Produces a normal QQ-plot with simulated envelope of residuals for regression models used to deal with zero-excess in count data.
# S3 method for zeroinflation
envelope(
object,
rep = 20,
conf = 0.95,
type = c("quantile", "response", "standardized"),
plot.it = TRUE,
identify,
...
)A matrix with the following four columns:
Lower limit | the quantile (1 - conf)/2 of the random sample of size rep of the \(i\)-th order |
statistic of the type-type residuals for \(i=1,2,...,n\), | |
Median | the quantile 0.5 of the random sample of size rep of the \(i\)-th order |
statistic of the type-type residuals for \(i=1,2,...,n\), | |
Upper limit | the quantile (1 + conf)/2 of the random sample of size rep of the \(i\)-th order |
statistic of the type-type residuals for \(i=1,2,...,n\), | |
Residuals | the observed type-type residuals. |
an object of the class zeroinflation.
an (optional) positive integer which allows to specify the number of replicates which should be used to build the simulated envelope. As default, rep is set to 25.
an (optional) value in the interval \((0,1)\) indicating the confidence level which should be used to build the pointwise confidence intervals, which conform the simulated envelope. As default, conf is set to 0.95.
an (optional) character string which allows to specify the required type of residuals. The available options are: (1) the difference between the observed response
and the fitted mean ("response"); (2) the standardized difference between the observed response and the fitted mean ("standardized"); (3) the randomized quantile
residual ("quantile"). As default, type is set to "quantile".
an (optional) logical switch indicating if the normal QQ-plot with simulated envelope of residuals is required or just the data matrix in which it is based. As default, plot.it is set to TRUE.
an (optional) positive integer value indicating the number of individuals to identify on the QQ-plot with simulated envelope of residuals. This is only appropriate if plot.it=TRUE.
further arguments passed to or from other methods. If plot.it=TRUE then ... may be used to include graphical parameters to customize the plot. For example, col, pch, cex, main, sub, xlab, ylab.
The simulated envelope is builded by simulating rep independent realizations of the response variable for each
individual, which is accomplished taking into account the following: (1) the model assumption about the distribution of
the response variable; (2) the estimates of the parameters in the linear predictor; and (3) the estimate of the
dispersion parameter. The interest model is re-fitted rep times, as each time the vector of observed responses
is replaced by one of the simulated samples. The type-type residuals are computed and then sorted for each
replicate, so that for each \(i=1,2,...,n\), where \(n\) is the number of individuals in the sample, there is a random
sample of size rep of the \(i\)-th order statistic of the type-type residuals. Therefore, the simulated
envelope is composed of the quantiles (1 - conf)/2 and (1 + conf)/2 of the random sample of size rep of
the \(i\)-th order statistic of the type-type residuals for \(i=1,2,...,n\).
Atkinson A.C. (1985) Plots, Transformations and Regression. Oxford University Press, Oxford.
Dunn P.K., Smyth G.K. (1996) Randomized Quantile Residuals. Journal of Computational and Graphical Statistics 5, 236-244.
envelope.lm, envelope.glm, envelope.overglm
####### Example 1: Self diagnozed ear infections in swimmers
data(swimmers)
fit <- zeroinf(infections ~ frequency | location, family="nb1(log)", data=swimmers)
envelope(fit, rep=30, conf=0.95, type="quantile", col="red", pch=20, col.lab="blue",
col.axis="blue", col.main="black", family="mono", cex=0.8)
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