The three engines at a glance | Setup | PCA: components from total variance | EFA: factors from common variance | How close are EFA and PCA loadings? | ESEM: EFA with full model diagnostics | Loading standard errors and confidence intervals | Per-level fit: what it tells you (and what it doesn't) | The key distinction | Reporting fit with tidy() and autoplot() | Should you care about fit in a bass-ackwards workflow? | How much do the edges differ? | Choosing an engine | Missing data | FIML for continuous PCA/EFA | Which option to use? | Correlation-matrix input | Constraints | suggest_k() with a correlation matrix | Performance with many items (ESEM) | References

k is a decision, not an output | The five criteria | PA-PC — Parallel Analysis (PC basis) | PA-FA — Parallel Analysis (FA basis) | MAP — Minimum Average Partial | VSS-1 and VSS-2 — Very Simple Structure | CD — Comparison Data | Summary table | Running suggest_k() | The diagnostic plot | Matching the criterion to your engine | The arguments | criteria — which criteria to compute | cor — correlation basis | n_iter — Monte Carlo iterations | seed — reproducibility | k_max — ceiling for the search | When the criteria agree — and when they don't | A worked recommendation for the BFI | References

Setup | Encoding sign and magnitude | sign_by — how direction is shown | magnitude_by — how |r| is shown | Filtering edges | cut_show — minimum |r| to display | Edge colors | color_pos / color_neg — custom direction colors | Monochrome mode | mono = TRUE — a black-and-white convenience wrapper | Correlation labels | show_r / r_digits — annotate edges with r values | Node labels | node_labels — rename individual factors | label_template() — generate the scaffold | Structural simplifications | primary_only = TRUE — show only primary-parent edges | Level labels | show_level_labels / level_label_size | Arrowheads | show_arrows = FALSE — plain line ends | Edge width | edge_linewidth — uniform vs. |r|-scaled width | Layout orientation | direction = "horizontal" — left-to-right layout | Legend | legend = FALSE — suppress all guides | Worked example: publication-ready figure | Saving plots | Diagnostic scree / criteria plot: autoplot.suggest_k() | References

Reading a factor with top_items() | Cross-loadings are signal | Showing item wording instead of codes | The sign convention: negative does not mean "low" | Naming in a hierarchy | Borrowing names for the upper levels | Applying your names | Making the names stick with set_factor_labels() | The Forbes letter convention | Starting from a blank slate | References

The problem: which factor solution is right? | Data | Step 1: How many factors? suggest_k() | Step 2: Fit the hierarchy ackwards() | Step 3: Summarize the result | High-level summary | Step 4: Visualize the hierarchy autoplot() | Adjusting the diagram | Step 5: Dig into the factors tidy() | Reading each factor — top_items() | Factor loadings (tidy) | Between-level edges | Variance explained | Step 6: Score observations augment() | Using scores for downstream analysis | Scoring new data (train/test) | Summary: the basic toolkit | Next steps | References

Why Pearson underestimates for ordinal items | The polychoric solution | Automatic detection | Seeing the difference | Correlation matrices | Loadings | Between-level edges | WLSMV for ESEM with ordinal items | Practical guidance: when to use polychoric | References

The problem: depth is where bass-ackwards analyses go wrong | Three verbs, three different questions | Setup | Step 1: Screen the plausible depth range with suggest_k() | Step 2: Gate the depth on replicability with comparability() | Step 3: Fit the hierarchy to the gated depth | Step 4: Find what perpetuates without differentiating — prune() | How sure are we about these edges? boot_edges() | Step 5: Interpret with the built-in guardrails | Step 6: Validate downstream, out of sample | Common mistakes this workflow prevents | Summary: the workflow in six calls | References

The data | Fitting the 10-level hierarchy | Skip-level structure | The redundancy chase | A chain, worked | Why the direct criterion matters here | The pruned-factor diagram | Fidelity | References

The limitation of adjacent-only edges | Setup | Computing every between-level correlation with pairs = "all" | Reading the skip-level edge table | Reading the strongest edge with care | Pruning: identifying redundant factors | Chains of near-identical factors with prune(x, "redundant") | The pruned-factor diagram | Inspecting structural similarity with prune(x, "artifact") | Structural artifact signals | Tuning the thresholds | Practical interpretation | References

1. What is axis reliability? | 2. A worked example | 3. Reading the components | 4. Caveats to keep in mind | 5. Wrap-up | References

Beyond the built-in plots | The circular canvas | The coordinate system | Moving the center | Moving the amplitude axis | Placing SSM results in the circle | Restyling the canvas | Composing custom layers | Trajectories across occasions | The same change as movement on the circle | The angle axis for linear plots | Relationship to the built-in plots | References

1. Two questions to ask before interpreting an SSM analysis | 2. Does the instrument fit a circumplex? | Fitting the circular process model | Reading the fit indices | Comparing model variants | 3. Can you trust your confidence intervals? | What Zimmermann & Wright (2017) found | Simulating coverage for your own analysis | When to trust SSM parameters | 4. Does the instrument have circumplex structure at all? | The five tests | Where the cutoffs come from | Reading the classifications | How this complements the CPM fit | 5. Ipsatization and what it costs | 6. Wrap-up | References

1. The question growth modeling answers | 2. From repeated measures to a coordinate table | 3. One joint model, not three separate ones | 4. From fixed effects to $(a(t), d(t))$ with intervals | 5. Certification: when $d(t)$ intervals are not interpretable | 6. A caution about REML intervals at small samples | 7. The unwrap alternative: angle_unwrap() | 8. Caveats and upgrades | References

1. Generalizing the basic analyses | Generalizing to multiple means | Generalizing to multiple measures | Generalizing to multiple groups and multiple measures | 2. Contrast analyses | Contrasts between groups' means | Contrasts between measures in a group | Contrasts between groups' correlations | 3. Taxonomy of analysis types | 4. Working with SSM tables | Basic customizations of tables | 5. Working with SSM figures | Exporting figures as files | Wrap-up | References

1. Background and Motivation | Circumplex models, scales, and data | The Structural Summary Method | Understanding the SSM parameters | 2. Example data: jz2017 | 3. Mean-based SSM Analysis | Conducting SSM for a group's mean scores | Visualizing the results with a table and figure | 4. Correlation-based SSM Analysis | Conducting SSM for a group's correlations with an external measure | 5. Wrap-up | References

1. Why a Bayesian SSM? | 2. The cosine model as a linear regression | 3. Fitting the model with brms | 4. From posterior draws to SSM summaries | 5. The induced prior on amplitude | 6. Where to go next

1. Why a latent SSM? | 2. The measurement model | 3. Estimating a latent profile | 4. Where the confidence intervals come from | 5. What the parameters mean now | 6. Two questions about group differences | 7. Invariance-gated latent contrasts | 8. When to trust it: limitations | 9. Relation to the literature | References

1. Overview of Instrument-related Functions | 2. Loading and Examining Instrument Objects | Previewing the available instruments | Loading a specific instrument | Examining an instrument in-depth | 3. Instrument-related Tidying Functions | Ipsatizing item-level data | Scoring item-level data | Standardizing scale-level data | 4. Wrap-up

Setup and Installation | Step-by-Step Guide | 1. Start the Server | 2. Finding and Managing Models | 3. Loading Models | 4. Chatting | 5. Teardown

Setup and Installation | Step-by-Step Guide | 1. Start the Background Daemon | 2. Start the Local Server | 3. Finding and Managing Models | 4. Loading Models | 5. Chatting | 6. Teardown and Cleanup | Bonus: Pipeline Automation