Okay, you have the 1910 and 1920 census already. I looked for Andrew and family in the 1930 census but couldn't find him. I did find his WW I Draft Registration Card at ancestry, but nothing shows up for his immigration record.
I see he immigrated in 1902 and the 1920 census says he was naturalized in 1917. Does PA have a state genealogical society? Perhaps they could put you on the right track to find immigration papers based on where he was living in 1917?

My connection to the BERTA family is only through marriage. My mother-in-law's step-father was a BERTA from
Timosoara, Hungary. That city is now in Romania -- the borders were moved after WW II.
Sorry I couldn't be more help.