Pulsar timing arrays (PTAs) use precision pulsar timing to detect nanohertz gravitational waves (GWs) from sources such as supermassive black hole binary systems. However, there are many effects that are dependent on the observing radio frequency that may add noise to the timing data on the same scale as that of the expected signal from the GWs. These effects include dispersion measure variations, pulse scattering, and scintillation due to the interstellar medium (ISM), as well as pulse profile evolution with radio frequency. To characterize and model these effects, we have analyzed multi-hour observations of seven millisecond pulsars currently used by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) PTA to determine the noise contribution of these ISM to the pulsar timing data. We have further explored the covariances between these effects within a pulsar timing model using simulated data with the Pulsar Signal Simulator Python package. The simulations not only show how the covariances between these parameters, but also how they affect the precision of the pulsar timing. These studies are critical for understanding the noise in the PTA since proper modeling and mitigation of these effects are necessary for the detection of GWs.