name: op-mat-reliability
description: Scale reliability of a battery — Cronbach's alpha, standardized alpha, McDonald's omega (one-factor minres), mean inter-item r, per-item item-total r / alpha if deleted / mean / sd — with reverse-keyed items flipped before the fold; listwise or pairwise, weighted.
kind: operator
category: MAT
operator: MAT_RELIABILITY
type: reference
applies_to: process, compose, predict
examples_tags: [matrix, correlation-analysis]
Slot and members as for op-mat-covariance; at least 2 items.
Use when
How consistently a set of rating items measures one thing, before you add them up into a score, with a check of how each item fits the rest.
Questions it answers:
- Are these five satisfaction questions reliable enough to average into one score?
- Which item in this battery fits the others worst and should be dropped?
Use something else:
MAT_CORRELATIONwhen you only want to see which items go together, pair by pair.
Params
| Name | Type | Default | Description |
|---|---|---|---|
reverse | [fields] | none | Reverse-keyed items: x’ = min + max − x before the fold. |
scale_min, scale_max | number | the vector’s | Battery range; both or neither, required with reverse. Absent: a kind: "scale" vector’s bounds (vector-metrics). |
repair | nearest | none | Fit omega on the nearest correlation matrix. |
missing, max_drop_share, weight, encoding | As op-mat-correlation. |
Inputs
Integer / float items.
Output
primary: inter-item correlation. scalars: alpha, alpha_standardized, omega, mean_inter_item_r. vectors (axis order): item_total_r (corrected), alpha_if_deleted (null at 2 items), item_mean, item_sd. Pairwise auxiliary.n; warnings. No p-values.
omega = (Σλ)² / ((Σλ)² + Σψ) from the minres fit (the model form, not psych::omega’s observed-total omega.tot, which reads lower on a misfit battery).
Reading the output
scalars.alpha: Cronbach’s alpha: how consistently the items measure one shared quality, from the share of the summed score’s spread that the items share. 1 means the items move in lockstep; it can fall below 0 when items pull against each other, which usually means a reverse-worded item was not reversed.- Caveat: A high alpha does not show the items measure only one thing.
scalars.alpha_standardized: Alpha computed on the items’ correlations instead of their raw spreads: the alpha the battery would have if every item were first put on the same scale.
Components
n, n_null, n_listwise_dropped; pairwise min_pair_n / max_pair_n; weighted sum_weights, n_eff, n_weight_invalid; iterations, converged when the omega fit ran.
Gotchas
reversewithout the range, or an item value outside it:PROCESSING_CONFIG(never clamped or inferred).- omega null + warning: 2 items (
PULSE_MATRIX_NOT_IDENTIFIED), a Heywood fit (PULSE_MATRIX_HEYWOOD), non-PSD pairwise input withoutrepair(PULSE_MATRIX_NOT_PSD). Alpha always computes. - Negative alpha usually means an unreversed item.
See
pulse_examples_search tags=[matrix, correlation-analysis]- Skills:
matrix-results,op-mat-correlation,weighting,vector-metrics