REITs are an investment. They are a form of business that PAY you via collecting rent from tenants and passing on the proceeds to shareholders.
A house is a thing, a consumer good. It is NOT an investment. thinking that it will grow, in REAL dollars, is a speculative bet. It does not pay you anything (you can turn it into an investment by renting out a room, however). It does save you in paying rent, so in that sense one could argue it is "sort of" an investment since you don't have to pay rent. But a house is a consumer good, it COSTS you money and MAY keep up with inflation over time but only if you continuously put money into upkeep.
So, no, a house is not a replacement for a REIT. My bigger question is 1) why do you feel the need to tilt towards REITs and 2) if you are just now buying a house I assume you are young, why do you hold bonds?