Foehn Classification Based on a Two-Component Mixture Model

This is the main method of the foehnix package to estimate two-component mixture models for automated foehn classification.

foehnix(
  formula,
  data,
  switch = FALSE,
  filter = NULL,
  family = "gaussian",
  control = foehnix.control(family, switch, ...),
  ...
)

# S3 method for foehnix
logLik(object, ...)

# S3 method for foehnix
nobs(object, ...)

# S3 method for foehnix
AIC(object, ...)

# S3 method for foehnix
BIC(object, ...)

# S3 method for foehnix
IGN(object, ...)

# S3 method for foehnix
edf(object, ...)

# S3 method for foehnix
print(x, ...)

# S3 method for foehnix
formula(x, ...)

# S3 method for foehnix
summary(object, eps = 1e-04, detailed = FALSE, ...)

Arguments

formula: an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.
data: a regular (not necessarily strictly regular) time series object of class zoo containing the variables for the two-part mixture model.
switch: logical. If set to TRUE the two estimated components will be switched. This is important if the covariate for the components (left hand side of input formula is smaller for cases with foehn than for cases without foehn, e.g., when using the temperature difference as main covariate.
filter: a named list can be provided to apply a custom (simple) filter to the observations on data. Can be used to e.g., prespecify a specific wind sector for foehn winds. Please read the manual of the foehnix_filter method for more details and examples.
family: character (at the moment "gaussian" or "logistic") or an object of class foehnix.family.
control: additional control arguments, see foehnix.control.
...: forwarded to foehnix.control
object: a foehnix object (input for S3 methods)
x: a foehnix object (input for S3 methods)
eps: threshold for posterior probabilities used in summary. numeric value, default 1e-4.
detailed: boolean, default FALSE. If TRUE, additional information will be returned.

Value

Returns an object of class foehnix.

Log-likelihood sum (numeric).

Number of observations (integer) used to train the model.

Returns the Akaike information criterion (numeric).

Bayesian information criterion (numeric).

Ignorance (mean negative log-likelihood; numeric).

Effective degrees of freedom.

Returns the formula of the model (formula).

Object of class summary.foehnix.

Details

The two-component mixture model can be specified via formula object where the left hand side of the formula contains the 'main' variable explaining the two components (only one variable), the right hand side of the formula specifies the concomitant variables (multiple variables allowed). As an example: let's assume that our zoo object data contains the following columns:

ff: observed wind speed at target site
rh: observed relative humidity at target site
diff_t: (potential) temperature difference between target site and a station upstream of the foehn wind direction

The specification for formula could e.g. look as follows:

ff ~ 1: the two components of the mixture model will be based on the observed wind speed (ff), no concomitant model (right hand side is simply 1).
ff ~ rh: similar to the specification above, but using observed relative humidity (rh) as concomitant.
ff ~ rh + diff_t: as above but with an additional second concomitant variable (observed temperature difference, diff_t).
diff_t ~ ff + rh: using temperature difference as the main variable for the two components while ff and rh are used as concomitants. Note: in this case it will be required to set switch = TRUE as lower values of diff_t indicate less stratified conditions where the occurrence of foehn is more likely. If switch = FALSE the two components (foehn and no foehn) may be interchanged and the model will return "probabilities of not observing foehn".

Note that these are just examples and have to be adjusted given data availability, location, structure/names of the variables in the data object.

The optional input filter allows to specify simple or complex filters (see foehnix_filter for details). This allows to add additional constraints, e.g., adding a filter on the observed wind direction to ensure that only events within a specific wind sector (the main foehn wind direction) are classified as "foehn".

References

Plavcan D, Mayr GJ, Zeileis A (2014). Automatic and Probabilistic Foehn Diagnosis with a Statistical Mixture Model. Journal of Applied Meteorology and Climatology. 53(3), 652--659. doi:10.1175/JAMC-D-13-0267.1

Gr\"un B, Leisch F (2007). Fitting Finite Mixtures of Generalized Linear Regressions in R. Computational Statistics \& Data Analysis. 51(11), 5247--5252. doi:10.1016/j.csda.2006.08.014

Gr\"un B, Leisch F (2008). FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters. Journal of Statistical Software, Articles. 28(4), 1--35. doi:10.18637/jss.v028.i04

Fraley C, Raftery AE (2002). Model-Based Clustering, Discriminant Analysis, and Density Estimation. Journal of the American Statistical Association. 97(458), 611--631. doi:10.1198/016214502760047131

Author

Reto Stauffer