checkNorm {synlik}

Checking the multivariate normal approximation.

Description

Given an object of class synlik this routine provides a graphical check of whether the distribution of the random summary statistics is multivariate normal.

Usage

checkNorm(object, param = object@param, nsim = 1000, observed = NULL,
  cex.axis = 1, cex.lab = 1, ...)

Arguments

object

An object of class synlik or a matrix where each row is a random vector.

param

A vector of model's parameters at which the summary statistics will be simulated.

nsim

number of summary statistics to be simulated if object is of class synlik, otherwise it is not used.

observed

A vector of observed summary statistics. By default NULL, so object@data will be used as observed statistics. It will be looked at only if object is a matrix.

cex.axis

Axis scale expansion factor.

cex.lab

Axis label expansion factor.

...

additional arguments to be passed to object@simulator and object@summaries. In general I would avoid using it and including in object@extraArgs everything they need.

Details

The method is from section 7.5 of Krzanowski (1988). The replicate vectors of summary statistic S are transformed to variables which should be univariate chi squared r.v.s with DoF given by the number of rows of S. An appropriate QQ-plot is produced, and the proportion of the data differing substantially from the ideal line is reported. Deviations at the right hand end of the plot indicate that the tail behaviour of the Normal approximation is poor: in the context of synthetic likelihood this is of little consequence. Secondly, s is transformed to a vector which should be i.i.d. N(0,1) under multivariate normality, and a QQ plot is produced. Unfortunately this approach is not very useful unless the dimension of s is rather large. In simulations, perfectly MVN data produce highly variable results, so that the approach lacks any real power.

Value

Mainly produces plots and prints output. Also an array indicating proportion of simulated statistics smaller than observed.

Author(s)

Simon N. Wood, maintained by Matteo Fasiolo <[e-mail]>.

References

Krzanowski, W.J. (1988) Principles of Multivariate Analysis. Oxford.

Examples

#### Create Object
data(ricker_sl)

#### Simulate from the object
ricker_sl@data <- simulate(ricker_sl)
ricker_sl@extraArgs$obsData <- ricker_sl@data 

#### Checking multivariate normality
checkNorm(ricker_sl)

# With matrix input
checkNorm(matrix(rnorm(200), 100, 2))