Cronbach Alpha is usually a bad choice, because it depends on very strong assumptions. With composite reliability, do you mean omega? There are quite a number of homogenity indicators, that are more suitable than cr a and which are easily computable via the the psych package in r. Please have a look at https://www.researchgate.net/publication/313852796_Thanks_Coefficient_Alpha_We%27ll_Take_it_From_Here where you can find a fantastic discussion about the different measures and on how to compute them. A good choice could be the greatest lower bound (GLB) or Revelle's Omega.

Best regards,

Wolfgang

Article Thanks Coefficient Alpha, We’ll Take it From Here

Cronbach Alpha is usually a bad choice, because it depends on very strong assumptions. With composite reliability, do you mean omega? There are quite a number of homogenity indicators, that are more suitable than cr a and which are easily computable via the the psych package in r. Please have a look at https://www.researchgate.net/publication/313852796_Thanks_Coefficient_Alpha_We%27ll_Take_it_From_Here where you can find a fantastic discussion about the different measures and on how to compute them. A good choice could be the greatest lower bound (GLB) or Revelle's Omega.

Best regards,

Wolfgang

Article Thanks Coefficient Alpha, We’ll Take it From Here

I agree with Wolfgang. Cronbachs alpha is the "traditional" test for internal consistency, but it has been known since its inception (noted by Cronbach himself) to be very, very dependent on the number of items. 

Carmines, Edward G and Zeller, Richard A. Reliability and Validity Assessment. 1979. SAGE. London.

I'd be inclined to go with the standard in the research literature that you're working with. If the papers in your research have set a precedent for working with construct validity using Cronbach's alpha - then I would consider keeping the work in line with the standard in your field.