TY - JOUR

T1 - A normal-probit-binomial model for the analysis of repeated sum scores from multi-item questionnaires

AU - Nooraee, Nazanin

AU - Molenberghs, Geert

AU - Ormel, Johan

AU - van den Heuvel, Edwin R.

N1 - Publisher Copyright:
© 2022 Taylor & Francis Group, LLC.

PY - 2024/6

Y1 - 2024/6

N2 - Sum scores from questionnaire data are frequently analyzed under the normality assumption which is not always tenable due to for instance the skewness of the distribution, or the discreteness of the sum scores for small number of items. Alternatively, an ordinal regression analysis can be applied, but this approach seems appropriate only for very small number of items. The current state-of-the-art approach is to apply a beta-binomial model, though the beta-binomial model does not simply connect to item-response theory models that may describe the underlying items of the questionnaire, and it is more cumbersome to fit to multi domain sum scores or repeated longitudinal single sum scores. This paper proposes a normal-probit-binomial model for repeated sum scores that has an item level interpretation under certain assumptions without having to analyze the individual items. All parameters, the temporal correlation coefficients, and the mean difficulty parameter were almost unbiasedly estimated, irrespective of the set of item difficulty parameters. The coverage probability of the 95% confidence intervals were close to the nominal level, except for the correlation coefficients that were slightly liberal. Our model performed slightly better than the beta-binomial model on cross-sectional data and it handles missing items easily.

AB - Sum scores from questionnaire data are frequently analyzed under the normality assumption which is not always tenable due to for instance the skewness of the distribution, or the discreteness of the sum scores for small number of items. Alternatively, an ordinal regression analysis can be applied, but this approach seems appropriate only for very small number of items. The current state-of-the-art approach is to apply a beta-binomial model, though the beta-binomial model does not simply connect to item-response theory models that may describe the underlying items of the questionnaire, and it is more cumbersome to fit to multi domain sum scores or repeated longitudinal single sum scores. This paper proposes a normal-probit-binomial model for repeated sum scores that has an item level interpretation under certain assumptions without having to analyze the individual items. All parameters, the temporal correlation coefficients, and the mean difficulty parameter were almost unbiasedly estimated, irrespective of the set of item difficulty parameters. The coverage probability of the 95% confidence intervals were close to the nominal level, except for the correlation coefficients that were slightly liberal. Our model performed slightly better than the beta-binomial model on cross-sectional data and it handles missing items easily.

KW - Item response theory

KW - Latent variable model

KW - Longitudinal data analysis

KW - Missing item

KW - Mixed models

UR - http://www.scopus.com/inward/record.url?scp=85133655306&partnerID=8YFLogxK

U2 - 10.1080/03610918.2022.2092140

DO - 10.1080/03610918.2022.2092140

M3 - Article

AN - SCOPUS:85133655306

SN - 0361-0918

VL - 53

SP - 2880

EP - 2897

JO - Communications in Statistics: Simulation and Computation

JF - Communications in Statistics: Simulation and Computation

IS - 6

ER -