summary.singleRmargin {singleRcapture}

Statistical tests of goodness of fit.

Description

Performs two statistical test on observed and fitted marginal frequencies. For G test the test statistic is computed as: \[G = 2\sum_{k}O_{k}\ln{\left(\frac{O_{k}}{E_{k}}\right)}\] and for \(\chi^{2}\) the test statistic is computed as: \[\chi^{2} = \sum_{k}\frac{\left(O_{k}-E_{k}\right)^{2}}{E_{k}}\] where \(O_{k},E_{k}\) denoted observed and fitted frequencies respectively. Both of these statistics converge to \(\chi^2\) distribution asymptotically with the same degrees of freedom.

The convergence of \(G, \chi^2\) statistics to \(\chi^2\) 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.

Usage

## 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.

Value

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")