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Background  Longitudinal invariance is a perquisite for a valid comparison of oral health-related quality of life (OHRQoL) scores over time. Item response theory (IRT) models can assess measurement invariance and allow better estimation of the associations between predictors and latent construct. By extending IRT models, this study aimed to investigate the longitudinal invariance of the two 8-item short forms of the Child Perception Questionnaire (CPQ 11–14 ) regression short form (RSF:8) and item-impact short form (ISF:8) and identify factors associated with adolescents’ OHRQoL and its change.    Methods  All students from S1 and S2 (equivalent to US grades 6 and 7) who were born in April 1997 and May 1997 (at age 12) from 45 randomly selected secondary schools were invited to participate in this study and followed up after 3 years. Data on the CPQ 11–14  RSF:8 and CPQ 11–14  ISF:8, demographics, oral health behavior and status were collected. Explanatory graded response models were fitted to both short forms of the CPQ 11–14  data for assessing longitudinal invariance and factors associated with OHRQoL. The Bayesian estimation method – Monte Carlo Markov Chain (MCMC) with Gibbs sampling was adopted for parameter estimation and the credible intervals were used for inference.    Results  Data from 649 children at age 12 at baseline and 415 children at age 15 at follow up were analyzed. For the 12 years old children, healthier oral health behavior, better gum status, families with both parents employed and parents’ education level were found to be associated with better OHRQoL. Four items among the 2 short forms lacked longitudinal invariance. With statistical adjustment of longitudinal invariance, OHRQoL were found improved in general over the 3 years but no predictor was associated with OHRQoL in follow-up. For those with decreased family income, their OHRQoL had worsened over 3 years.    Conclusions  IRT explanatory analysis enables a more valid identification of the factors associated with OHRQoL and its changes over time. It provides important information to oral healthcare researchers and policymakers.    Electronic supplementary material  The online version of this article (10.1186/s12955-018-0879-x) contains supplementary material, which is available to authorized users.

Longitudinal measurement invariance and explanatory IRT models for adolescents’ oral health-related quality of life