added: $K^*$ in this Specification corresponds to validAspectCount in the dashboard's scMetrics field.
Communities (Louvain partition)Item #20 (Modularity) gains a one-line acknowledgement that the dashboard exposes the Louvain community assignments $c_i$ as a diagnostic (scMetrics.communities), supporting network visualizations but not used as an SC metric.
Pilarska & Suchańska (2014)Now cited in Methodological Notes at the discussion of $H$'s psychometric limits, where it was already in the References list but uncited in the body.
Cross-check with Dashboard Specification v1.21This release coordinates with the v1.21 dashboard-spec patches that fixed the Sakaki SC formula (was incorrectly shown ε-stabilized), the singleton + null-propagation edge-case rows (was silent), and the 22-vs-21 metric count framing (was oversimplified). The dashboard spec now matches this Specification on all three points.

Changes from v1.0

ChangeDetail
Scott H (renamed)Formerly "Linville H." The $H$ statistic was created by Scott (1969); Linville adopted it. Display key: scottH.
OL citationNow cites Rafaeli-Mor et al. (1999, Appendix B) with Tversky (1977) asymmetry rationale.
Sakaki SCAttribution corrected to Sakaki (2004), who introduced the SC = K/OL composite. Components from Rafaeli-Mor et al. (1999).
Sakaki SC nullReturns null when OL = 0 (mathematically undefined). No epsilon-stabilized variant. Standard practice: exclude from analysis.
Singleton handling$W_k$ = null (not 0) when $|A_k| < 2$. Derived metrics propagate null. New tracking fields: singletonAspectCount, validAspectCount.
AST labelExplicitly labeled as "reconstructed operationalization" — not a canonical published formula.
Volume → DistributednessRenamed. Not a geometric volume; scales with $K$. Dashboard key: distributedness.
BalanceNormalized version is the only version. Raw removed. Dashboard key: balanceIndex.
Dashboard keysEvery metric now has an explicit dashboard key mapping and tooltip documentation.
ReferencesAdded Scott (1969), Sakaki (2004), Tversky (1977), Jaccard (1912), Newman (2006), Shannon (1948).

Data Structure and Conventions

Each participant provides:

  • $K$ self-aspects
  • A set of attributes/traits
  • Each aspect $A_k$ contains a subset of attributes
  • Attributes may appear in multiple aspects

Optional (for spatial metrics): attribute coordinates in $\mathbb{R}^d$.

Global Notation

  • $K$ = number of self-aspects
  • $K^*$ = number of valid aspects (≥2 attributes) — used for W-dependent metrics. Cross-document note: $K^*$ in this Specification corresponds to validAspectCount in the dashboard's scMetrics field; the count of singleton aspects ($K - K^*$) is exposed as singletonAspectCount.
  • $A_k$ = set of attributes in aspect $k$
  • $|A_k|$ = number of attributes in aspect $k$
  • $X$ = set of all unique attributes used across aspects
  • $|X|$ = number of unique attributes
  • $x_{ka}$ = coordinate vector for attribute $a$ in aspect $k$
  • $\mu_k$ = centroid of aspect $k$
  • $d(\cdot,\cdot)$ = distance metric (default: Euclidean)
  • $\epsilon = 10^{-6}$ (recommended stabilizer for denominators of W-dependent and distance-dependent metrics; not used for Sakaki SC, which returns null when OL = 0)

Singleton Aspect Handling — critical, new in v2

When $|A_k| < 2$:

  • $W_k$ = null (not 0)
  • Aspect is excluded from W-dependent metric computation
  • Track: singletonAspectCount, validAspectCount
  • If all aspects are singletons ($K^* = 0$) → W-dependent metrics return null

Rationale. Setting $W_k = 0$ for singletons artificially inflates Crystallization, IRI, Isolation Ratio, and AST ratios. Null propagation is the mathematically honest approach.

Affected metrics: Within Spread ($W$), AST SC, Crystallization, Isolation Ratio, IRI.

