There is a Frank and Rosetta Smith in Branch County in the 1920 and 1930 censuses.
1920 Census, Quincy, Branch County, Michigan
Frank W. Smith, born Indiana, age 55
Rosetta E. Smith, born Indiana age 55
Reuben R. Smith, born Michigan age 15
This appears to be the same family in 1940 in Hillsdale County, Michiganhttp://search.ancestry.com/cgi-bin/sse.dll?indiv=1&rank=...