We apply the polytomous version of the Lord–Wingersky algorithm (Lord and Wingersky 1984; Thissen et al. 1995). Details and examples of the algorithm are provided by Thissen et al. (1995) and Cai (2015, pp. 537–541).
A T-score to summed-score table can be made with the R package PROsetta (Choi et al.,2021) and the function getRSSS. It can also be made with commercial software IRT PRO and flexMIRT. It appears that PROC IRT does not have this particular scoring feature, but perhaps others on the forum can comment on this. Regardless, for this to be valid for PROMIS items, standard PROMIS item parameters need to be supplied, which requires permission.
References:
Lord, F. M., & Wingersky, M. S. (1984). Comparison of IRT true-score and equipercentile observed-score equatings. Applied Psychological Measurement, 8(4), 453–461.
Cai, L. (2015). Lord–Wingersky algorithm version 2.0 for hierarchical item factor models with applications in test scoring, scale alignment, and model fit testing. Psychometrika, 80(2), 535–559.
Choi, S. W., Lim, S., Schalet, B. D., Kaat, A. J., & Cella, D. (2021). PROsetta: An R Package for Linking Patient-Reported Outcome Measures. Applied Psychological Measurement, 01466216211013106.
Thissen, D., Pommerich, M., Billeaud, K., & Williams, V. S. (1995). Item response theory for scores on tests including polytomous items with ordered responses. Applied Psychological Measurement, 19(1), 39–49.
