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binest

Estimation of group-level means and standard deviations from binned (coarsened) count data. All three functions fit the same heteroskedastic ordered probit (HETOP) model, in which each group’s values are normally distributed around a mean and SD of its own. They differ only in how they fit it, and they share a common output structure:

• fast_hetop() — fits each group separately, solving closed-form truncated-normal score equations. Linear in the number of groups times the number of bins. This is the preferred function in the package.
• mle_hetop() — maximizes the likelihood over all groups at once. Returns the same estimates as fast_hetop(estimator = "ML"), far more slowly. Deprecated in favor of fast_hetop().
• fh_hetop() — fits the model by MCMC, placing a prior over the group parameters and reporting posterior means. Deprecated in favor of fast_hetop().

This package was previously called HETOP and was maintained by J. R. Lockwood; it is renamed and extended to reflect the broader functionality now included.

Installation

# install.packages("remotes")
remotes::install_github("paulvonhippel/binest")

(Or install.packages("binest") for the released version on CRAN.)

A quick example

library(binest)
data(tx_g6_math_2018)

ngk <- with(tx_g6_math_2018,
            cbind(unsatisfactory, approaches, meets, masters))
cuts <- c(1536, 1653, 1772)

## `scope` is required: Texas reports counts for every tested student,
## so each district's students are its whole population and the only
## uncertainty is the binning. Use scope = "sample" when the units are
## a sample from a larger population, which adds sampling error to the
## reported SEs.
fit <- fast_hetop(ngk, cutpoints_known = TRUE, cutpoints = cuts,
                  scope = "population")
cor(fit$est_raw$mean, tx_g6_math_2018$reported_mean)

See vignette("binest") for a full comparison of the three functions on the Texas STAAR Grade 6 mathematics data.

References

• Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London A, 222, 309-368.
• Lockwood, J. R., Castellano, K. E., & Shear, B. R. (2018). Flexible Bayesian models for inferences from coarsened, group-level achievement data. JEBS, 43(6), 663-692.
• Reardon, S. F., Shear, B. R., Castellano, K. E., & Ho, A. D. (2017). Using heteroskedastic ordered probit models to recover moments of continuous test score distributions from coarsened data. JEBS, 42(1), 3-45.
• Sheppard, W. F. (1898). On the calculation of the most probable values of frequency-constants for data arranged according to equidistant divisions of a scale. PLMS, 29, 353-380.

License

GPL (>= 2).

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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