A. Quantity

Legacy metrics quantifying the count and dimensional spread of self-aspects.

1. Number of Self-Aspects (NSA)

A simple count of distinct self-aspects in a participant's mapping.

$$NSA = K$$

Inputs:

  • $K$ = total number of self-aspects

Dashboard key: nsa

Attribution: Linville, 1985.

In plain language

How many distinct "hats" you wear — e.g., professor, parent, athlete, musician. Each one is a self-aspect.

2. Scott H

Information-theoretic measure of dimensional differentiation in trait sorting.

$$H = \log_2(n) - \frac{\sum_i n_i \log_2(n_i)}{n}$$

Inputs:

  • $n$ = total number of attributes available for sorting
  • $n_i$ = number of attributes in unique group combination $i$

Attribution. The $H$ statistic was developed by Scott (1969) as a measure of the number of independent dimensions underlying a cognitive sorting. Linville (1985, 1987) adopted it as her primary operationalization of self-complexity. The field conventionally called it "Linville's H," but the mathematics are Scott's.

Dashboard key: scottH

Interpretation

  • Higher $H$ → more differentiation in sorting patterns.
  • Strongly influenced by number of selected traits.
  • Does not cleanly measure overlap or independence.
  • Poor internal consistency when valence is considered (Rafaeli-Mor et al., 1999).
  • Confounds number of aspects with overlap — the central critique motivating Rafaeli-Mor et al.'s component decomposition.

Notes

  • A group combination is the pattern of aspect membership for a trait.
  • Combinations with $n_i = 0$ are excluded.
In plain language

How differently you sort your traits across roles. If every role uses the same traits, $H$ is low. If each role draws from its own unique mix, $H$ is high. Think of it as measuring how varied your trait-sorting patterns are.

B. Overlap

Component metrics for trait redundancy across aspects (Rafaeli-Mor et al., 1999).

3. Overlap (OL) — directed formulation

Average asymmetric pairwise trait recycling across all ordered aspect pairs.

$$OL = \frac{\sum_i \left(\sum_j \frac{C_{ij}}{T_j}\right)}{K(K-1)}$$

Inputs:

  • $C_{ij}$ = number of shared attributes between aspects $i$ and $j$
  • $T_j$ = total attributes in the referent aspect $j$
  • $K$ = number of aspects
  • $i$ and $j$ vary from 1 to $K$ ($i \neq j$)
  • Division by zero: skip pair if $T_j = 0$

Attribution. Formalized by Rafaeli-Mor et al. (1999, Appendix B) as a standalone component metric. The directed (asymmetric) formulation follows Tversky (1977, p. 328): "similarity should not be treated as a symmetric relation." All ordered pairs $(i, j)$ where $i \neq j$ are evaluated, producing $K(K-1)$ comparisons (not $\binom{K}{2}$). Rafaeli-Mor et al. demonstrated that $OL$ has robust split-half reliability even under valence-based splitting ($\beta = .55\text{–}.56$), unlike Scott $H$ which drops to near-zero.

Dashboard key: overlapOL

Citation: Rafaeli-Mor et al., 1999; directed formulation per Tversky, 1977.

In plain language

How much your roles recycle the same traits. If "disciplined" shows up in every role you define, overlap is high. Low overlap means each role has its own distinctive character.

4. Pairwise Overlap (Jaccard, mean) — auxiliary

Symmetric pairwise overlap averaged across all aspect pairs, useful for visualization and SRI.

$$OL_{ij} = \frac{|A_i \cap A_j|}{|A_i \cup A_j|}$$
$$\bar{J} = \frac{2}{K(K-1)} \sum_{i<j} OL_{ij}$$

Interpretation

  • Higher values → more overlap → less independence.
  • Symmetric (unlike OL) — does not capture directional asymmetry.
  • Recommended for visualization, network edge weights, and SRI computation.

Dashboard key: meanJaccard

Citation: Jaccard, 1912; applied per Rafaeli-Mor et al., 1999.

