Pulse Documentation

name: op-mat-collinearity
description: Collinearity check of candidate regression predictors (no response) — VIF and tolerance per predictor, Belsley's condition indices and variance-decomposition proportions (uncentered with the intercept, or centered), listwise or pairwise, weighted.
kind: operator
category: MAT
operator: MAT_COLLINEARITY
type: reference
applies_to: process, compose, predict
examples_tags: [matrix, correlation-analysis]

Slot and members as for op-mat-covariance. Members are the predictors only.

Use when

Whether candidate predictors overlap so much that a regression on them would give unstable coefficients, and which ones are tangled.

Questions it answers:

• Before I model satisfaction on these eight ratings, are any of them so related that their effects cannot be told apart?
• Which of these predictors are near-duplicates of the others?

Params

Inputs

Integer / float members.

Output

primary: the predictors’ correlation R. vectors: vif (diag R⁻¹), tolerance (1/VIF), condition_indices (ascending, first 1). auxiliary.variance_decomposition: kind rectangular, a row per variable ((intercept) first unless center), columns D1…Dq in condition-index order, rows sum to 1; pairwise auxiliary.n. scalars: condition_number, max_vif.

Reading the output

• scalars.max_vif: The largest variance inflation factor among the predictors (each one’s is also listed): how many times larger that predictor’s coefficient variance is than it would be if it were unrelated to the other predictors. 1 means no overlap; tolerance, its reciprocal, is the share of the predictor’s spread the others do not explain.
• primary.values: The predictors’ correlation table that the variance inflation factors and the centered diagnostics are read from: each off-diagonal cell is the correlation of its row and column predictors, from -1 to +1.

Components

n, n_null, n_listwise_dropped; pairwise min_pair_n / max_pair_n; weighted sum_weights, n_eff, n_weight_invalid.

Gotchas

• Uncentered (default) flags collinearity with the intercept; VIF is the same either way.
• Exactly or near-exactly collinear predictors (rank tolerance): fatal PULSE_MATRIX_SINGULAR with dependent_fields. Non-PSD pairwise R: fatal PULSE_MATRIX_NOT_PSD unless repair.
• VIF unbanded: 5 / 10 are rules of thumb only.

See

• pulse_examples_search tags=[matrix, correlation-analysis]
• Skills: matrix-results, op-mat-correlation, op-reg-ols, weighting