It is advisable to eliminate it and run it again, although if you have a structure from a previous study you can confirm the model using AFC.

It is advisable to drop and run EFA once again. Before EFA you should do the relatability test using cronbac alpha here also u can get reason for dropping any item or items.

Considering your case, you should drop that item first which is having cross loading with negative higher magnitude. Drop only one item each time run the EFA unit and unless u get the recommended values.

Dear Evangelia,

with using the Big 5 in a CFA model, you enter hell as in Dante's Inferno :) These are messy measures and signify the problems embedded in psychometrics as no other case. In principle, there is nothing problematic with having double loadings. That does only mean that a certain item is caused by two latent variables in the model. The fact that causal sources of an item response are multi-factorial is nothing spectacular. Normally, these sources are kept in the error term of the indicator. In a model with double loadings, you have the special case that one of these further sources is already explicitly modelled as a (further) latent variable. The most important question is whether the overall factor structure is correct and the latent variables are meaningful. Hence, my question would be whether the double loading was estimated as a remedy of a prior misfit and if model cleanly fits with the estimated double loading ( I doubt that).

With regard to the former, and as in any other model re-specification-after-misfit, you enter the exploratory road and run the risk to get a sample-specific result. That should simply be acknowledged. The other problem is that the model may be structurally misspecified and a (potentially nonsensical) double loading just a sign of that. This will be revealed once you incorporated other variables in the model that should be related to the latent variables. It is a usual finding that one has a fitting CFA and then when including further variables, the misspecification becomes obvious.

Finally, your interpretation of the double loading is a bit shaky which hopefully got clear when reading the lines above.

Hence, you could delete the items but if scenario #2 is the case, you simply hide problems. Enrich the model with further variables and test it further.

Best,

Holger