2021 Career Award for Lifetime Achievement
Measurement models focus on what needs to be measured and model violations are potential measurement distorters. Switching perspectives, the violations are a potential source of information about aspects of underlying processes that would otherwise remain unnoticed, and the violations may also have consequences for how to treat resulting measurements, even when the violations are considered as minor. I will discuss three cases of measurement model violations. Two refer to residual dependencies and the third is possibly of that type as well. Example 1. Ability and speed are two different dimensions of test responses. A closer look shows that there are item-level dependencies between response time and accuracy which may inform us about the response process and the unresolved issue of power versus speed in cognitive ability tests. Example 2. Using fMRI to measure brain activation shows that brain activation and ability are related, but a closer look again shows that there are residual item-level dependencies, which can inform us about cognitive processes. I will make the more general claim that under certain conditions item-level dependencies can be generalized to within-person dependencies across items. Example 3. Because most measurement models have only approximate fit, it seems reasonable to conjecture that most psychological measures are approximate and most likely confounded in variable ways. Unfortunately, the approximate nature is ignored when investigating relationships between variables. With a small simulation study, I will show that this leads to underestimated uncertainty and to p-values that are too small. Ignoring the approximate nature of measures may also have led to the continuing belief that all null hypotheses are false (the so-called crud factor). These are just three examples, there are more. Taking a closer look at model violations and their consequences, even in the presence of a reasonable goodness of fit, can be useful for other purposes than improving model fit.