PIT: Non-randomized Probability Integral Transformation In glarma: Generalized Linear Autoregressive Moving Average Models

Description

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

Usage

 ```1 2``` ```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" <[email protected]> and "Cenanning Li" <[email protected]>

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

 ```1 2 3 4 5 6 7 8 9``` ```### 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) ```

glarma documentation built on Feb. 9, 2018, 6:08 a.m.