Heckman sample selection with standardized data

[Nitin Jain]

Hi, My model has non-linear and interaction terms and of different units so I plan to standardize the variables. The unstandardized dependent variable has either missing or non-zero continuous values. Should I standardize on the full data comprising the observations with missing dependent variable or after removing these observations? If I do the latter, then can I do the Heckman's sample selection test on the unstandardized data? Kindly advise. Thanks.