cv4postpr: Leave-one-our cross validation for model selection ABC
In bcm-uga/abc: Tools for Approximate Bayesian Computation (ABC)

Description Usage Arguments Details Value See Also Examples

This function performs a leave-one-out cross validation for model selection with ABC via subsequent calls to the function postpr.

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cv4postpr(index, sumstat, postpr.out = NULL, nval, tols, method,
subset = NULL, kernel = "epanechnikov", numnet = 10, sizenet = 5, lambda
= c(0.0001,0.001,0.01), trace = FALSE, maxit = 500, ...)

`index`	a vector of model indices. It can be character or numeric and will be coerced to factor. It must have the same length as the number of rows in `sumstat` to indicate which row of `sumstat` belong to which model.
`sumstat`	a vector, matrix or data frame of the simulated summary statistics.
`postpr.out`	an object of class `"postpr"`, optional. If supplied, all arguments passed to `postpr` are extracted from this object, except for `sumstat`, `index`, and `tols`, which always have to be supplied as arguments.
`nval`	the size of the cross-validation sample for each model.
`tols`	a single tolerance rate or a vector of tolerance rates.
`method`	a character string indicating the type of simulation required. Possible values are `"rejection"`, `"mnlogistic"`, `"neuralnet"`. See `postpr` for details.
`subset`	a logical expression indicating elements or rows to keep. Missing values in `index` and/or `sumstat` are taken as `FALSE`.
`kernel`	a character string specifying the kernel to be used when `method` is `"loclinear"` or `"neuralnet"`. Defaults to `"epanechnikov"`. See `density` for details.
`numnet`	the number of neural networks when `method` is `"neuralnet"`. Defaults to 10. It indicates the number of times the function `nnet` is called.
`sizenet`	the number of units in the hidden layer. Defaults to 5. Can be zero if there are no skip-layer units. See `nnet` for more details.
`lambda`	a numeric vector or a single value indicating the weight decay when `method` is `"neuralnet"`. See `nnet` for more details. By default, 0.0001, 0.001, or 0.01 is randomly chosen for each of the networks.
`trace`	logical, `TRUE` switches on tracing the optimization of `nnet`. Applies only when `method` is `"neuralnet"`.
`maxit`	numeric, the maximum number of iterations. Defaults to 500. Applies only when `method` is `"neuralnet"`. See also `nnet`.
`...`	other arguments passed to `nnet`.

For each model, a simulation is selected repeatedly to be a validation simulation, while the other simulations are used as training simulations. Each time the function postpr is called to estimate the parameter(s).

Ideally, we want nval to be equal to the number of simulations for each model, however, this might take too much time. Users are warned not to choose a too large number of simulations (especially when the neural networks are used). Beware that the actual number of cross-validation estimation steps that need to be performed is nval*the number of models.

The arguments for the function postpr can be supplied in two ways. First, simply give them as arguments when calling this function, in which case postpr.out can be NULL. Second, via an existing object of class "postpr", here postpr.out. WARNING: when postpr.out is supplied, the same sumstat and param objects have to be used as in the original call to postpr. Column names of sumstat and param are checked for match.

See summary.cv4postpr for calculating the prediction error from an object of class "cv4postpr" and plot.cv4postpr for visualizing the misclassification of the models using barplots.

An object of class "cv4postpr", which is a list with the following elements

`call`	The original calls to `postpr` for each tolerance rates.
`cvsamples`	Numeric vector of length `nval`*the number of models, indicating which rows of `sumstat` were used as validation values.
`tols`	The tolerance rates.
`true`	The true models.
`estim`	The estimated model probabilities.
`method`	The method used.
`names`	A list of two elements: `model` contains the model names, and `statistics.names` the names of the summary statistics.
`seed`	The value of `.Random.seed` when `cv4postpr` is called.

postpr, summary.cv4postpr, plot.cv4postpr

require(abc.data)
data(human)
###Reduce the sample size of the simulations to reduce the running time.
###Do not do that with your own data!
ss<-c(1:1000,50001:51000,100001:101000)
cv.modsel <- cv4postpr(models[ss], stat.3pops.sim[ss,], nval=5, tols=c(.05,.1), method="rejection") 
summary(cv.modsel)
plot(cv.modsel, names.arg=c("Bottleneck", "Constant", "Exponential"))