In plain language

Of all the traits two roles use combined, what fraction do they share? If your professor-self and athlete-self together use 20 traits but only 2 appear in both, that's low overlap (0.10). This is measured for every pair of roles, then averaged.

C. Composite

Single-ratio composite that combines quantity and overlap into one index.

5. Sakaki Self-Complexity

Ratio composite SC = NSA / OL, undefined when overlap is zero.

$$SC = \frac{NSA}{OL}$$

Edge case. If $OL = 0$, $SC$ = null (undefined). Division by zero is mathematically undefined. Standard practice in the literature is to exclude participants with zero overlap from SC analysis. No epsilon-stabilized variant is provided. The v1 stabilized version ($SC_\epsilon = K / (OL + \epsilon)$) has been removed — it was an engineering convenience, not a methodological choice.

Attribution. The composite $SC = NASPECTS/OL$ was introduced by Sakaki (2004, p. 129), who cited Rafaeli-Mor et al. (1999) for the component measures. Importantly, Rafaeli-Mor et al. proposed studying NSA and OL as separate components and explicitly argued against collapsing them into a single index. Sakaki combined them into a ratio for use as a predictor of mood-incongruent recall.

Dashboard key: sakakiSC

Citation: Sakaki, 2004; components from Rafaeli-Mor et al., 1999.

In plain language

A ratio of how many roles you have to how much they overlap. Many roles with little recycling = high complexity. Few roles that all look the same = low complexity. Undefined when there is zero overlap (every role uses entirely unique traits).

D. Geometry (AST)

Spatial metrics built on distance between self-aspect centroids relative to within-aspect spread. These are a reconstructed operationalization based on Schleicher & McConnell (2005); they are not an exact reproduction of a published formula.

6. Aspect Centroid

The mean coordinate position of attributes within a given self-aspect.

$$\mu_k = \frac{1}{m_k} \sum_{a=1}^{m_k} x_{ka}$$

Inputs:

  • $m_k$ = number of attributes in aspect $k$
  • $x_{ka}$ = coordinate of attribute $a$

Computational primitive. Used internally to compute the spatial metrics in §D (B, B̄, W, AST SC, AST SC norm) and the Spillover Risk Index in §G (#19). Not stored as a standalone field in the dashboard's scMetrics.

In plain language

The "center of gravity" of a role — where it lives in trait-space. If your athlete-self is defined by "competitive," "driven," and "energetic," the centroid is the average position of those three traits.

7. Between-Aspect Separation (B)

Total pairwise distance between all aspect centroids.

$$B = \sum_{i<j} d(\mu_i, \mu_j)$$

Dashboard key: betweenSeparation

Citation: Reconstructed from Schleicher & McConnell, 2005.

In plain language

How far apart your roles are from each other overall. A professor-self and an athlete-self that use very different traits will be far apart; two roles built from similar traits will be close together. This sums all those distances.

8. Mean Separation (B̄)

Average pairwise distance between aspect centroids; comparable across different $K$.

$$\bar{B} = \frac{2}{K(K-1)} \sum_{i<j} d(\mu_i, \mu_j)$$

Dashboard key: meanSeparation

Citation: Reconstructed from Schleicher & McConnell, 2005.

In plain language

The average distance between any two roles. Same idea as total separation, but adjusted so it doesn't grow just because you have more roles.

9. Within-Aspect Spread (W)

Average internal dispersion of attributes within a self-aspect, then averaged across valid aspects.

$$W_k = \frac{1}{\binom{m_k}{2}} \sum_{a<b} d(x_{ka}, x_{kb})$$
$$W = \frac{1}{K^*} \sum_{k : |A_k| \geq 2} W_k$$

Critical (v2 change). If $|A_k| < 2$, $W_k$ = null (not 0). $K^*$ = count of valid aspects (those with ≥2 attributes). If $K^* = 0$, $W$ = null, and all W-dependent metrics return null.

