coconots (version 2.0.1)

cocoPit: Probability Integral Transform Based Model Assessment Procedure

Description

Computes the probability integral transform (PIT) and provides the non-randomized PIT histogram for assessing absolute performance of a fitted model as proposed by Czado et al. (2009).

Usage

cocoPit(coco, J = 10, conf.alpha = 0.05, julia = FALSE)

Value

an object of class cocoPit. It contains the probability integral transform values, p-value of the chi-square goodness of fit test and information on the model specifications.

Arguments

coco

An object of class coco

J

Number of bins for the histogram (default: 10)

conf.alpha

Significance level for the confidence intervals (default: 0.05)

julia

if TRUE, the PIT is computed with julia (default: FALSE)

Author

Manuel Huth

Details

The adequacy of a distributional assumption for a model is assessed by checking the cumulative non-randomized PIT distribution for uniformity. A useful graphical device is the PIT histogram, which displays this distribution to J equally spaced bins. We supplement the graph by incorporating approximately \(100(1 - \alpha)\%\) confidence intervals obtained from a standard chi-square goodness-of-fit test of the null hypothesis that the J bins of the histogram are drawn from a uniform distribution. For details, see Jung, McCabe and Tremayne (2016).

References

Czado, C., Gneiting, T. and Held, L. (2009) Predictive model assessment for count data. Biometrics 65, 1254--61.

Jung, R. C., McCabe, B.P.M. and Tremayne, A.R. (2016). Model validation and diagnostics. In Handbook of Discrete Valued Time Series. Edited by Davis, R.A., Holan, S.H., Lund, R. and Ravishanker, N.. Boca Raton: Chapman and Hall, pp. 189--218.

Jung, R. C. and Tremayne, A. R. (2011) Convolution-closed models for count time series with applications. Journal of Time Series Analysis, 32, 3, 268--280.

Examples

lambda <- 1
alpha <- 0.4
set.seed(12345)
data <- cocoSim(order = 1, type = "Poisson", par = c(lambda, alpha), length = 100)
fit <- cocoReg(order = 1, type = "Poisson", data = data)

#PIT R implementation
pit_r <- cocoPit(fit)
plot(pit_r)