  Nonresponse is present in almost all surveys and can severely bias estimates.
It is usually distinguished between unit and item nonresponse: in the former,
we completely fail to have information from a unit selected in the sample,
while in the latter, we observe only part of the information on the selected
unit. Unit nonresponse is usually dealt with by reweighting: each unit selected
in the sample has associated a sampling weight and an unknown response
probability; the initial sampling weight is multiplied by the inverse of
estimated response probability. Item nonresponse is usually dealt with by
imputation. By noting that for a particular survey variable, we just have
observed and unobserved values, in this work we exploit the connection between
unit and item nonresponse. In particular, we assume that the factors that drive
unit response are the same as those that drive item response on selected
variables of interest. Response probabilities are then estimated by using a
logistic regression with a latent covariate that measures such will to respond
and that can explain part of the unknown behavior of a unit to participate in
the survey. The latent covariate is estimated using latent trait models. Such
approach is particularly relevant for sensitive items and, therefore, can
handle non-ignorable nonresponse. Auxiliary information known for both
respondents and nonrespondents can be included either in the latent variable
model or in the logistic model. The approach can be also used when auxiliary
information is not available, and we focus here on this case. The theoretical
properties of the proposed estimators are sketched and simulations studies are
conducted to illustrate their finite size sample performance.
