Inference for the Bernoulli distribution

Functions involved in making inferences about the probability of success in a Bernoulli distribution.

fit_bernoulli(data)

# S3 method for bernoulli
logLikVec(object, pars = NULL, ...)

# S3 method for bernoulli
nobs(object, ...)

# S3 method for bernoulli
coef(object, ...)

# S3 method for bernoulli
vcov(object, ...)

# S3 method for bernoulli
logLik(object, ...)

# S3 method for bernoulli
alogLik(x, cluster = NULL, use_vcov = TRUE, ...)

Arguments

data

A numeric vector of outcomes from Bernoulli trials: 0 for a failure, 1 for a success. Alternatively, a logical vector with FALSE for a failure and TRUE for a success.

pars

A numeric parameter vector of length 1 containing the value of the Bernoulli success probability.

...

Further arguments to be passed to the functions in the sandwich package meat (if cluster = NULL), or meatCL (if cluster is not NULL).

x, object

A fitted model object returned from fit_bernoulli().

cluster

A vector or factor indicating from which cluster each observation in data originates.

use_vcov

A logical scalar. Should we use the vcov S3 method for x (if this exists) to estimate the Hessian of the independence loglikelihood to be passed as the argument H to adjust_loglik? Otherwise, H is estimated inside adjust_loglik using optimHess.

Value

fit_bernoulli returns an object of class "bernoulli", a list with components: logLik, mle, nobs, vcov, data, obs_data, where data are the input data and obs_data are the input data after any missing values have been removed, using na.omit.

logLikVec.bernoulli returns an object of class "logLikVec", a vector length length(data) containing the likelihood contributions from the individual observations in data.

Details

fit_bernoulli: fit a Bernoulli distribution

logLikVec.bernoulli: calculates contributions to a loglikelihood based on the Bernoulli distribution. The loglikelihood is calculated up to an additive constant.

nobs, coef, vcov and logLik methods are provided.

See also

Binomial. The Bernoulli distribution is the special case where size = 1.

Examples

# Set up data
x <- exdex::newlyn
u <- quantile(x, probs = 0.9)
exc <- x > u

# Fit a Bernoulli distribution
fit <- fit_bernoulli(exc)

# Calculate the loglikelihood at the MLE
res <- logLikVec(fit)

# The logLik method sums the individual loglikelihood contributions.
logLik(res)
#> 'log Lik.' -939.9109 (df=1)

# nobs, coef, vcov, logLik methods for objects returned from fit_bernoulli()
nobs(fit)
#> [1] 2894
coef(fit)
#>       prob 
#> 0.09986178 
vcov(fit)
#>              prob
#> prob 3.106061e-05
logLik(fit)
#> 'log Lik.' -939.9109 (df=1)

# Adjusted loglikelihood
# Create 5 clusters each corresponding approximately to 1 year of data
cluster <- rep(1:5, each = 579)[-1]
afit <- alogLik(fit, cluster = cluster, cadjust = FALSE)
summary(afit)
#>          MLE       SE adj. SE
#> prob 0.09986 0.005573 0.01831