Three theoretical descriptions, namely, the local description, the flux tube integrated description and the ballooning-mode type description, of the equatorial plasma instability are presented for comparisons. On the basis of physical considerations it is argued that the ballooning-mode type description is comparatively the most accurate and complete description of plasma instability in the equatorial ionosphere where the inhomogeneous plasma is embedded in a dipole magnetic field. The growth rates obtained from the ballooning-mode type description are therefore the most accurate growth rates. In comparison, the local description overestimates the growth rates up to a certain altitude and then underestimates them, while the flux tube integrated description underestimates the growth rates at almost all altitudes where the growth rates are significant. This is shown for two sets of ionospheric plasma conditions. It is further pointed out that only the ballooning-mode type description provides useful information on the wavelength dependence of the growth rates as well as on the spatial profiles of the excited modes. The localized spatial structures of the linear modes along the magnetic field line that are found in the ballooning-mode type description are expected to impose topological constraints on the nonlinear evolution of the instability and thus to play an important role in the determination of the nonlinear state of the plasma.