Recover the "discoverability coefficient".

Description

Estimates the effect of the degree on the rate of sampling. Also known as the "coefficient of discoverability" in the oil-discovery literature [2]. Formally, we estimate theta and beta_0 assuming that beta_k:= beta_0 * k^theta.

Usage

1
  getTheta(rds.object, bin=1, robust=TRUE)

Arguments

rds.object

A rds-object with a estimates component as returned by estimate.b.k

bin

Bin degree counts. See Note.

robust

Should beta_0 and theta be recovered from beta_k using a robust method (default) or not.

Value

A list including the following components:

log.beta_0

The log of beta_0 in beta_k:= beta_0 * k^theta.

theta

theta in beta_k:= beta_0 * k^theta.

Note

If degree counts have been binned by initializeRdsObject (for variance reduction), the same value has to be supplied to getTheta for correct estimation.

Author(s)

Jonathan D. Rosenblatt john.ros.work@gmail.com

References

[1] Berchenko, Yakir, Jonathan Rosenblatt, and Simon D. W. Frost. "Modeling and Analyzing Respondent Driven Sampling as a Counting Process."" arXiv:1304.3505. HTTP://arXiv.org/abs/1304.3505. [2] Bloomfield, P., K.S. Deffeyes, B. Silverman, G.S. Watson, Y. Benjamini, and R.A. Stine. Volume and Area of Oil Fields and Their Impact on Order of Discovery, 1980. http://www.osti.gov/scitech/servlets/purl/6037591.

See Also

estimate.b.k, initializeRdsObject, makeRdsSample

Examples

1
# See in estimate.b.k()