I would create your own index fund of REITs if you are interested in diversified income investing.
Index funds are great for equities, but there are excellent opportunities to invest in mid cap REITs that are far from fully valued - while certain popular REITs get overvalued frequently such as O.
Some of these are too high to buy right now, but here are some of the REITs I own:
BPR
DEA
CCI
AIV
CIO
CONE
GMRE
VER
Then there are others such as WPC that are overvalued but I will be purchasing on a dip.
Once some of your in-scope REITs reach a fair to cheap valuation, (you can use price to NAV, see how well the dividend is covered, history of dividend growth, etc - it's not too hard to determine), you buy.
And then you just buy more on the dips.
Brad Thomas has good analyses but I avoid certain industries like lodging and retail that are especially susceptible to cyclical and secular trends respectively. I never buy something because "aw, it's not THAT bad" because you're essentially trying to call the bottom. IE Tanger outlets, which Brad gets a lot of crap for his bullishness on.