  In this paper, we make a deep analysis for the five typical interacting
holographic dark energy models with the interaction terms $Q=3\beta
H_{0}\rho_{\rm{de}}$, $Q=3\beta H_{0}\rho_{\rm{c}}$, $Q=3\beta
H_{0}(\rho_{\rm{de}}+\rho_{\rm c})$, $Q=3\beta
H_{0}\sqrt{\rho_{\rm{de}}\rho_{\rm c}}$, and $Q=3\beta
H_{0}\frac{\rho_{\rm{de}}\rho_{c}}{\rho_{\rm{de}}+\rho_{\rm c}}$, respectively.
We obtain observational constraints on these models by using the type Ia
supernova data (the Joint Light-curve Analysis sample), the cosmic microwave
background data (Planck 2015 distance priors), the baryon acoustic oscillations
data, and the direct measurement of the Hubble constant. We find that the
values of $\chi_{\rm min}^2$ for all the five models are almost equal
(around~699), indicating that the current observational data equally favor
these IHDE models. In addition, a comparison with the cases of interaction term
involving the Hubble parameter $H$ is also made.