Dashboard key: withinSpread

Additional keys: singletonAspectCount, validAspectCount

Citation: Reconstructed from Schleicher & McConnell, 2005.

In plain language

How diverse the traits within a single role are. A role defined by just "competitive" and "driven" is tight and focused. One spanning "creative," "anxious," "nurturing," and "bold" is spread out. $W$ is the average spread across all your roles. Singleton aspects (only 1 attribute) are excluded — they don't have enough data to compute internal spread.

10. AST Self-Complexity

Signal-to-noise ratio of total between-aspect separation to within-aspect spread.

$$SC_{AST} = \frac{B}{W + \epsilon}$$

Returns null when $W$ = null (all aspects are singletons).

Dashboard key: astSC

Citation: Reconstructed operationalization based on Schleicher & McConnell, 2005.

In plain language

Are your roles far apart relative to how spread out each one is internally? Think of it as signal-to-noise for identity separation. High values mean your roles are clearly distinct from one another; low values mean the differences between roles are small compared to the messiness within them.

11. Normalized AST Complexity

Same idea as AST SC, but using mean rather than total separation; comparable across different $K$.

$$SC_{AST}^{norm} = \frac{\bar{B}}{W + \epsilon}$$

Returns null when $W$ = null.

Dashboard key: astSCnorm

Citation: Reconstructed operationalization based on Schleicher & McConnell, 2005.

In plain language

Same idea as AST complexity, but using average (rather than total) separation. This makes the metric comparable across people who have different numbers of roles.

E. Structure

Derived structural metrics capturing coherence, scale, and independence of the identity system. Novel metrics developed by Sean P. Mullen, PhD, University of Illinois Urbana-Champaign.

12. Crystallization

Inverse of within-aspect spread; tighter aspects score higher.

$$Crystallization = \frac{1}{W + \epsilon}$$

Returns null when $W$ = null (all aspects are singletons).

Interpretation

  • High → internally coherent, tightly defined aspects.
  • Low → diffuse, loosely organized aspects.

Dashboard key: crystallization

Attribution: Novel — Mullen.

In plain language

How tightly defined your roles are. A person with crisp, clear-cut identities (narrow trait clusters) scores high. Someone whose roles feel fuzzy and amorphous — traits scattered everywhere — scores low.

13. Distributedness

Number of aspects scaled by mean separation; captures breadth of identity distribution.

$$D = K \cdot \bar{B}$$

Interpretation

  • Higher → expansive identity space (many, well-separated aspects).
  • Lower → constrained identity space.

Limitations

  • Not a true geometric "volume" — scales linearly with $K$.
  • Should not be interpreted as physical space.
  • Captures breadth of identity distribution that complexity indices ($H$, SC) do not isolate.

Dashboard key: distributedness

Attribution: Novel — Mullen.

In plain language

How much total "identity real estate" you occupy. Many well-separated roles = high distributedness, like rooms spread across a big house. Few overlapping roles = low distributedness, like everything crammed into one studio apartment.

14. Isolation Ratio

Mean separation between aspects scaled by within-aspect spread.

$$Isolation = \frac{\bar{B}}{W + \epsilon}$$

Returns null when $W$ = null.

Interpretation

  • High → aspects are far apart relative to their internal spread.
  • Low → aspects bleed into one another.

Dashboard key: isolationRatio

Attribution: Novel — Mullen.

In plain language

How independent your roles feel from one another. High means your work-self and your parent-self barely touch — what happens in one stays in one. Low means they blur together.

15. Identity Rigidity Index (IRI)

Mean of inverse within-aspect spreads across valid aspects; how locked-in each role's trait profile is.

$$IRI = \frac{1}{K^*} \sum_{k : |A_k| \geq 2} \frac{1}{W_k + \epsilon}$$

Returns null when $K^* = 0$ (all aspects are singletons). Singleton aspects excluded from summation.

Interpretation

  • High $IRI$ → tight, well-defined (rigid) aspects.
  • Low $IRI$ → diffuse, loosely defined aspects.

