name: op-mat-factor
description: Exploratory factor analysis of a battery — minres, principal-axis or maximum-likelihood extraction from the SMC, varimax / promax / oblimin rotation, loadings (p × k), communalities, uniquenesses, variance accounted, rmsr, the empirical chi-square, KMO and Bartlett, ML's likelihood chi-square, TLI, RMSEA with its interval and BIC; listwise or pairwise, weighted.
kind: operator
category: MAT
operator: MAT_FACTOR
type: reference
applies_to: process, compose, predict
examples_tags: [matrix, correlation-analysis]
As op-mat-covariance; always correlation.
Use when
Which hidden qualities a set of related measures reflects, and how strongly each measure is tied to each, before building scale scores.
Questions it answers:
- Do these twelve attitude questions reflect two or three underlying qualities, and which questions go with which?
- Which items in this battery tie weakly to every quality and could be dropped?
Params
factors— int k ≤ p orkaiser(default).extraction—minres(default),principal_axis,ml.rotation—none(default),varimax,promax,oblimin;kappa(4) /gamma(0) for promax / oblimin.repair—nearest.conf_level—ml, default 0.9: RMSEA interval coverage.missing,max_drop_share,weight,encoding:op-mat-correlation.
Inputs
Integer / float members.
Output
primary: loadings F1…Fk. auxiliary: unrotated, factor_correlation; vectors: communalities, uniquenesses. scalars: fit figures (rmsr, kmo, …); ml adds likelihood_chisq, tli, rmsea, bic.
Reading the output
primary.values: Each cell is a loading: how strongly the row’s measure is tied to the column’s factor. Without a rotation, or with varimax, it is the correlation between the two; under promax or oblimin it is the measure’s own tie to that factor with the other factors held fixed. A factor is named by the measures with the largest loadings.scalars.bartlett_p: a p-value. Below alpha (0.05 unless the request sets another) the result is called significant; that is not the same as important, so read the effect size for how big it is.
Components
n, n_null, n_listwise_dropped; pairwise min_pair_n / max_pair_n; weighted sum_weights, n_eff, n_weight_invalid.
Gotchas
- (p − k)² < p + k: null fit,
PULSE_MATRIX_NOT_IDENTIFIED. - Uniqueness ≤ 0:
PULSE_MATRIX_HEYWOOD; cap hit:PULSE_MATRIX_NOT_CONVERGED. mlneeds positive-definite R and enough rows.
See
pulse_examples_search tags=[matrix, correlation-analysis]- Skills:
multivariate-outputs,op-mat-pca