My only suggestion would be to try and locate either naturalization records for Edward and Alice Mona or try to determine if a Will was probated. Either of these documents MIGHT indicate the names of his parents. Edward emigrated to Canada in 1906 and Alice Mona in 1907, according to the 1911 Canadian census, so an application to naturalize would have followed sometime after.

You might try to get some help from the National Archives of Canada - http://www.collectionscanada.ca/index-e.html.

Another excellent site is the Ontario Archives at http://www.archives.gov.on.ca/english/index.html. In both cases, scroll down to the “Genealogy” section.

I did a cursory search on Frances Coakley’s site for the surname Rome and found in the Brown's Directory 1894], the following entry:

Rome Joseph, 48 Maughold-street – could he be connected to Alice?

You might want to seek out a Last Will & Testament for Edward and/or Alice Mona, and you can make enquiries at the following office:

Archives of Ontario
77 Grenville Street, Unit 300
Toronto, ON
M5S 1B3
Tel.: (416) 327-1600 or
1-800-668-9933 (Toll-Free Number – Ontario only)
Fax: (416) 327-1999
reference@archives.gov.on.ca

When I did a search at the Ontario Cemetery Finding Aid site, using the surnames SCHMIDT and CLAGUE, the following 3 were included.

SCHMIDT Clarence J./Memory Gardens, Section A/Waterloo,Woolwich/WW-5464
CLAGUE Edward R./Thornhill Community/ York, Markham/LDS971.354V3l
CLAGUE Mona L. (Moore)/Thornhill Community/York, Markham/LDS971.354V3l
(Perhaps the "Moore" name might be a clue?)

Best of luck.