Scale, Dimension Reduction & Classify

Three menu groups for multivariate work: assessing a set of items as a scale, reducing many variables to a few, and grouping or classifying cases.

Scale → Reliability Analysis

When to use it. To check whether a set of items (e.g. questionnaire questions) measure one underlying construct consistently.

Dialog. Move the item variables into the list.

Output. Cronbach's alpha for the scale, plus item-total statistics — how each item correlates with the rest and what alpha would become if the item were dropped. Low item-total correlation flags an item that does not belong.

Scale → Intraclass Correlation

When to use it. To measure the reliability or agreement of ratings when several raters score the same subjects (inter-rater reliability), or one measure is repeated (test-retest). The data are a wide layout: one column per rater, one row per subject.

Dialog. Move the rater columns into the Raters list and pick a confidence interval level (95% by default).

Output. A table of the six Shrout & Fleiss ICC forms, each with its confidence interval, F test and significance, plus the ANOVA mean squares they are built from. Pick the form from your design:

• One-way vs two-way — one-way if each subject is rated by a different random set of raters; two-way if the same raters score every subject.
• Absolute agreement vs consistency — agreement if the raters' actual values must match; consistency if a constant offset between raters is acceptable.
• Single vs average measures — single if one rater's score will be used; average if you will use the mean of all raters.

ICC reuses the two-way variance decomposition of the repeated-measures ANOVA. Values near 1 mean highly reliable ratings; near 0, no better than chance.

Dimension Reduction → Factor

When to use it. To find a small number of latent factors behind many correlated variables. (Testing a structure you already hypothesize is the complementary procedure — see Confirmatory Factor Analysis.)

Dialog. Move the variables in. In Options choose:

• Extraction — principal components (default), principal-axis factoring, or exact-discrepancy maximum likelihood;
• Rotation — none, Varimax (orthogonal) or Promax (oblique);
• Scree plot — on by default, the eigenvalues as a marked line with the Kaiser criterion line at 1 (the classic pick-the-elbow view);
• save factor scores back as new variables.

Output. Communalities, total variance explained, the component/factor matrix (loadings), the scree plot, and — for ML — a goodness-of-fit χ² test. Oblique rotation adds Pattern, Structure and Factor-Correlation matrices.

Example. Reduce the body-measurement and blood-pressure variables to a couple of interpretable factors.

Classify

Analyze → Classify. Four ways to group or classify cases.

K-Means Cluster

Partition cases into a fixed number K of clusters. Reports the final cluster centers, an ANOVA of how each variable separates the clusters, the cluster sizes, and (optionally saved) each case's cluster membership and distance. A random seed in Options makes a random start reproducible.

Hierarchical Cluster

Build a nested clustering by agglomeration (single, complete, average or Ward linkage). Reports the agglomeration schedule, a dendrogram of the merge tree (on by default; a very wide tree is rendered as its last merges, with collapsed clusters sized in parentheses and a note saying so), and, optionally, each case's membership at a chosen number of clusters.

Scope limits. Capped at 200 cases by default, because the method's cost grows steeply with case count (cubic in time, quadratic in memory). Raise Maximum cases — or set it to 0 to remove the limit — to cluster more; the result then carries a note that the cap was lifted. The agglomeration honours the Weight Cases setting: each case enters as a cluster of its own weight, so the size-weighted linkages (between-groups average, Ward) are weighted. Single and complete linkage use nearest/furthest distances, which do not depend on how many times a case is counted, so they are unaffected.

Two-Step Cluster

Find the number of clusters automatically (minimising a BIC criterion) or fix it. Reports the auto-clustering BIC table, the centers, the counts and the saved membership. Handles larger datasets via a pre-clustering pass.

Discriminant

When. Predict a known group membership from scale predictors (the supervised counterpart to clustering).

Dialog. A grouping variable and the predictor variables. Options add forward/backward stepwise selection (by Wilks' lambda) and classification / cross-validation (resubstitution and leave-one-out confusion matrices).

Output. Canonical discriminant functions, eigenvalues and canonical correlations, the overall Wilks' lambda, Fisher classification functions, and the classification results table with percent correctly classified. A Plot… option draws the combined-groups canonical scatter (optionally with a territorial map).

Scope limits. Leave-one-out cross-validation is capped at 500 cases and the canonical-scores table behind the plot at 2000 cases, since both are expensive on large datasets. Each cap is configurable in the dialog (0 removes it); when a cap applies, the output says the cross-validation was skipped or the table truncated, and how to lift it. The analysis honours the Weight Cases setting: the case weight is a frequency weight, folded into the group means, the within- and between-groups scatter, and the classification tallies.

Example. Predict Diabetic (Yes/No) from BMI, FastingGlucose, Age and SystolicBP, with leave-one-out cross-validation to gauge real accuracy.

ROC Curve

When. Judge how well a continuous score (a measurement, or a fitted probability from logistic regression) separates two known classes — the standard way to assess a diagnostic test or a binary classifier. Analyze → ROC Curve… (a top-level item, next to Classify).

Dialog. A Test variable (the numeric score) and a State variable (the true class). Set the Value of state (positive) to whichever state value marks the positive / condition-present case (default 1); every other value is taken as negative. Positive if test value is chooses whether a larger score (the default) or a smaller one points to a positive case. Plot ROC curve is on by default.

Output. The Area Under the Curve (AUC) with its standard error, confidence interval and the asymptotic significance of the test against chance (AUC = 0.5); the Coordinates of the Curve (sensitivity and 1 − specificity at every cut-point); and the Optimal Cut-Point maximising Youden's J (sensitivity + specificity − 1). The plot draws the curve on the unit square against the chance diagonal, annotates the AUC, and marks the optimal cut-point.

The AUC equals the Mann-Whitney U statistic divided by the number of positive×negative pairs (ties counted as half) — the probability that a random positive scores above a random negative. A natural workflow is to fit a binary Logistic regression, save its predicted probabilities, and run ROC on that saved column.

Example. Assess FastingGlucose as a screen for Diabetic (positive value 1): read the AUC, and take the cut-point that best balances sensitivity and specificity.

Choosing among them

• Are the groups known? → Discriminant (supervised).
• Groups unknown, want a fixed number → K-Means.
• Groups unknown, want the structure / a dendrogram-style schedule → Hierarchical.
• Groups unknown, want the count chosen for you → Two-Step.
• Checking that items form one scale → Reliability.
• Measuring rater / repeated-measurement agreement → Intraclass Correlation.
• Reducing many variables to a few → Factor.