Probability Integral Transform Based Model Assessment Procedure
Probability Integral Transform Based Model Assessment Procedure
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).
cocoPit(coco, J =10, conf.alpha =0.05, julia =FALSE)
Arguments
coco: An object of class coco
J: Number of bins for the histogram (default: 10)
conf.alpha: Confidence level for the confidence bands.
julia: if TRUE, the PIT is computed with Julia.
Returns
an object of class cocoPit. It contains the The probability integral transform values, its p-values and information on the model specifications.
Details
The adequacy of a distributional assumption for a model is checked 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−α)% 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).
Examples
lambda <-1alpha <-0.4set.seed(12345)data <- cocoSim(order =1, type ="Poisson", par = c(lambda, alpha), length =100)#julia_installed = TRUE ensures that the fit object#is compatible with the julia cocoPit implementation fit <- cocoReg(order =1, type ="Poisson", data = data)#PIT R implementationpit_r <- cocoPit(fit)
References
Czado, C., Gneiting, T. and Held, L. (2009) Predictive model assessment for count data. Biometrics 65 , 1254--61.
Jung, Robert C., Brendan P. M. McCabe, and Andrew R. Tremayne. (2016). Model validation and diagnostics. In Handbook of Discrete Valued Time Series. Edited by Richard A. Davis, Scott H. Holan, Robert Lund and Nalini Ravishanker. 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.