We model the nonresponse probabilities as logistic functions of the outcome variable and other covariates in the survey sampling study with callback. The identification aspect of this callback model is investigated. Semi-parametric maximum likelihood estimators of the parameters in the response probabilities are proposed and studied. As a result, an efficient estimator of the mean of the outcome variable is constructed using the estimated response probabilities. Moreover, if a regression model for conditional mean of the out-come variable given some covariate is available, then we can obtain an even more efficient estimate of the mean of the outcome variable by fitting the regression model using an adjusted least squares method based on the estimated underlying distributions of the observed values. Simulation results show the proposed method is more efficient compared with some existing competitors. The method is applied to data from a survey of health spending in a population of individuals aged 50-70 years, where non-response can may be related to health.