  In this paper, we examine two types of interacting holographic dark energy
model using Pantheon supernova data, BAO BOSS DR12, CMB Planck 2015, fgas (gas
mass fraction) and SZ/Xray (Sunyaev-Zeldovich effect and X-ray emission) data
from galaxy clusters (GC). In particular, we considered the Holographic Ricci
dark energy and Extended holographic Ricci dark energy models. During this
analysis we considered seven type of phenomenological interaction terms (three
linear and four non-linear) $Q_1=3Hb\rho_{D}$, $Q_2=3Hb\rho_{m}$,
$Q_3=3Hb\left(\rho_{D}+\rho_m\right)$,
$Q_4=3Hb\left(\rho_{D}+\frac{\rho_{D}^2}{\rho_{D}+\rho_m}\right)$,
$Q_5=3Hb\left(\rho_{m}+\frac{\rho_{m}^2}{\rho_{D}+\rho_m}\right)$,
$Q_6=3Hb\left(\rho_{D}+\rho_{m}+\frac{\rho_{D}^2}{\rho_{D}+\rho_m}\right)$,
$Q_7=3Hb\left(\rho_{D}+\rho_{m}+\frac{\rho_{m}^2}{\rho_{D}+\rho_m}\right)$
respectively. To find the best model we apply Akaike Information Criterion
(AIC) and Bayesian Information Criterion (BIC) and use the $\Lambda$CDM as the
referring model for comparison. Using AIC and BIC models selection method we
note that the $Q_1$ and $Q_4$ interaction terms are favored by observational
data within the context of the holographic Ricci dark energy models. The
obtained results also demonstrated that the considered types of holographic
Ricci dark energy model are not favored by observational data since the
$\Lambda$CDM is considered as the reference model. We also observed that the
values of the deceleration parameter and the transition redshift for all models
are compatible with the latest observational data and Planck 2015. In addition,
we studied the jerk parameter for all models. Using our modified CAMB code, we
observed that the interacting models suppress the CMB spectrum at low
multi-poles and enhances the acoustic peaks.
