betta_random: modelling total diversity with random effects

Description

This function extends betta() to permit random effects modelling.

Usage

betta_random(chats, ses, X = NA, groups)

Arguments

chats

A vector of estimates of total diversity at different sampling locations.

ses

The standard errors in chats, the diversity estimates.

A numeric matrix of covariates corresponding to fixed effects. If not supplied, an intercept-only model will be fit.

groups

A categorical variable representing the random-effects groups that each of the estimates belong to.

Value

table: A coefficient table for the model parameters. The columns give the parameter estimates, standard errors, and p-values, respectively. This model is only as effective as your diversity estimation procedure; for this reason please confirm that your estimates are appropriate and that your model is not misspecified. betta_pic may be useful for this purpose.
cov: Estimated covariance matrix of the parameter estimates.
ssq_u: The estimate of the heterogeneity variance.
ssq_g: Estimates of within-group variance. The estimate will be zero for groups with only one observation.
homogeneity: The test statistic and p-value for the test of homogeneity.
global: The test statistic and p-value for the test of model explanatory power.
blups: The conditional expected values of the diversity estimates (conditional on the random effects). Estimates of variability for the random effects case are unavailable at this time; please contact the maintainer if needed.

References

Willis, A., Bunge, J., and Whitman, T. (2015). Inference for changes in biodiversity. arXiv preprint.

Examples

Run this code

betta_random(c(2000, 3000, 4000, 3000), c(100, 200, 150, 180),
             X = cbind("Int"=1, "Cont_var"=c(100, 150, 100, 50)),
             groups = c("a", "a", "a", "b"))

## handles missing data
betta_random(c(2000, 3000, 4000, 3000), c(100, 200, 150, NA),
             groups= c("a", NA, "b", "b"))