Non-randomized Probability Integral Transformation

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Description

Functions to produce the non-randomized probability integral transform (PIT) to check the adequacy of the distributional assumption of the GLARMA model.

Usage

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glarmaPredProb(object)
glarmaPIT(object, bins = 10)

Arguments

object

An object of class "glarma", obtained from a call to glarma.

bins

Numeric; the number of bins used in the PIT.

Details

These functions are used for the assessment of predictive distributions in discrete data. They obtain the predictive probabilities and the probability integral transformation for a fitted GLARMA model.

Value

glarmaPredProb returns a list with values:

upper

the predictive cumulative probabilities used as the upper bound for computing the non-randomized PIT.

lower

the predictive cumulative probabilities used as the lower bound for computing the non-randomized PIT.

glarmaPIT returns a list with values:

upper

the predictive cumulative probabilities used as the upper bound for computing the non-randomized PIT.

lower

the predictive cumulative probabilities used as the lower bound for computing the non-randomized PIT.

conditionalPIT

the conditional probability integral transformation given the observed counts.

PIT

the probability integral transformation.

Author(s)

"David J. Scott" <d.scott@auckland.ac.nz> and "Cenanning Li" <cli113@aucklanduni.ac.nz>

References

Czado, Claudia and Gneiting, Tilmann and Held, Leonhard (2009) Predictive model assessment for count data. Biometrics, 65, 1254–1261.

Jung, Robert.C and Tremayne, A.R (2011) Useful models for time series of counts or simply wrong ones? Advances in Statistical Analysis, 95, 59–91.

Examples

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### Example from Davis, Dunsmuir Wang (1999)
## MA(1,2,5), Pearson Residuals, Fisher Scoring
data(Polio)
y <- Polio[, 2]
X <- as.matrix(Polio[, 3:8])
glarmamod <- glarma(y, X, thetaLags = c(1,2,5), type = "Poi", method = "FS",
                    residuals = "Pearson", maxit = 100, grad = 2.22e-16)
glarmaPredProb(glarmamod)
glarmaPIT(glarmamod)