WWI Draft Registration lists Maude as spouse. There are several US Census (1910, 1930, 1940) which list a William Edgar with wife Maude. Children listed are Myrtle, Lois, Willie, Grady, Alvin, and Pauline. See US Census 1910, and US Census 1930 for follow up.
"United States World War I Draft Registration Cards, 1917-1918," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KZX7-FSB : 12 December 2014), William Edgar, 1917-1918; citing Dickens County, Texas, United States, NARA microfilm publication M1509 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,953,189.
"Texas Deaths, 1890-1976," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K3X8-B1F : 5 December 2014), William Edgar, 29 Jan 1962; citing certificate number 08262, State Registrar Office, Austin; FHL microfilm 2,116,932.