{"doi":"10.31234/osf.io/sug68","title":"Using joint probability density to create informative, unidimensional indices: A new method using pain and psychiatric severity as examples","abstract":"Background. Dimension reduction methods do not always reduce their underlying indicators to a single dimension. Furthermore, such methods are usually based on optimality criteria that require discarding some information. The joint probability density functions (joint pdf or JPD) can be considered as unidimensional indices. We compare such JPD indices with some traditional scoring methods.Methods. We introduced unidirectionality and co-directionality as basic requirements for a joint pdf to become an index. we then provided an argument to demonstrate its maximal informativeness property. Using all possible joint pdf conditional specifications, we estimated the JPD index. We then applied the method to two data sets: first, on the 7 Brief Pain Inventory Interference scale (BPI-I) items obtained from 8,889 US Veterans with chronic pain and, second, on a novel measure based on administrative data, the Manifestations of Psychiatric Severity Index (MoPSI), for 912 US Veterans who had applied for Department of Veterans Affairs disability benefits. We used measures of monotone dependence (e.g., Spearman’s rho) to assess unidirectionality and co-directionality. We used Shannon’s entropy to compare uncertainties (informativeness) in the BPI-I JPD score to standard BPI-I scores and to the estimated person’s parameters of Partial Credit Rasch modeling of BPI-I items. JPD score and person’s parameter were compared for the MoPSI.Results. All three distinct BPI-I scores’ rankings were highly monotonically dependent (pairwise rho>0.98). The MoPSI’s JPD score rank correlation with the Rasch person’s parameter was also very high (rho=0.98). Compared to standard or Rasch scoring methods, Shannon’s entropy was smaller for BPI-I and for MoPSI JPD scores. With the fixed precision, the BPI-I’s JPD scoring method generated 7,778 unique person-scores compared to 71 unique person-scores generated by standard or Rasch scoring. The MOPSI’s JPD scoring method generated 121 unique person-scores compared to 21 unique person-scores generated by Rasch modeling. Conclusions. While agreeing with more traditional scoring methods, the JPD scoring method benefits from the optimality foundations on which it is built, with the additional ability to provide more detailed ordering of subjects due to its maximal informativeness property.","journal":"PsyArXiv (OSF Preprints)","year":2023,"id":399009,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9506,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2023-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":402609,"name":"Barbara Clothier","orcid":"0000-0002-9932-4245","position":1,"is_corresponding":false},{"id":1175144,"name":"Maureen Murdoch","orcid":"0000-0002-8674-382X","position":2,"is_corresponding":false},{"id":402614,"name":"Siamak Noorbaloochi","orcid":"0000-0002-9094-1036","position":0,"is_corresponding":true}],"reference_count":31,"raw_metadata":null,"created_at":"2026-07-19T01:19:51.724387Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}