Residuals for a vector generalized linear model (VGLM) object.
residualsvglm(object, type = c("working", "pearson", "response",
"deviance", "ldot", "stdres", "rquantile"), matrix.arg = TRUE)If that residual type is undefined or inappropriate
or not yet implemented,
then NULL is returned,
otherwise a matrix or vector of residuals is returned.
Object of class "vglm",
i.e., a vglm fit.
The value of this argument can be abbreviated.
The type of residuals to be returned.
The default is the first one: working residuals
corresponding to
the IRLS algorithm. These are defined for all models.
They are sometimes added to VGAM plots of estimated
component functions (see plotvgam).
Pearson residuals for GLMs, when squared and summed over the data set, total to the Pearson chi-squared statistic. For VGLMs, Pearson residuals involve the working weight matrices and the score vectors. Under certain limiting conditions, Pearson residuals have 0 means and identity matrix as the variance-covariance matrix.
Response residuals are simply the difference between the observed values and the fitted values. Both have to be of the same dimension, hence not all families have response residuals defined.
Deviance residuals are only defined for models with
a deviance function. They tend to GLMs mainly.
This function returns a NULL for those models
whose deviance is undefined.
Randomized quantile residuals (RQRs)
(Dunn and Smyth, 1996)
are based on
the p-type function being fed into
qnorm.
For example, for the default exponential
it is qnorm(pexp(y, rate = 1 / fitted(object))).
So one should expect these residuals to have a
standard normal distribution if the model and data agree well.
If the distribution is discrete then randomized
values are returned; see
runif and
set.seed.
For example, for the default poissonff
it is
qnorm(runif(length(y), ppois(y - 1, mu), ppois(y, mu)))
where mu is the fitted mean.
The following excerpts comes from their writings.
They highly recommend quantile residuals for
discrete distributions
since plots
using deviance and Pearson residuals may contain
distracting patterns.
Four replications of the quantile residuals are recommended
with discrete distributions because they
have a random component.
Any features not preserved across all four sets
of residuals are considered artifacts of the randomization.
This type of residual is continuous even for
discrete distributions;
for both discrete and continuous distributions,
the quantile residuals have an exact standard normal
distribution.
The choice "ldot" should not be used currently.
Standardized residuals are currently
only defined for 2 types of models:
(i) GLMs
(poissonff,
binomialff);
(ii) those fitted
to a two-way table of counts, e.g.,
cumulative,
acat,
multinomial,
sratio,
cratio.
For (ii),
they are defined in Section 2.4.5 of Agresti (2018)
and are also the output from the "stdres" component
of chisq.test.
For the test of independence
they are a useful type of residual.
Their formula is
(observed - expected) / sqrt(V), where V is
the residual cell variance
(also see Agresti, 2007, section 2.4.5).
When an independence null hypothesis is true, each
standardized residual (corresponding to a cell in the table)
has a a large-sample standard normal distribution.
Currently this function merely extracts the table of counts
from object
and then computes the standardized residuals like
chisq.test.
Logical, which applies when if the pre-processed
answer is a vector or a 1-column matrix.
If TRUE then the
value returned will be a matrix, else a vector.
This function may change in the future, especially those whose definitions may change.
This function returns various kinds of residuals, sometimes depending on the specific type of model having been fitted. Section 3.7 of Yee (2015) gives some details on several types of residuals defined for the VGLM class.
Standardized residuals for GLMs are described in
Section 4.5.6 of Agresti (2013) as the ratio of
the raw (response) residuals divided by their
standard error.
They involve the generalized hat matrix evaluated
at the final IRLS iteration.
When applied to the LM,
standardized residuals for GLMs simplify to
rstandard.
For GLMs they are basically
the Pearson residual divided by the square root of 1 minus the
leverage.
Agresti, A. (2007). An Introduction to Categorical Data Analysis, 2nd ed., New York: John Wiley & Sons. Page 38.
Agresti, A. (2013). Categorical Data Analysis, 3rd ed., New York: John Wiley & Sons.
Agresti, A. (2018). An Introduction to Categorical Data Analysis, 3rd ed., New York: John Wiley & Sons.
Dunn, P. K. and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5, 236--244.
resid,
vglm,
chisq.test,
hatvalues.
pneumo <- transform(pneumo, let = log(exposure.time))
fit <- vglm(cbind(normal, mild, severe) ~ let, propodds, pneumo)
resid(fit) # Same as having type = "working" (the default)
resid(fit, type = "response")
resid(fit, type = "pearson")
resid(fit, type = "stdres") # Test for independence
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