From the research I have done and the input of everyone on this forum topic, I think it is clear the interest is attributed to the use of the proceeds of the loan as described in IRS Publication 535.
The second question that is not as clearly answered in the IRS materials is whether the proceeds can be allocated to repaying your personal funds from a purchase and subsequent rehab. Many investors purchase properties for cash and later cash out via a mortgage on the property to recoup some or all of their original investment.
I have come to the conclusion, and I believe Steven Hamilton II agreed above, that the proceeds received, up to the amount of the initial investment, can be allocated to repayment of the investment and therefore the interest can be deducted on Schedule E.
While I can't find any IRS rules specifically stating this (nor any opposing) I think there is more support for this approach than there is for declaring it non-deductible.
Publication 535 states " Generally, mortgage interest paid or accrued on real estate you own legally or equitably is deductible." and "Certain expenses you pay to obtain a mortgage cannot be deducted as interest. These expenses, which include mortgage commissions, abstract fees, and recording fees, are capital expenses. If the property mortgaged is business or income-producing property, you can amortize the costs over the life of the mortgage. "
The instructions for Form 1040 Schedule E state "If you have a mortgage on your rental property, enter on line 12 the amount of interest you paid for 2011 to banks or other financial institutions."
Publication 527 states "You can deduct mortgage interest you pay on your rental property. When you refinance a rental property for more than the previous outstanding balance, the portion of the interest allocable to loan proceeds not related to rental use generally cannot be deducted as a rental expense. "
Example: An investment property is purchased for $50k in cash. Then the property is rehabbed for an additional $30k in cash. Two years later, a cash out mortgage is taken against the property for $100k. The $100k would be deposited into a separate bank account as recommended in the procedures in Publication 535. $80k would be allocated to the original, non-financed, investment and would be available for immediate personal or business use. The remaining $20k could be allocated to non-financed investment in another property, or could be used to invest in a new property. 80% of the interest would be recorded on the Schedule E for the investment property the mortgage is secured by, the other 20% of the interest would be recorded on the Schedule E for the property which the $20k is allocated to.