countSTAR (version 1.0.2)

predict.lmstar: Predict method for response in STAR linear model

Description

Outputs predicted values based on an lmstar fit and optionally prediction intervals based on the the (plug-in) predictive distribution for the STAR linear model

Usage

# S3 method for lmstar
predict(object, newdata = NULL, interval = FALSE, level = 0.95, N = 1000, ...)

Value

Either a a vector of predictions (if interval=FALSE) or a matrix of predictions and bounds with column names fit, lwr, and upr

Arguments

object

Object of class "lmstar" as output by lm_star

newdata

An optional matrix/data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

interval

logical; whether or not to include prediction intervals (default FALSE)

level

Level for prediction intervals

N

number of Monte Carlo samples from the posterior predictive distribution used to approximate intervals; default is 1000

...

Ignored

Details

If interval=TRUE, then predict.lmstar uses a Monte Carlo approach to estimating the (plug-in) predictive distribution for the STAR linear model. The algorithm iteratively samples (i) the latent data given the observed data, (ii) the latent predictive data given the latent data from (i), and (iii) (inverse) transforms and rounds the latent predictive data to obtain a draw from the integer-valued predictive distribution.

The appropriate quantiles of these Monte Carlo draws are computed and reported as the prediction interval.

Examples

# Simulate data with count-valued response y:
x = seq(0, 1, length.out = 100)
y = rpois(n = length(x), lambda = exp(1.5 + 5*(x -.5)^2))

# Estimate model--assume a quadratic effect (better for illustration purposes)
fit = lm_star(y~x+I(x^2), transformation = 'sqrt')

#Compute the predictive draws for the test points (same as observed points here)
#Also compute intervals using plug-in predictive distribution
y_pred = predict(fit, interval=TRUE)

# Plot the results
plot(x, y, ylim = range(y, y_pred), main = 'STAR: Predictions and 95% PI')
lines(x,y_pred[,"fit"], col='black', type='s', lwd=4)
lines(x, y_pred[,"lwr"], col='darkgray', type='s', lwd=4)
lines(x, y_pred[,"upr"], col='darkgray', type='s', lwd=4)