An application of Bayesian measurement invariance to modelling cognition over time in the English Longitudinal Study of Ageing

OBJECTIVES: Recommended cut‐off criteria for testing measurement invariance (MI) using the comparative fit index (CFI) vary between −0.002 and −0.01. We compared CFI results with those obtained using Bayesian approximate MI for cognitive function. METHODS: We used cognitive function data from Waves 1–5 of the English Longitudinal Study of Ageing (ELSA; Wave 1 n = 11,951), a nationally representative sample of English adults aged ≥50. We tested for longitudinal invariance using CFI and approximate MI (prior for a difference between intercepts/loadings ~N(0,0.01)) in an attention factor (orientation to date, day, week, and month) and a memory factor (immediate and delayed recall, verbal fluency, and a prospective memory task). RESULTS: Conventional CFI criteria found strong invariance for the attention factor (CFI + 0.002) but either weak or strong invariance for the memory factor (CFI −0.004). The approximate MI results also supported strong MI for attention but found 9/20 intercepts or thresholds were noninvariant for the memory factor. This supports weak rather than strong invariance. CONCLUSIONS: Within ELSA, the attention factor is suitable for longitudinal analysis but not the memory factor. More generally, in situations where the appropriate CFI criteria for invariance are unclear, Bayesian approximate MI could alternatively be used.