R: Pseudo goodness-of-fit test for a normal mixture model

NMixPseudoGOF {mixAK}

R Documentation

Pseudo goodness-of-fit test for a normal mixture model

Description

It takes a (fitted) normal mixture, creates hyperrectangles according to a specified grid, computes probability masses in each hyperrectangle derived from the (fitted) normal mixture. From computed probability masses expected frequencies (using the sample size of supplied data) are computed and compared to frequencies observed in supplied data. From expected and observed frequencies, a Pearson chi-squared like statistic is computed and returned together with residuals derived from that statistic.

Also pseudo degrees of freedom are returned which are equal to a number of hyperrectangles minus number of free parameters of the normal mixture. For a K-component mixture of dimension p, the number of free parameters is computed as

q = K-1 + K\cdot p + K\cdot p(p+1)/2

Note that computation of q does not take into account the positive (semi-)definiteness restriction on covariance matrices.

WARNING: There is no statistical theory developed that would guarantee that computed chi-squared like statistics follows a chi-squared distribution with computed pseudo degrees of freedom under the null hypothesis that the distribution that generated the data is a normal mixture. This function serves purely for descriptive purposes!

Usage

NMixPseudoGOF(x, ...)

## Default S3 method:
NMixPseudoGOF(x, scale, w, mu, Sigma, breaks, nbreaks=10, digits=3, ...)

## S3 method for class 'NMixMCMC'
NMixPseudoGOF(x, y, breaks, nbreaks=10, digits=3, ...)

Arguments

`x`	data object (see argument `y` below) for `NMixPseudoGOF.default` function. An object of class `NMixMCMC` for `NMixPseudoGOF.NMixMCMC` function.
`y`	a numeric vector, matrix or data frame with the data. It is a numeric vector if `p` is one. It is a matrix or data frame with `p` columns if `p > 1`.
`scale`	a two component list giving the `shift` and the `scale`. If not given, shift is equal to zero and scale is equal to one.
`w`	a numeric vector with mixture weights. The length of this vector determines the number of mixture components.
`mu`	a matrix with mixture means in rows. That is, `mu` has `K` rows and `p` columns, where `K` denotes the number of mixture components and `p` is dimension of the mixture distribution.
`Sigma`	a list with mixture covariance matrices.
`breaks`	a numeric vector or a list with the breaks defining the hyperrectangles. It is a numeric vector if `p` is equal to one. It is a list of length `p` of numeric vectors. Each component of the list determines the breaks for each margin.
`nbreaks`	a number or a numeric vector with the number of breaks for each margin. It is only used if the argument `breaks` is not given to determine sensible break values.
`digits`	a number or a numeric vector with the number of digits to which the breaks should be rounded in the case they are created by the function. If it is a vector then different rounding may be used for each margin.
`...`	optional additional arguments.

Value

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