Your Robert H. Allen seems to have been a mystery man who only signed up for one census (1910 in Dunklin Co.) It indicated he was born 1869. He was a "boarder", widow and no children with him.

Onthe Internet I did find some info about him, provider by another researcher. Apparently Robert married Sarah A. Pierce circa 1888 and they had 4 children: Linus ( born 3/13/1890, died a couple days later); Tora Myrtle (b. 2/29/1892, died 11/12/1964, married Peter Hartle); Otto (b. 2/2/1894, died 4/1986 in Butler Co., Mo.); and Clarence Lowell (b.1/6/1900). Supposedly, Sarah died 1/16/1900 (possibly due to complications in Clarence's birth). She was born 3/15/1870.

Son Otto was living with his grandparents (Elexander Pierce) on the 1900 census in Bollinger Co., Mo. Onthe 1910 census he lived in Bollinger Co. with Edward and Minnie Bark (Barks ?). On the 1920 census he lived in Cape Girardeau Co. During this period I dont know where -or with whom- Tora was living. By 1920 she probably was married.
On the 1900 census Clarence was living in Bollinger Co., but I dont know with whom.

This isnot much, but hopefully it helps you some. Bob Eddings , no relation.