Bill. W6WRT wrote:
"If the roof is made of non-conductor material such as wood or
composition shingle, the antenna will not "see" it and the height above
ground is the important thing."

Yes, at least one of the important things. Antenna elevation is
important to lower the elevation angle of propagation. It`s also
possible there are noise generators within the house which make
reception more difficult when a conductive roof isn`t present to shield
the roof mounted antenna from noise. A small separation can make a large
difference in noise source "signal" strength. A one wavelength
separation can lower noise source received level by 22 dB. Then 6 dB
more every time the distance doubles after the initial 22 dB loss. It`s
best to have receiving antennas located well away from noise sources.

Best regards, Richard Harrison, KB5WZI