Statistical Foundations for a Google Play User-Review Sentiment Index: Signal Fusion, Shrinkage, Distributional Validation, and Dynamic Smoothing

Marco Mandap

The decision problem is whether valence among the users who write reviews of an app has changed enough to warrant investigation of a release, outage, or support issue. We propose a statistical specification for that decision, applied to written Google Play reviews collected under a declared locale, language, sort order, retrieval cap, and window rule. That endpoint returns a selected collection rather than a random sample, so the index describes review writers under the declared protocol and not all app users. What is new is not a sentiment classifier but an auditable interface: an ordinal threshold model is the preferred representation of star ratings, a calibrated two-signal generalized least-squares estimator is retained as an interpretable linear approximation when held-out labels support its conditional-unbiasedness assumption, the estimand is declared before the estimator, and every downstream module--uncertainty, diagnostics, and regularization--is tied to that declaration. The framework separates the latent average of a fixed collected set from the mean of a protocol-defined population of review writers, so measurement and between-review variation are not conflated, and…