Dependent latent class partial credit models for careless and insufficient effort responding in online survey data

Careless and insufficient effort responding (C/IER) can significantly compromise the quality of survey data. Traditional indicator-based detection methods rely on threshold settings and neglect the uncertainty of identification, which can be addressed by mixture models. Recent studies have piloted a novel family of dependent latent class item response theory (DLC-IRT) models, in which item-level response times (RTs) are assumed to predict response engagement. This approach features the use of RTs without imposing strong distributional assumptions, but has only been applied to cognitive tests with dichotomous items. The present study thus extends the DLC-IRT models to account for C/IER to Likert-type items in an online survey, proposing two variants of dependent latent class partial credit models with two-level prediction (DLC-PCM-TL). The DLC-PCM-TL1 includes a simplified general intercept in its prediction model whereas the DLC-PCM-TL2 retains item-specific intercepts as previous DLC-IRT models. Model selection between the DLC-PCM-TL1 and DLC-PCM-TL2 and parameter recovery of each model are investigated under several simulated conditions. An illustrated example on a publicly available dataset is also provided, mainly to showcase the consistency of model-implied C/IER probabilities with multiple conventional indicators, and DLC-PCM-TL model adjustments of item parameters and trait estimates relative to a customary PCM.