Is this the family that you are looking for at Orchard, Wayne, Illinois in 1910?
Household Gender Age Birthplace selfWilburt W BrattonM 24y IllinoisFather born in Ohio, Mother in Illinois wifeKatie R BrattonF 18y IllinoisBoth parents born in Illinois dauAlpha I BrattonF y 7m Illinois Source: https://familysearch.org/pal:/MM9.1.1/MKFW-ZS5
By 1920 the family is in Carmi Township Carmi Third, White, Illinois.I can't look at the actual census, only the transcription, and it looks like his name has been mis-transcribed as William, but the wife and child are the same: Household Gender Age Birthplace selfWilliam BrattonM 33y Illinois wifeKattie BrattonF 28y Illinois dauAlpha BrattonF 10y Illinois dauVeta BrattonF 8y Illinois dauDorcas BrattonF 5y Illinois sonKelfus BrattonM 11m Illinois Source:https://familysearch.org/pal:/MM9.1.1/MJZQ-WX6
He shows up again in the 1930 census of Carmi, White, Illinois: Household Gender Age Birthplace headWilbur W BrattonM 44 Illinois wifeKatie BrattonF 38 Illinois daughterAlpha BrattonF 20 Illinois daughterDarcus BrattonF 15 Illinois sonKellus BrattonM 11 Illinois sonJoseph BrattonM 9 Illinois sonJohnny BrattonM 6 Illinois sonDavid BrattonM 4 Illinois sonJames BrattonM 2 Illinois Source:https://familysearch.org/pal:/MM9.1.1/X39M-YYL
and the 1940 census of Carmi, Carmi Township, White, Illinois: Household Gender Age Birthplace headW Willis BrattonM 54 Illinois wifeKatie BrattonF 48 Illinois sonKellus BrattonM 21 Illinois sonJoseph BrattonM 19 Illinois sonJohn E BrattonM 16 Illinois sonDavid BrattonM 14 Illinois sonJames Herbert BrattonM 12 Illinois sonWilbert BrattonM 8 Illinois Source:https://familysearch.org/pal:/MM9.1.1/KWRY-8SC