Glossary
Short definitions + “what students usually confuse it with”.
A
Absolute fit
Fit measures that evaluate how well the model reproduces the observed covariance structure (e.g., χ², SRMR).
AIC / BIC
Information criteria for comparing models (typically non-nested too). Lower is better (with caveats).
C
CFA (Confirmatory Factor Analysis)
A measurement model where latent variables explain covariances among observed indicators via factor loadings.
CFI / TLI
Incremental fit indices comparing your model to a baseline (independence) model.
Cluster-robust standard errors
A correction to SEs/p-values when observations are clustered (e.g., students in classrooms) without explicitly fitting a multilevel model.
Configural / Metric / Scalar invariance
Levels of measurement invariance across groups/time: - configural: same pattern of loadings - metric: equal loadings - scalar: equal loadings + intercepts (or thresholds for ordinal)
D
DWLS / WLSMV
Common estimators for ordinal indicators. Naming can be confusing: the practical takeaway is that ordinal models often use a weighted least squares approach with robust corrections.
E
Equivalent models
Different path diagrams that imply the same covariance structure (same global fit). Fit alone cannot identify the “true” causal story.
EPC (Expected Parameter Change)
How much a parameter estimate would change if a fixed constraint were freed; often reported with modification indices.
F
FIML (Full Information Maximum Likelihood)
A likelihood-based approach to handle missing data under MAR assumptions (with ML-family estimators).
Fit indices (global)
Summaries of how well the overall model fits (CFI/TLI/RMSEA/SRMR/χ²).
Fit indices (local)
Diagnostics for specific parts of a model (residuals, MI/EPC, standardized residual covariances).
I
Identification
Whether model parameters can be uniquely estimated from the data (rules of thumb help, but do not guarantee identification).
Intercepts vs thresholds (ordinal)
- Intercepts: continuous indicator mean structure - Thresholds: cut-points that map a continuous latent response to ordinal categories
L
Latent variable
Unobserved construct inferred from observed indicators.
Latent interaction
An interaction between latent variables (e.g., F1 × F2 predicting Y). Estimation/interpretation differs from standard linear SEM.
M
Measurement model
The part of SEM that links indicators to latent factors (loadings, intercepts/thresholds, residual variances).
MI (Modification Index)
A statistic indicating how much χ² would drop if a fixed parameter were freed. Useful but easy to abuse.
Missingness (MCAR/MAR/MNAR)
Assumptions about why data are missing: - MCAR: unrelated to observed/unobserved variables - MAR: related to observed variables - MNAR: related to unobserved values themselves
R
RMSEA
A parsimony-adjusted fit index; usually reported with a confidence interval.
S
SAM (Structural After Measurement)
A two-stage estimation strategy: estimate measurement first, then structural relations using implied latent moments.
SEM (Structural Equation Model)
An integrated model including both measurement (latent variables) and structural relations (regressions/covariances among latents/observeds).
SRMR
A fit index based on standardized residuals (difference between observed and model-implied covariances/correlations).
T
Two-step mindset
A practical workflow: evaluate measurement quality before interpreting structural relations.
If you want to add to this glossary during the course, just make a PR / issue or send the term + how you’d define it.