The effect of measurement quality on targeted structural model fit indices: A comment on lance, beck, fan, and carter (2016)

Lance, Beck, Fan, and Carter (2016) recently advanced 6 new fit indices and associated cutoff values for assessing data-model fit in the structural portion of traditional latent variable path models. The authors appropriately argued that, although most researchers' theoretical interest rests with the latent structure, they still rely on indices of global model fit that simultaneously assess both the measurement and structural portions of the model. As such, Lance et al. proposed indices intended to assess the structural portion of the model in isolation of the measurement model. Unfortunately, although these strategies separate the assessment of the structure from the fit of the measurement model, they do not isolate the structure's assessment from the quality of the measurement model. That is, even with a perfectly fitting measurement model, poorer quality (i.e., less reliable) measurements will yield a more favorable verdict regarding structural fit, whereas better quality (i.e., more reliable) measurements will yield a less favorable structural assessment. This phenomenon, referred to by Hancock and Mueller (2011) as the reliability paradox, affects not only traditional global fit indices but also those structural indices proposed by Lance et al. as well. Fortunately, as this comment will clarify, indices proposed by Hancock and Mueller help to mitigate this problem and allow the structural portion of the model to be assessed independently of both the fit of the measurement model as well as the quality of indicator variables contained therein.