Limitations

  • Inflated by small within-aspect variance.
  • Sensitive to number of attributes per aspect.

Dashboard key: rigidityIndex

Attribution: Novel — Mullen.

In plain language

How locked-in each role is. Rigid roles have narrow, fixed trait profiles — you always describe your athlete-self with the exact same words. Flexible roles are loosely defined and might shift depending on context.

F. Connectivity

How attributes bridge across aspects, driving cross-identity spillover. Novel metrics developed by Sean P. Mullen, PhD, University of Illinois Urbana-Champaign.

16. Bridge Load (per attribute)

Number of aspects an individual attribute appears in.

$$BridgeLoad(x) = \sum_{k=1}^{K} \mathbf{1}(x \in A_k)$$

Computational primitive. Used internally to compute Mean Bridge Load (#17) and Proportion Shared Attributes (#18). Not stored as a standalone field in the dashboard's scMetrics. The dashboard does, however, expose the per-attribute Bridge Load values within the network visualization tooltips and aspect-attribute CSV export rows, so individual attribute connectivity is auditable downstream.

Attribution: Novel — Mullen.

In plain language

For a given trait, how many roles does it connect? "Empathy" appearing in your parent-self, therapist-self, and friend-self has a bridge load of 3. It's a bridge connecting three parts of your identity.

17. Mean Bridge Load (Bridge Centrality)

Average number of aspects spanned by each unique attribute.

$$BC_{mean} = \frac{1}{|X|} \sum_{x \in X} BridgeLoad(x)$$

Interpretation

  • High values → many cross-aspect connectors (greater spillover pathways).
  • Low values → more isolated aspects.

Limitations

  • Depends on attribute assignment process.
  • Sensitive to trait redundancy — identical words across aspects drive this up.

Dashboard key: meanBridgeLoad

Attribution: Novel — Mullen.

In plain language

On average, how many roles does each trait touch? If most of your traits only appear in one role, this is low. If your traits tend to show up across many roles, this is high — meaning there are lots of pathways for experiences in one role to ripple into others.

18. Proportion Shared Attributes

Fraction of unique attributes that appear in more than one aspect.

$$PropShared = \frac{|\{x \in X : BridgeLoad(x) > 1\}|}{|X|}$$

Dashboard key: propShared

Attribution: Novel — Mullen.

In plain language

What fraction of your traits show up in more than one role? If 15 out of 30 traits appear in multiple roles, PropShared = 0.50. High values mean your identity is highly interconnected; low values mean your roles are built from mostly unique traits.

G. Network

Metrics that treat the identity system as a graph, with aspects as nodes and attribute overlap as edges.

19. Spillover Risk Index (SRI)

Connection-weighted inverse distance, capturing how easily strain travels across aspects.

$$SRI = \frac{2}{K(K-1)} \sum_{i<j} \frac{w_{ij}}{d(\mu_i,\mu_j) + \epsilon}$$

Inputs:

  • $w_{ij}$ = connection strength between aspects $i$ and $j$

Recommended $w_{ij}$ (default: Jaccard overlap):

$$w_{ij} = \frac{|A_i \cap A_j|}{|A_i \cup A_j|}$$

Interpretation

  • High $SRI$ → high spillover risk (strong overlap + close proximity).
  • Low $SRI$ → compartmentalized, buffered structure.

Limitations

  • Sensitive to both overlap AND spatial distance.
  • May be unstable when distance ≈ 0.
  • Interpretation depends on embedding quality (the coordinate space used for attributes).

Dashboard key: spilloverRisk

Attribution: Novel — Mullen. Captures a risk dimension that pure overlap or pure distance metrics miss.

In plain language

If something bad happens in one role, how likely is it to bleed into others? This is driven by roles that share many traits and sit close together in trait-space. A bad day at work is more likely to ruin your evening at home if your work-self and parent-self share a lot of the same traits and feel closely connected.

