GOF: GammaModel::GOF
In UCL/GammaModel: Modelling age-at-death profiles using the Gamma distribution

Description Usage Arguments Details Value References Examples

View source: R/functions.R

Estimates Goodness of Fit of the counts to the age-class model, using the Chi-squared test.

1	GOF(counts, model, N = 1e+04)

`counts`	A one-row data frame comprising integer counts, with column names in capital letters. Formatting requirements detailed in `checkCountsFormat`.
`model`	A one-row data frame specifying the age-class model probabilities. Age-classes as column names.
`N`	Positive integer specifying the number of random arrangements to generate.

The general approach to calculating a p-value for n observed counts given the model probabilities is to calculate the probability of each possible arrangement of the n counts, then sum the probabilities that are smaller or equal to the probability of the observed arrangement.

This approach can be easily achieved if each count was assigned to only one class, but becomes computationally expensive when dealing with the additional problem of multi-class assignments.

Instead, the p-value can be estimated by generating random arrangements of the observed data (this naturally takes care of the different frequencies of each arrangement), calculating a p-value for each using a chi- squared test, then calculating the mean p-value. With a large number of random arrangements this approaches the exact probability of the observed data being as or more extreme.

This should not be confused methods of combining p-values such as Fisher's, which solves the different problem of combining p-values from independent trials.

P-value in scientific notation, with two significant figures.

Pearson, K., 1900. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 50, 157-175

    # How well does the 'FON1' data fit Payne's meat model 
    data(Neolithic)
    data(models.payne)
    counts <- Neolithic['FON1',] 
    model <- models.payne['meat',]
    GOF(counts, model)