# Print, Summary and other Standard Methods for `"hhh4"`

Objects

`hhh4_methods.Rd`

Besides `print`

and `summary`

methods there are also some standard
extraction methods defined for objects of class `"hhh4"`

resulting
from a call to `hhh4`

.
The implementation is illustrated in Meyer et al. (2017, Section 5),
see `vignette("hhh4_spacetime")`

.

## Usage

```
# S3 method for hhh4
print(x, digits = max(3, getOption("digits") - 3), ...)
# S3 method for hhh4
summary(object, maxEV = FALSE, ...)
# S3 method for hhh4
coef(object, se = FALSE, reparamPsi = TRUE,
idx2Exp = NULL, amplitudeShift = FALSE, ...)
# S3 method for hhh4
fixef(object, ...)
# S3 method for hhh4
ranef(object, tomatrix = FALSE, intercept = FALSE, ...)
# S3 method for hhh4
coeflist(x, ...)
# S3 method for hhh4
formula(x, ...)
# S3 method for hhh4
nobs(object, ...)
# S3 method for hhh4
logLik(object, ...)
# S3 method for hhh4
vcov(object, reparamPsi = TRUE,
idx2Exp = NULL, amplitudeShift = FALSE, ...)
# S3 method for hhh4
confint(object, parm, level = 0.95,
reparamPsi = TRUE, idx2Exp = NULL, amplitudeShift = FALSE, ...)
# S3 method for hhh4
residuals(object, type = c("deviance", "response"), ...)
```

## Arguments

- x, object
an object of class

`"hhh4"`

.- digits
the number of significant digits to use when printing parameter estimates.

- maxEV
logical indicating if the summary should contain the (range of the) dominant eigenvalue as a measure of the importance of the epidemic components. By default, the value is not calculated as this may take some seconds depending on the number of time points and units in

`object$stsObj`

.- ...
For the

`print`

,`summary`

,`fixef`

,`ranef`

, and`coeflist`

methods: arguments passed to`coef`

.

For the remaining methods: unused (argument of the generic).- reparamPsi
logical. If

`TRUE`

(default), the overdispersion parameter from the negative binomial distribution is transformed from internal scale (-log) to standard scale, where zero corresponds to a Poisson distribution.- se
logical switch indicating if standard errors are required

- idx2Exp
integer vector selecting the parameters which should be returned on exp-scale. Alternatively,

`idx2Exp = TRUE`

will exp-transform all parameters except for those associated with`log()`

covariates or already affected by`reparamPsi`

or`amplitudeShift`

.- amplitudeShift
logical switch indicating whether the parameters for sine/cosine terms modelling seasonal patterns (see

`addSeason2formula`

) should be transformed to an amplitude/shift formulation.- tomatrix
logical. If

`FALSE`

(default), the vector of all random effects is returned (as used internally). However, for random intercepts of`type="car"`

, the number of parameters is one less than the number of regions and the individual parameters are not obviously linked to specific regions. Setting`tomatrix`

to`TRUE`

returns a more useful representation of random effects in a matrix with as many rows as there are regions and as many columns as there are random effects. Here, any CAR-effects are transformed to region-specific effects.- intercept
logical. If

`FALSE`

(default), the returned random effects represent zero-mean deviations around the corresponding global intercepts of the*log*-linear predictors. Setting`intercept=TRUE`

adds these global intercepts to the result (and implies`tomatrix=TRUE`

).- parm
a vector of numbers or names, specifying which parameters are to be given confidence intervals. If missing, all parameters are considered.

- level
the confidence level required.

- type
the type of residuals which should be returned. The alternatives are

`"deviance"`

(default) and`"response"`

.

## Value

The `coef`

-method returns all estimated (regression)
parameters from a `hhh4`

model.
If the model includes random effects, those can be extracted with

`ranef`

, whereas `fixef`

returns the fixed parameters.
The `coeflist`

-method extracts the model coefficients in a list
(by parameter group).

The `formula`

-method returns the formulae used for the
three log-linear predictors in a list with elements `"ar"`

,

`"ne"`

, and `"end"`

.
The `nobs`

-method returns the number of observations used
for model fitting.
The `logLik`

-method returns an object of class

`"logLik"`

with `"df"`

and `"nobs"`

attributes.
For a random effects model, the value of the *penalized*

log-likelihood at the MLE is returned, but degrees of freedom are
not available (`NA_real_`

).
As a consequence, `AIC`

and `BIC`

are only
well defined for models without random effects;
otherwise these functions return `NA_real_`

.

The `vcov`

-method returns the estimated
variance-covariance matrix of the *regression* parameters.
The estimated variance-covariance matrix of random effects is
available as `object$Sigma`

.
The `confint`

-method returns Wald-type confidence
intervals (assuming asymptotic normality).

The `residuals`

-method extracts raw (`"response"`

) or
scaled (`"deviance"`

) residuals from the model fit similar to

`residuals.glm`

for Poisson or NegBin GLM's.

## References

Meyer, S., Held, L. and Höhle, M. (2017):
Spatio-temporal analysis of epidemic phenomena using the R package
surveillance.
*Journal of Statistical Software*, **77** (11), 1-55.
doi:10.18637/jss.v077.i11