Blog/Structural Analysis

Statistics

Structural Analysis

Factors, PCA, reliability, and SEM

SK

Skari Team

Skari

July 2026·13 min read

PCA

PCA finds the axes of greatest variance — the long arrow (PC1) captures most of the spread.

PC1PC2

Some of the most important things we measure can't be measured directly. Satisfaction, brand loyalty, anxiety, trust — none of these has a single column in your data. Instead you have a battery of survey items that each catch a piece of it. Structural analysis is the family that recovers the hidden construct from those pieces.

It answers questions the other families can't: how many underlying dimensions do these twenty items really measure? Do the items hang together well enough to trust? And how does one latent construct drive another? These are questions about structure — the machinery beneath the surface.

Note

The core idea is the latent variable — something real you can't observe directly, only infer from the pattern across many measured items. Structural analysis is how you find and validate it.

Finding the Dimensions: Factor Analysis and PCA

When many measured variables are correlated, they may be reflecting a smaller number of underlying factors. Factor analysis and PCA both compress correlated columns into a few dimensions — the axes of greatest shared variation, as the arrows above show — but with different intent.

MethodGoal
PCACompress variance into components — reduce dimensions
Exploratory factor analysis (EFA)Discover the latent factors behind the items
Confirmatory factor analysis (CFA)Test whether a proposed factor structure fits

PCA is the fast, linear default for compression; the PCA guide covers it in depth. Factor analysis goes further, positing that unseen factors cause the observed correlations.

Do the Items Hang Together? Reliability

Before you average ten items into a "satisfaction score," you have to know they measure the same thing. Reliability analysis checks that internal consistency.

  • Cronbach's alpha — the standard internal-consistency coefficient, from 0 to 1
  • Around 0.7 or above is usually considered acceptable
  • Item-level diagnostics show which question weakens the scale

Watch out

Averaging items into a scale without checking reliability is a leap of faith. A low alpha means the items don't cohere — the composite score is measuring noise as much as the construct.

How Constructs Relate: Mediation, Moderation, SEM

Once you have validated constructs, structural analysis models how they connect — not just whether A relates to B, but through what and under what conditions.

MethodQuestion it answers
MediationDoes A affect B through a mechanism M?
ModerationDoes the A→B effect change with a condition W?
Structural equation modeling (SEM)A whole network of constructs and paths at once

SEM ties it all together — latent factors, their reliability, and the paths between them — into a single model of how the constructs drive one another.

Scale First

Watch out

Factor analysis and PCA chase variance, so a variable in large units will dominate purely for being bigger. Standardize the items first, or the structure you recover tracks your units instead of your constructs.

Structural Analysis in the SKARI Statistical Lab

SKARI's Statistical Lab treats structural analysis as its own family — the tools for latent variables, from discovery to validation to path models.

  • Principal Component Analysis (PCA) and exploratory / confirmatory factor analysis
  • Reliability analysis with Cronbach's alpha and item-level diagnostics
  • Mediation and moderation analysis
  • Structural equation modeling (SEM) for construct networks
  • Standardization in the Data Editor so structure reflects constructs, not units

Takeaway

You go from a wall of correlated survey items to validated constructs and a model of how they relate — the difference between raw questionnaire data and a measured theory.

Frequently Asked Questions

PCA or factor analysis?

PCA to compress variance and reduce dimensions; factor analysis to model the latent factors that cause the observed correlations. Related math, different purpose.

What's a good Cronbach's alpha?

Around 0.7 or higher is commonly treated as acceptable, though it depends on the field and the stakes.

When do I need SEM?

When you have several latent constructs and want to test a whole network of relationships among them at once, rather than one pair at a time.

Key Takeaways

Finds

Factors

latent variables

Checks

Alpha

reliability

Models

Paths

SEM

First

Scale

standardize

Structural analysis recovers what you can't measure directly. Reduce correlated items to their underlying dimensions, confirm the scale is reliable, and model how the constructs relate — and a questionnaire becomes a validated measurement of something real.

Takeaway

When the thing you care about has no column, structural analysis builds it — from the pattern across the items that circle it.

PCA & Dimensionality Reduction

The compression workhorse

Data Normalization

The scaling structure depends on

Correlation ≠ Causation

Reading the relationships