fit: Fit exponential models to incidence data
In reconhub/incidence: Compute, Handle, Plot and Model Incidence of Dated Events

Description Usage Arguments Value Author(s) See Also Examples

The function fit fits two exponential models to incidence data, of the form: log(y) = r * t + b
where 'y' is the incidence, 't' is time (in days), 'r' is the growth rate, and 'b' is the origin. The function fit will fit one model by default, but will fit two models on either side of a splitting date (typically the peak of the epidemic) if the argument split is provided. When groups are present, these are included in the model as main effects and interactions with dates. The function fit_optim_split() can be used to find the optimal 'splitting' date, defined as the one for which the best average R2 of the two models is obtained. Plotting can be done using plot, or added to an existing incidence plot by the piping-friendly function add_incidence_fit().

fit(x, split = NULL, level = 0.95, quiet = FALSE)

fit_optim_split(
  x,
  window = x$timespan/4,
  plot = TRUE,
  quiet = TRUE,
  separate_split = TRUE
)

## S3 method for class 'incidence_fit'
print(x, ...)

## S3 method for class 'incidence_fit_list'
print(x, ...)

`x`	An incidence object, generated by the function `incidence()`. For the plotting function, an `incidence_fit` object.
`split`	An optional time point identifying the separation between the two models. If NULL, a single model is fitted. If provided, two models would be fitted on the time periods on either side of the split.
`level`	The confidence interval to be used for predictions; defaults to 95%.
`quiet`	A logical indicating if warnings from `fit` should be hidden; FALSE by default. Warnings typically indicate some zero incidence, which are removed before performing the log-linear regression.
`window`	The size, in days, of the time window either side of the split.
`plot`	A logical indicating whether a plot should be added to the output (`TRUE`, default), showing the mean R2 for various splits.
`separate_split`	If groups are present, should separate split dates be determined for each group? Defaults to `TRUE`, in which separate split dates and thus, separate models will be constructed for each group. When `FALSE`, the split date will be determined from the pooled data and modelled with the groups as main effects and interactions with date.
`...`	currently unused.

For fit(), a list with the class incidence_fit (for a single model), or a list containing two incidence_fit objects (when fitting two models). incidence_fit objects contain:

$model: the fitted linear model
$info: a list containing various information extracted from the model (detailed further)
$origin: the date corresponding to day '0'

The $info item is a list containing:

r: the growth rate
r.conf: the confidence interval of 'r'
pred: a data.frame containing predictions of the model, including the true dates (dates), their numeric version used in the model (dates.x), the predicted value (fit), and the lower (lwr) and upper (upr) bounds of the associated confidence interval.
doubling: the predicted doubling time in days; exists only if 'r' is positive
doubling.conf: the confidence interval of the doubling time
halving: the predicted halving time in days; exists only if 'r' is negative
halving.conf: the confidence interval of the halving time

For fit_optim_split, a list containing:

df: a data.frame of dates that were used in the optimization procedure, and the corresponding average R2 of the resulting models.
split: the optimal splitting date
fit: an incidence_fit_list object containing the fit for each split. If the separate_split = TRUE, then the incidence_fit_list object will contain these splits nested within each group. All of the incidence_fit objects can be retrieved with get_fit().
plot: a plot showing the content of df (ggplot2 object)

Thibaut Jombart thibautjombart@gmail.com, Zhian N. Kamvar zkamvar@gmail.com.

the incidence() function to generate the 'incidence' objects. The get_fit() function to flatten incidence_fit_list objects to a list of incidence_fit objects.

if (require(outbreaks)) { withAutoprint({
 dat <- ebola_sim$linelist$date_of_onset

 ## EXAMPLE WITH A SINGLE MODEL

 ## compute weekly incidence
 i.7 <- incidence(dat, interval=7)
 plot(i.7)
 plot(i.7[1:20])

 ## fit a model on the first 20 weeks
 f <- fit(i.7[1:20])
 f
 names(f)
 head(get_info(f, "pred"))

 ## plot model alone (not recommended)
 plot(f)

 ## plot data and model (recommended)
 plot(i.7, fit = f)
 plot(i.7[1:25], fit = f)

## piping versions
if (require(magrittr)) { withAutoprint({
  plot(i.7) %>% add_incidence_fit(f)


  ## EXAMPLE WITH 2 PHASES
  ## specifying the peak manually
  f2 <- fit(i.7, split = as.Date("2014-10-15"))
  f2
  plot(i.7) %>% add_incidence_fit(f2)

  ## finding the best 'peak' date
  f3 <- fit_optim_split(i.7)
  f3
  plot(i.7) %>% add_incidence_fit(f3$fit)
})}

})}