A non-local-thermodynamic-equilibrium level population model of the first and second ionization stages of iron, nickel, and cobalt is used to fit a sample of XShooter optical + near-infrared (NIR) spectra of Type Ia supernovae (SNe Ia). From the ratio of the NIR lines to the optical lines limits can be placed on the temperature and density of the emission region. We find a similar evolution of these parameters across our sample. Using the evolution of the FeII 12 570-7155Å line as a prior in fits of spectra covering only the optical wavelengths we show that the 7200 Å feature is fully explained by [Fe II] and [Ni II] alone. This approach allows us to determine the abundance of Ni II/FeII for a large sample of 130 optical spectra of 58 SNe Ia with uncertainties small enough to distinguish between Chandrasekhar mass (MCh) and sub-Chandrasekhar mass (sub-MCh) explosion models. We conclude that the majority (85 per cent) of normal SNe Ia have a Ni/Fe abundance that is in agreement with predictions of sub-MCh explosion simulations of ∼Z⊙ progenitors. Only a small fraction (11 percent) of objects in the sample have a Ni/Fe abundance in agreement with MCh explosion models.