Weighted sums in latent variable models silently convert ordinal indicators to interval.

Evidence

This automatic conversion is so common that it is almost never noticed. For example, to get an estimated value for observations in latent variable models, one uses the factor scores in a weighted sum of the indicators. No matter what the original scale type of those indicators, they are automatically converted by the weighted sum into interval-level indicators. — Gary Goertz, Social Science Concepts and Measurement, 832

Categorization

• XREF: Speaks directly to anyone running factor analysis or SEM, where factor scores are treated as continuous without justification. — connects to: Treating Likert responses as interval data distorts estimates when aggregating across disparate items — Ruiqian Li and Paul Froese, The Duality of American Christian…, 96
• SEED: Possible essay: ‘The Interval Scale You Never Chose’ — how routine statistical procedures impose measurement assumptions no one argues for.