Using joint probability density to create most informative unidimensional indices: a new method using pain and...

Area of Science:

• Statistics
• Data Science
• Psychometrics

Background:

• Traditional dimension reduction methods often discard information or fail to produce a single composite score.
• Existing methods rely on optimality criteria that may not capture the full data structure.

Purpose of the Study:

• To introduce the joint probability density function (JPD) as a novel, highly informative composite score for dimension reduction.
• To demonstrate the JPD's superiority over traditional methods in preserving information.

Main Methods:

• Developed a probabilistic unsupervised dimension reduction method utilizing the JPD of multivariate data.
• Applied JPD estimation using conditional specifications and parametric models to two datasets: the Brief Pain Inventory (BPI-I) and a mental health severity index (MoPSI).
• Assessed unidirectionality and codirectionality using Spearman's rank correlation and compared JPD scores with factor scores and IRT person parameters using Pearson Divergence and Shannon entropy.

Main Results:

• The JPD was successfully estimated and applied as a scoring index for both the BPI-I and MoPSI datasets.
• JPD scores exhibited monotonic dependence with traditional scores, indicating consistent ranking.
• JPD scores demonstrated the smallest Shannon entropy and maximum Pearson Divergence, confirming their greater informativeness.

Conclusions:

• Unsupervised probabilistic dimension reduction using JPD is feasible and provides a highly informative index.
• JPD scoring preserves all indicator information with minimal assumptions, outperforming traditional methods when their assumptions are violated.
• The study demonstrated practical implementation steps for JPD model specification, estimation, and scoring.