The only Edward Mackay in Sutherland in 1881 is Edward Mackay (I regularise the spelling), aged 43, at a place recorded as Lerin (various mistranscriptions of the name are found in the census returns over the years). The place is Leirinmore (a simple Leirin with any spelling isn't recorded anywhere in Sutherland, but maybe the place was known simply as Leirin to the locals in these years). Leirinmore is on the north coast and Badcall, by Loch Inchard, lies on the opposite side of the county. In 1881 we find Edward Mackay 43 with his wife Flora, 32, and children Jane 5 and James 3. They are still there in 1891, with Edward 54, Flora 43, Jane 16, James 14, John 8, George 6, Mary Ann 4, and Edward's mother-in-law, Jane Macdonald, 85, b. Durness
Edward Mackay married Flora Forbes Macdonald in 1875, Registration District of Durness, Sutherland. Edward died, aged 80, in 1918.
Edward is recorded as aged 14, at home with father James and mother Mary in the 1851 Census returns.
There's no recorded marriage of an Edward Mackay to a Christina anything anywhere in Scotland until we see an Edward Mackay marrying a Christina Jamieson in Edinburgh in 1894 and they appear in Hawick in Roxburghshire in 1901. Edward is a "dish hawker", both he and his wife were born in Perthshire.