20. Identity Modularity (Q)

Newman modularity over the weighted aspect-overlap graph; do roles form clean clusters?

Graph construction

  • Nodes = aspects
  • Edge weight = $w_{ij}$ (e.g., Jaccard overlap)

Let:

  • $A_{ij}$ = weighted adjacency matrix
  • $k_i = \sum_j A_{ij}$ (node strength)
  • $m = \frac{1}{2}\sum_{ij} A_{ij}$ (total edge weight)
  • $c_i$ = community assignment for node $i$ (via community detection)
  • $\delta(c_i, c_j)$ = 1 if same community, else 0
$$Q = \frac{1}{2m} \sum_{ij} \left( A_{ij} - \frac{k_i k_j}{2m} \right)\delta(c_i, c_j)$$

Interpretation

  • High $Q$ → well-separated identity modules.
  • Low $Q$ → entangled / blended identity structure.

Implementation notes

  • Use a weighted community detection algorithm (e.g., Louvain) to obtain $c_i$.
  • If $m = 0$ (no edges), set $Q = 0$ (no modular structure).
  • Resolution limit applies to very small networks ($K < 5$).
  • The Louvain community assignments $c_i$ are exposed in the dashboard as a diagnostic side-product (scMetrics.communities, an array of integer community labels indexed by aspect order). They support the network visualization (color-coding aspects by detected community) and the cohort-comparison aspect-overlap view, but they are not an SC metric in the academic sense and are not reported in the Interpretation Summary.

Dashboard key: modularity (with diagnostic side-product communities)

Citation: Newman, 2006 (modularity); Blondel et al., 2008 (Louvain community detection).

In plain language

Do your roles form natural clusters — like a "work cluster" (professor, researcher, mentor) and a "home cluster" (parent, partner, friend) — or is everything tangled together? High modularity means clean clusters with clear boundaries between them.

H. Distribution

How evenly the identity system allocates resources across aspects.

21. Identity Entropy

Shannon entropy over the proportional sizes of self-aspects.

Let:

$$p_k = \frac{|A_k|}{\sum_{j=1}^{K} |A_j|}$$

Then:

$$H_{identity} = -\sum_{k=1}^{K} p_k \log(p_k)$$

Interpretation

  • High entropy → evenly distributed identity composition.
  • Low entropy → dominance of one or a few aspects.

Normalized version

$$H_{norm} = \frac{H_{identity}}{\log(K)}$$

Range: 0–1. Use the normalized version for cross-participant comparison (raw entropy scales with $K$).

Dashboard keys: identityEntropy, identityEntropyNorm

Citation: Shannon, 1948 (information entropy).

In plain language

Are your roles evenly sized, or does one dominate? A person who's 90% "work-self" and 10% everything else has low entropy — most of their identity eggs are in one basket. Someone who invests equally across roles has high entropy, meaning a more balanced portfolio.

22. Balance Index (Normalized)

One minus the relative standard deviation of aspect sizes; approaches 1.0 at perfect equality.

Using $p_k$ from the entropy section:

$$Balance = 1 - \frac{\mathrm{std}(p_k)}{\mathrm{std}_{max}}$$

Where $\mathrm{std}_{max}$ is the maximum possible standard deviation for a $K$-category distribution.

Interpretation

  • High balance → evenly weighted identities (approaching 1.0 = perfect equality).
  • Low balance → dominance imbalance across aspects.

Notes. This is the normalized version. Not comparable across different $K$ without normalization — and this metric already includes it. The raw variant ($1 - \sigma$) has been removed.

Dashboard key: balanceIndex

Attribution: Novel — Mullen.

In plain language

Same intuition as entropy but measured differently: how equal is the "weight" you give to each role? If one role has 15 traits and the rest have 2 each, balance is low. If all roles are roughly the same size, balance is high.

Interpretation Summary

A compact lookup view across all 22 metrics, with dashboard keys, section, attribution, and plain-language gloss.

