summary.singleRmargin function

Statistical tests of goodness of fit

Performs two statistical test on observed and fitted marginal frequencies. For G test the test statistic is computed as: \loadmathjax

\mjsdeqn G = 2\sum _kO_k\ln \left (\frac O_kE_k\right )

and for \mjseqn \chi ^2 the test statistic is computed as: \mjsdeqn \chi ^2 = \sum _k\frac \left (O_k-E_k\right )^2E_k

where \mjseqn O_k,E_k denoted observed and fitted frequencies respectively. Both of these statistics converge to \mjseqn \chi ^2 distribution asymptotically with the same degrees of freedom.

The convergence of \mjseqn G, \chi ^2 statistics to \mjseqn \chi ^2 distribution may be violated if expected counts in cells are too low, say < 5, so it is customary to either censor or omit these cells.

## S3 method for class 'singleRmargin'
summary(object, df, dropl5 = c("drop", "group", "no"), ...)

Arguments

• object: object of singleRmargin class.
• df: degrees of freedom if not provided the function will try and manually but it is not always possible.
• dropl5: a character indicating treatment of cells with frequencies < 5 either grouping them, dropping or leaving them as is. Defaults to drop.
• ...: currently does nothing.

Returns

A chi squared test and G test for comparison between fitted and observed marginal frequencies.

Examples

# Create a simple model
Model <- estimatePopsize(
  formula = capture ~ ., 
  data = netherlandsimmigrant, 
  model = ztpoisson, 
  method = "IRLS"
)
plot(Model, "rootogram")
# We see a considerable lack of fit
summary(marginalFreq(Model), df = 1, dropl5 = "group")