For a non-probability sample, Meng (2018) decomposes the error of the sample
mean into the data-defect correlation (rho, the population correlation between
the target variable and the participation indicator), the sampling fraction and
the problem difficulty. The effective sample size a probability sample would need
to match the same mean-squared error is
$$n_{\mathrm{eff}} = \frac{f/(1-f)}{\rho^2}, \qquad f = n/N,$$
which does not depend on the outcome except through rho. Because rho on the
target variable is not observable from the sample alone, data_defect() returns
the effective size across a grid of plausible residual rho (read it as an
ignorance range, not a single number), plus the measurable selection strength on
the covariates used for pseudo-weighting (the largest correlation between an
auxiliary and participation, which pseudo-weighting neutralises).
Usage
data_defect(object, ddc_grid = c(0.001, 0.005, 0.01, 0.05, 0.1))Arguments
- object
a prepped non-probability
weighting_spec(fromprep(), built withweighting_spec(..., nonprob = TRUE)).- ddc_grid
the residual data-defect correlations to tabulate. Positive values; only their magnitude matters.
Value
a list (class weightflow_data_defect) with the sample size n, the
estimated population size N (the sum of the final weights), the fraction f,
the sensitivity grid (ddc, n_eff), and aux, a data frame of the
covariate-participation correlations (or NULL when the recipe has no
pseudo-weighting step).
References
Meng, X.-L. (2018). Statistical paradises and paradoxes in big data (I). Annals of Applied Statistics 12(2), 685-726.