Residuals for a vector generalized linear model (VGLM)
 object.

residualsvglm

An implementation of about 6 major classes of
statistical regression models. The central algorithm is
Fisher scoring and iterative reweighted least squares.
At the heart of this package are the vector generalized linear
and additive model (VGLM/VGAM) classes. VGLMs can be loosely
thought of as multivariate GLMs. VGAMs are data-driven
VGLMs that use smoothing. The book "Vector Generalized
Linear and Additive Models: With an Implementation in R"
(Yee, 2015) <DOI:10.1007/978-1-4939-2818-7> gives details of
the statistical framework and the package. Currently only
fixed-effects models are implemented. Many (100+) models and
distributions are estimated by maximum likelihood estimation
(MLE) or penalized MLE. The other classes are RR-VGLMs
(reduced-rank VGLMs), quadratic RR-VGLMs, doubly constrained
RR-VGLMs, quadratic RR-VGLMs, reduced-rank VGAMs,
RCIMs (row-column interaction models)---these classes perform
constrained and unconstrained quadratic ordination (CQO/UQO)
models in ecology, as well as constrained additive ordination
(CAO). Hauck-Donner effect detection is implemented.
Note that these functions are subject to change;
see the NEWS and ChangeLog files for latest changes.

Thomas Yee

VGAM

Vector Generalized Linear and Additive Models

Cleve Moler

residualsvglm function

Residuals for a VGLM fit — residualsvglm

<dl>

 <dt>object</dt>
<dd>Object of class <code>"vglm"</code>,
 i.e., a <code>vglm</code> fit.

</dd>

 <dt>type</dt>
<dd>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 <code>plotvgam</code>). 

 
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 <code>NULL</code> for those models
 whose deviance is undefined.


Randomized quantile residuals (RQRs)
 (Dunn and Smyth, 1996)
 are based on
 the <code>p</code>-type function being fed into
 <code><a href='https://rdrr.io/r/stats/Normal.html'>qnorm</a></code>.
 For example, for the default <code>exponential</code>
 it is <code>qnorm(pexp(y, rate = 1 / fitted(object)))</code>.
 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
 <code><a href='https://rdrr.io/r/stats/Uniform.html'>runif</a></code> and
 <code><a href='https://rdrr.io/r/base/Random.html'>set.seed</a></code>.
 For example, for the default <code>poissonff</code>
 it is
 <code>qnorm(runif(length(y), ppois(y - 1, mu), ppois(y, mu)))</code>
 where <code>mu</code> 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 <code>"ldot"</code> should not be used currently.


Standardized residuals are currently
 only defined for 2 types of models:
 (i) GLMs
 (<code>poissonff</code>,
 <code>binomialff</code>);
 (ii) those fitted
 to a two-way table of counts, e.g.,
 <code>cumulative</code>,
 <code>acat</code>,
 <code>multinomial</code>,
 <code>sratio</code>,
 <code>cratio</code>.
 For (ii),
 they are defined in Section 2.4.5 of Agresti (2018)
 and are also the output from the <code>"stdres"</code> component
 of <code><a href='https://rdrr.io/r/stats/chisq.test.html'>chisq.test</a></code>.
 For the test of independence
 they are a useful type of residual.
 Their formula is
 <code>(observed - expected) / sqrt(V)</code>, where <code>V</code> 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 <code>object</code>
 and then computes the standardized residuals like 
 <code><a href='https://rdrr.io/r/stats/chisq.test.html'>chisq.test</a></code>.

 








</dd>

<dt>matrix.arg</dt>
<dd>Logical, which applies when if the pre-processed
 answer is a vector or a 1-column matrix.
 If <code>TRUE</code> then the
 value returned will be a matrix, else a vector.




</dd>

</dl>

Arguments

This function may change in the future, especially
 those whose definitions may change.

residualsvglm: Residuals for a VGLM fit

Description

Usage

Arguments

Value

Details

References

See Also

Examples