lnre.goodness.of.fit {zipfR}

Goodness-of-fit Evaluation of LNRE Models (zipfR)

Description

This function measures the goodness-of-fit of a LNRE model compared to an observed frequency spectrum, using a multivariate chi-squared test (Baayen 2001, p. 119ff).

Usage

  lnre.goodness.of.fit(model, spc, n.estimated=0, m.max=15)

Arguments

model

an LNRE model object, belonging to a suitable subclass of lnre.

spc

an observed frequency spectrum, i.e. an object of class spc. This can either be the spectrum on which the model parameters have been estimated, or a different, independent spectrum.

n.estimated

number of parameters of the LNRE model that have been estimated on spc. This number is automatically subtracted from the degrees of freedom of the resulting chi-squared statistic. When spc is an independent spectrum, n.estimated should always be set to the default value of 0.

m.max

number of spectrum elements that will be used to compute the chi-squared statistic. The default value of 15 is also used by Baayen (2001). For small samples, it may be sensible to use fewer spectrum elements, e.g. by setting m.max=10 or m.max=5. Depending on how many degrees of freedom have to be subtracted, m.max should not be chosen too low.

Details

By default, the number of spectrum elements included in the calculation of the chi-squared statistic may be reduced automatically in order to ensure that it is not dominated by the sampling error of spectrum elements with very small expected frequencies (which are scaled up due to the small variance of these random variables). As an ad-hoc rule of thumb, spectrum elements V_m with variance less than 5 are excluded, since the normal approximation to their discrete distribution is likely to be inaccurate in this case.

Automatic reduction is disabled when the parameter m.max is specified explicitly (use m.max=15 to disable automatic reduction without changing the default value).

Value

A data frame with one row and the following variables:

X2

value of the multivariate chi-squared statistic X^2

df

number of degrees of freedom of X^2, corrected for the number of parameters that have been estimated on spc

p

p-value corresponding to X^2

References

Baayen, R. Harald (2001). Word Frequency Distributions. Kluwer, Dordrecht.

See Also

lnre for more information about LNRE models

Examples

## load spectrum of first 100k Brown tokens
data(Brown100k.spc)

## use this spectrum to compute zm and gigp
## models
zm <- lnre("zm",Brown100k.spc)
gigp <- lnre("gigp",Brown100k.spc)

## lnre.goodness.of.fit with appropriate
## n.estimated value produces the same multivariate
## chi-squared test that is reported in a model
## summary

## compare:
zm
lnre.goodness.of.fit(zm,Brown100k.spc,n.estimated=2)

gigp
lnre.goodness.of.fit(gigp,Brown100k.spc,n.estimated=3)

## goodness of fit of the 100k models calculated on the
## whole Brown spectrum (although this is superset of
## 100k spectrum, let's pretend it is an independent
## spectrum, and set n.estimated to 0)

data(Brown.spc)

lnre.goodness.of.fit(zm,Brown.spc,n.estimated=0)
lnre.goodness.of.fit(gigp,Brown.spc,n.estimated=0)