  The recent proliferation of computers and the internet have opened new
opportunities for collecting and processing data. However, such data are often
obtained without a well-planned probability survey design. Such non-probability
based samples cannot be automatically regarded as representative of the
population of interest. Several classes of methods for estimation and
inferences from non-probability samples have been developed in recent years.
The quasi-randomization methods assume that non-probability sample selection is
governed by an underlying latent random mechanism. The basic idea is to use
information collected from a probability ("reference") sample to uncover latent
non-probability survey participation probabilities (also known as "propensity
scores") and use them in estimation of target finite population parameters. In
this paper, we review and compare theoretical properties of recently developed
methods of estimation survey participation probabilities and study their
relative performances in simulations.