MetricKeySectionAttributionPlain language
NSAnsaALinville, 1985How many hats you wear
Scott HscottHAScott, 1969; Linville, 1985How differently you sort traits across roles
OLoverlapOLBRafaeli-Mor et al., 1999How much roles recycle the same traits
Mean JaccardmeanJaccardBJaccard, 1912Symmetric pairwise overlap
Sakaki SCsakakiSCCSakaki, 2004Many unique roles vs. few similar ones
BbetweenSeparationDSchleicher & McConnell, 2005*Total distance between all role pairs
B̄meanSeparationDSchleicher & McConnell, 2005*Average distance between role pairs
WwithinSpreadDSchleicher & McConnell, 2005*How diverse traits are within a role
SCASTastSCDSchleicher & McConnell, 2005*Signal-to-noise for identity separation
SCAST normastSCnormDSchleicher & McConnell, 2005*Normalized AST (cross-participant)
CrystallizationcrystallizationEMullen (novel)How tightly defined each role is
DistributednessdistributednessEMullen (novel)Total identity real estate
IsolationisolationRatioEMullen (novel)Do roles stay in their own lanes?
IRIrigidityIndexEMullen (novel)How locked-in each role's trait profile is
Bridge LoadmeanBridgeLoadFMullen (novel)How many roles a trait connects
Prop SharedpropSharedFMullen (novel)Fraction of traits in multiple roles
SRIspilloverRiskGMullen (novel)Likelihood a bad day bleeds across roles
ModularitymodularityGNewman, 2006Do roles form clean clusters?
EntropyidentityEntropyHShannon, 1948Are roles evenly sized?
Entropy (norm)identityEntropyNormHShannon, 1948Normalized evenness (0–1)
BalancebalanceIndexHMullen (novel)Equity of identity weighting

* Reconstructed operationalization, not canonical formula.

Methodological Notes

  • Self-complexity includes both number and independence of aspects.
  • The Scott $H$ statistic is widely used but psychometrically limited — it confounds NSA with OL (Rafaeli-Mor et al., 1999); see Pilarska & Suchańska (2014) for a comprehensive review of measurement issues across the past 30 years of self-complexity research.
  • Overlap and number should be analyzed separately (Rafaeli-Mor et al., 1999).
  • Spatial (AST) metrics better capture theoretical structure than $H$ alone.
  • Attribute sharing drives spillover across identities.
  • Default distance: Euclidean; alternatives (city-block) should be logged.
  • Guard denominators with $\epsilon$ only where explicitly noted — do NOT silently stabilize primary values (e.g., Sakaki SC returns null, not $K/\epsilon$).
  • For singleton aspects: $|A_k| < 2$ → set $W_k$ = null, exclude from W-dependent metrics, track singleton count.
  • Log-transform or z-score metrics for visualization if needed.
  • Report normalized versions for cross-participant comparison (Scott $H$, Entropy, Balance, AST norm).

Reporting Guidelines

When reporting results:

  • Do not collapse these into a single scalar index.
  • Present metrics as a profile organized by dimension (see below).
  • Emphasize that outcomes likely depend on interactions among dimensions.
  • Report singleton aspect counts and any null-returning metrics with sample sizes.
  • Note the Sakaki SC exclusion count when $OL = 0$.
  • QuantityNSA
  • OverlapOL, Jaccard
  • GeometryB, W, SCAST
  • StructureCrystallization, Distributedness, Isolation, IRI
  • ConnectivityBridge metrics, SRI
  • NetworkQ (Modularity)
  • DistributionEntropy, Balance

Companion Specifications

Related framework documents that extend or interface with this measurement specification.

Identity Strength Index (ISI) Multi-dimensional profile summarizing differentiation, coherence, balance, integration, commitment, and positivity. Salience Specification Salience weighting and per-aspect importance modeling used alongside the core metric set. Identity Archetypes Profile-based classification scheme that interprets metric combinations as recognizable identity structures.

How to Cite

This is a living specification. Always include the version number when citing.

