Estimating the Joint Probability Density for Index Construction: Some Simplifications Using the TWEAK as Example
Maureen Murdoch, Barbara Ann Clothier, Siamak NoorbaloochiABSTRACT
Background
Index construction using the joint probability density (JPD) method is extremely robust and, unlike confirmatory factor analysis (CFA) or item response theory (IRT), puts few restrictions on underlying data. When input variables' numbers are large, however, JPD estimation can be difficult.
Objective
To assess two simplifications of JPD estimation using the TWEAK, a well validated screener for problematic drinking, and to compare these against the fully estimated JPD, the conventionally scored TWEAK, and TWEAK scores estimated through CFA and IRT.
Methods
Mailed survey of a nationally representative panel of 410 gender‐stratified, post‐9/11 Veterans with pending disability claims for posttraumatic stress disorder.
Results
Summary statistics for the TWEAK's fully estimated JPD and the two simplifications were very similar, and Spearman's correlations were 0.97–1.00 ( p s < 0.001). Spearman's correlations across the remaining scoring approaches were −0.84 to −0.90 ( p s < 0.001). All 6 scoring approaches identified differences in men's TWEAK scores by alcohol use diagnosis ( p s ≤ 0.02); the 3 JPD approaches did not reach statistical significance in the women. IRT analysis identified local dependence issues.
Conclusions
Our simplified estimations of JPD score were very similar to the fully estimated JPD and much easier to calculate. All 3 JPD estimations were highly concordant with more traditional scoring approaches.