vcd (version 1.4-13)

goodfit: Goodness-of-fit Tests for Discrete Data

Description

Fits a discrete (count data) distribution for goodness-of-fit tests.

Usage

goodfit(x, type = c("poisson", "binomial", "nbinomial"),
  method = c("ML", "MinChisq"), par = NULL)
# S3 method for goodfit
predict(object, newcount = NULL, type = c("response", "prob"), ...)
# S3 method for goodfit
residuals(object, type = c("pearson", "deviance",
"raw"), ...)
# S3 method for goodfit
print(x, residuals_type = c("pearson", "deviance",
"raw"), ...)

Value

A list of class "goodfit" with elements:

observed

observed frequencies.

count

corresponding counts.

fitted

expected frequencies (fitted by ML).

type

a character string indicating the distribution fitted.

method

a character string indicating the fitting method (can be either "ML", "MinChisq" or "fixed" if the parameters were specified).

df

degrees of freedom.

par

a named list of the (estimated) distribution parameters.

Arguments

x

either a vector of counts, a 1-way table of frequencies of counts or a data frame or matrix with frequencies in the first column and the corresponding counts in the second column.

type

character string indicating: for goodfit, which distribution should be fit; for predict, the type of prediction (fitted response or probabilities); for residuals, either "pearson", "deviance" or "raw".

residuals_type

character string indicating the type of residuals: either "pearson", "deviance" or "raw".

method

a character string indicating whether the distribution should be fit via ML (Maximum Likelihood) or Minimum Chi-squared.

par

a named list giving the distribution parameters (named as in the corresponding density function), if set to NULL, the default, the parameters are estimated. If the parameter size is not specified if type is "binomial" it is taken to be the maximum count. If type is "nbinomial", then parameter size can be specified to fix it so that only the parameter prob will be estimated (see the examples below).

object

an object of class "goodfit".

newcount

a vector of counts. By default the counts stored in object are used, i.e., the fitted values are computed. These can also be extracted by fitted(object).

...

currently not used.

Author

Achim Zeileis

Details

goodfit essentially computes the fitted values of a discrete distribution (either Poisson, binomial or negative binomial) to the count data given in x. If the parameters are not specified they are estimated either by ML or Minimum Chi-squared.

To fix parameters, par should be a named list specifying the parameters lambda for "poisson" and prob and size for "binomial" or "nbinomial", respectively. If for "binomial", size is not specified it is not estimated but taken as the maximum count.

The corresponding Pearson Chi-squared or likelihood ratio statistic, respectively, is computed and given with their \(p\) values by the summary method. The summary method always prints this information and returns a matrix with the printed information invisibly. The plot method produces a rootogram of the observed and fitted values.

In case of count distribtions (Poisson and negative binomial), the minimum Chi-squared approach is somewhat ad hoc. Strictly speaking, the Chi-squared asymptotics would only hold if the number of cells were fixed or did not increase too quickly with the sample size. However, in goodfit the number of cells is data-driven: Each count is a cell of its own. All counts larger than the maximal count are merged into the cell with the last count for computing the test statistic.

References

M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.

See Also

rootogram

Examples

## Simulated data examples:
dummy <- rnbinom(200, size = 1.5, prob = 0.8)
gf <- goodfit(dummy, type = "nbinomial", method = "MinChisq")
summary(gf)
plot(gf)

dummy <- rbinom(100, size = 6, prob = 0.5)
gf1 <- goodfit(dummy, type = "binomial", par = list(size = 6))
gf2 <- goodfit(dummy, type = "binomial", par = list(prob = 0.6, size = 6))
summary(gf1)
plot(gf1)
summary(gf2)
plot(gf2)

## Real data examples:
data("HorseKicks")
HK.fit <- goodfit(HorseKicks)
summary(HK.fit)
plot(HK.fit)

data("Federalist")
## try geometric and full negative binomial distribution
F.fit <- goodfit(Federalist, type = "nbinomial", par = list(size = 1))
F.fit2 <- goodfit(Federalist, type = "nbinomial")
summary(F.fit)
summary(F.fit2)
plot(F.fit)
plot(F.fit2)