I don't think that you need a theoretical backup or reference for deleting bad items. If you can show based on your CFA results that an item, for example, has too small a standardized loading to be seen as a valid and/or reliable measure or if the item otherwise doesn't align with its hypothesized factor, these results alone will provide sufficient justification for the removal of poor measures/items from the scale. This is especially true if there are also substantive reasons for item misfit (e.g., due to problems with item wording or redundancy).

Hi Daniel,

beyond what Christian said: Be careful however, as "bad items" can seem to be bad whereas the real reasons is that the original set of items is simple two-factorial and the bad items are actually good items of another factor. Of course, if you goal is to measure factor A, you may not be intrested that the bad items are good items for factor B. Only don't react too mechanistic.

Best,

Holger

Daniel Obande Haruna Item deletion is a standard specification practice in covariance-based SEM when indicators show low standardized factor loadings (0.50) or composite reliability (>0.70), while preserving content validity (pp. 112–115)—principles applicable analogously to CB-SEM; earlier editions like Hair et al. (2010) explicitly discuss deleting variables in CB-SEM for fit (p. 694). Kline (2016) endorses trimming weak indicators in CFA but warns against overfitting, recommending cross-validation (pp. 284–285, 309). Complementary sources include Brown (2015, pp. 135–140) for deleting low-loading items to ensure unidimensionality, and Anderson and Gerbing (1988) for refining measurement models pre-structurally. To defend your actions, document initial/post-modification fit indices, rationalize deletions theoretically, reassess validity/reliability, and report transparently (Boomsma, 2000). If deletions are extensive, consider alternatives like item parceling (Little et al., 2013). Best wishes with your PhD!