Measurement specification

Mullen, S. P. (2026). Self-complexity measurement specification (Version 2.2). Self-Complexity Research Network. https://selfcomplexityresearch.org/docs/measurement.html

@misc{mullen2026scspec,
  author       = {Mullen, Sean P.},
  title        = {Self-Complexity Measurement Specification},
  year         = {2026},
  version      = {2.2},
  publisher    = {Self-Complexity Research Network},
  url          = {https://selfcomplexityresearch.org/docs/measurement.html}
}

Citing the platform

Mullen, S. P. (2026). Everythingist self-space platform and research dashboard. Self-Complexity Research Network. https://selfcomplexityresearch.org

Use the specification citation when discussing metrics or formulas. Use the platform citation when discussing the app and dashboard as tools or infrastructure.

Citation note

These metrics extend prior frameworks:

  • Scott (1969) — $H$ statistic (cognitive dimensionality)
  • Linville (1985, 1987) — foundational self-complexity theory and buffering hypothesis
  • Rafaeli-Mor et al. (1999) — component decomposition (NSA + OL), psychometric critique of $H$
  • Sakaki (2004) — composite $SC = K/OL$ formulation
  • Schleicher & McConnell (2005) — distance-based associated systems approach
  • McConnell (2011) — multiple self-aspects framework (networked self-concept)

The present metrics (Sections E–H) formalize identity as a geometric-network system, extending the spatial intuition of Schleicher & McConnell into structural, connectivity, and distributional dimensions. Novel metrics (Sections E–H) developed by Sean P. Mullen, PhD, University of Illinois Urbana-Champaign.

References

  1. Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008. https://doi.org/10.1088/1742-5468/2008/10/P10008
  2. Jaccard, P. (1912). The distribution of the flora in the alpine zone. New Phytologist, 11(2), 37–50. https://doi.org/10.1111/j.1469-8137.1912.tb05611.x
  3. Linville, P. W. (1985). Self-complexity and affective extremity: Don't put all of your eggs in one cognitive basket. Social Cognition, 3(1), 94–120. https://doi.org/10.1521/soco.1985.3.1.94
  4. Linville, P. W. (1987). Self-complexity as a cognitive buffer against stress-related illness and depression. Journal of Personality and Social Psychology, 52(4), 663–676. https://doi.org/10.1037/0022-3514.52.4.663
  5. McConnell, A. R. (2011). The multiple self-aspects framework: Self-concept representation and its implications. Personality and Social Psychology Review, 15(1), 3–27. https://doi.org/10.1177/1088868310371101
  6. Newman, M. E. J. (2006). Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103(23), 8577–8582. https://doi.org/10.1073/pnas.0601602103
  7. Pilarska, A., & Suchańska, A. (2014). Self-complexity and self-concept differentiation: What have we been measuring for the past 30 years? Current Psychology, 34, 723–743. https://doi.org/10.1007/s12144-014-9285-7
  8. Rafaeli-Mor, E., Gotlib, I. H., & Revelle, W. (1999). The meaning and measurement of self-complexity. Personality and Individual Differences, 27, 341–356. https://doi.org/10.1016/S0191-8869(98)00247-5
  9. Sakaki, M. (2004). Effects of self-complexity on mood-incongruent recall. Japanese Psychological Research, 46(2), 127–134. https://doi.org/10.1111/j.0021-5368.2004.00244.x
  10. Schleicher, D. J., & McConnell, A. R. (2005). The complexity of self-complexity: An associated systems theory approach. Social Cognition, 23(5), 387–416. https://doi.org/10.1521/soco.2005.23.5.387
  11. Scott, W. A. (1969). Structure of natural cognitions. Journal of Personality and Social Psychology, 12(4), 261–278. https://doi.org/10.1037/h0027734
  12. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  13. Tversky, A. (1977). Features of similarity. Psychological Review, 84(4), 327–352. https://doi.org/10.1037/0033-295X.84.4.327

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