Fits a discrete (count data) distribution for goodness-of-fit tests.
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"), …)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.
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".
character string indicating the type of
residuals: either "pearson", "deviance" or
"raw".
a character string indicating whether the distribution should be fit via ML (Maximum Likelihood) or Minimum Chi-squared.
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).
an object of class "goodfit".
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.
A list of class "goodfit" with elements:
observed frequencies.
corresponding counts.
expected frequencies (fitted by ML).
a character string indicating the distribution fitted.
a character string indicating the fitting method (can
be either "ML", "MinChisq" or "fixed" if the
parameters were specified).
degrees of freedom.
a named list of the (estimated) distribution parameters.
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.
M. Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.
# NOT RUN {
## 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)
# }