If I Have a Weak Factor Loading in SEM Model, Should I Drop It?

If you have a factor loading that is near or below the .70 threshold, it does not mean you need to drop the indicator from the analysis. Complex or newly developed constructs will often have numerous indicators in an attempt to capture a comprehensive aspect of a construct. If you have numerous indicators that are strongly loading on the unobserved construct and an AVE value that is still exceeding .50, then I would suggest keeping the indicator. The weaker indicator could very well be helping to capture a unique component of the construct.That said, if the construct is nowhere near the threshold (< .60), this item is contributing very little in understanding the unobservable construct.With a factor loading lower than .60, you are barely explaining a third of the variance in the indicator. If this is the case, you should strongly consider dropping this indicator. This poor-performing indicator can create more unexplained variance in your model and ultimately hurt your ability to achieve convergent and discriminant validity. A word of caution should be given about deleting indicators in the measurement analysis. If you collect data on some phenomenon and in the analysis decide to start dropping indicators from your constructs, then you really need to have a second data collection to verify that your revised scales (without the dropped items) are valid. Having a single sample and dropping indicators sets you up for criticism that you are capitalizing on chance. If you cannot verify that changes you made in the scales are stable and not based on the unique aspects of that specific data collection, then criticism could ensue in regards to the validity of your results.That is why pretesting a survey or scales is so important, especially with an indicator that is being adapted into a new context or even if a relatively new construct is being measured.The pretest should be where indicators are dropped, and your final data collection should verify the structure and measurement of each construct established at the end of the pretest.

Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.