Question: Evaluating the Use of NSS Model for Yield Curve Fitting

I've recently attempted to model the yield curve using the Nelson-Siegel-Svensson (NSS) model by minimizing the sum of squared residuals. For this, I pulled a series of bonds from the same issuer, ranging from 1 to 25 years in maturity, all denominated in the same currency, senior unsecured, and with identical credit ratings.

After fitting the NSS model, I observed that:

• Some quoted yields lie above the NSS curve,
• Some lie below,
• And some align closely with the fitted curve.

I have a few questions regarding methodology and interpretation:

1. Is it appropriate to use Yield to Maturity (YTM) as the input for fitting the NSS model? Or should I be using spot rates or zero-coupon yields instead?
2. Can I interpret bonds with YTM above the NSS curve as "cheap" and those below as "rich"? Or is this an oversimplification?
3. Would a more accurate approach be to use the NSS model to interpolate spot rates for intermediate tenors, construct a spot curve, and then discount each bond's cash flows using these spot rates to assess fair value? I have a gut feeling this might be more robust than relying solely on YTM comparisons.