  This paper addresses the item ranking problem with associate covariates,
focusing on scenarios where the preference scores can not be fully explained by
covariates, and the remaining intrinsic scores, are sparse. Specifically, we
extend the pioneering Bradley-Terry-Luce (BTL) model by incorporating covariate
information and considering sparse individual intrinsic scores. Our work
introduces novel model identification conditions and examines the regularized
penalized Maximum Likelihood Estimator (MLE) statistical rates. We then
construct a debiased estimator for the penalized MLE and analyze its
distributional properties. Additionally, we apply our method to the
goodness-of-fit test for models with no latent intrinsic scores, namely, the
covariates fully explaining the preference scores of individual items. We also
offer confidence intervals for ranks. Our numerical studies lend further
support to our theoretical findings, demonstrating validation for our proposed
method
