Titan's upper atmosphere produces an ionosphere at high altitudes from photoionization and electron impact that exhibits complex chemical processes in which hydrocarbons and nitrogen-containing molecules are produced through ion-molecule reactions. The structure and composition of Titan's ionosphere has been extensively investigated by the Ion and Neutral Mass Spectrometer (INMS) onboard the Cassini spacecraft. We present a detailed study using linear correlation analysis, 1-D photochemical modeling, and empirical modeling of Titan's dayside ionosphere constrained by Cassini measurements. The 1-D photochemical model is found to reproduce the primary photoionization products of N2 and CH4. The major ions, CH5+, C2H5+, and HCNH+ are studied extensively to determine the primary processes controlling their production and loss. To further investigate the chemistry of Titan's ionosphere we present an empirical model of the ion densities that calculates the ion densities using the production and loss rates derived from the INMS data. We find that the chemistry included in our model sufficiently reproduces the hydrocarbon species as observed by the INMS. However, we find that the chemistry from previous models appears insufficient to accurately reproduce the nitrogen-containing organic compound abundances observed by the INMS. The major ion, HCNH+, is found to be overproduced in both the empirical and 1-D photochemical models. We analyze the processes producing and consuming HCNH+ in order to determine the cause of this discrepancy. We find that a significant chemical loss process is needed. We suggest that the loss process must be with one of the major components, namely C2H2, C2H4, or H2.