thresh_gam fits a Generalized Additive Model (GAM) with a threshold
formulation using the by argument in the smoothing function
s:
gam(IND ~ s(pressure1, by = threshold_variable_low) +
s(pressure 1, by = threshold threshold_variable_high)).
The threshold value is estimated from the data and chosen by minimizing
the GCV score (termed "gcvv" in the threshold-GAM object) over an interval
defined by the lower and upper quantiles (see the a and b
arguments respectively) of the threshold variable.
thresh_gam(model, ind_vec, press_vec, t_var, name_t_var, k, a, b)
| model | A single GAM object from the model tibble needed to extract the family and the link function. |
|---|---|
| ind_vec | A vector with the IND training observations (including or excluding defined outliers). |
| press_vec | A vector with the training observations (including or excluding defined outliers) of pressure 1 (i.e. the original significant pressure in the GAM(M)). |
| t_var | A vector with the training observations (including or excluding defined outliers) of the threshold variable (i.e. a second pressure variable). |
| name_t_var | The name of the threshold variable (pressure 2). t_var will be named after this string in the model formula. |
| k | Choice of knots (for the smoothing function |
| a | The lower quantile value of the selected threshold variable, which the estimated threshold is not allowed to exceed; the default is 0.2. |
| b | The upper quantile value of the selected threshold variable, which the estimated threshold is not allowed to exceed; the default is 0.8. |
The function returns a gam object with the additional class tgam.
All method functions for gam can be applied to this function. The object
has four additional elements:
mrThe threshold value of the best threshold-GAM.
mgcvThe GCV of the best threshold-GAM.
gcvvA vector of the GCV values of all fitted threshold-GAMs.
t_valA vector of all tested threshold values within the boundaries set by the lower and upper quantiles.
train_naA logical vector indicating missing values.
thresh_gam creates first a sequence of evenly spaced threshold values
within the boundaries set by the lower and upper quantiles (defined by a and b).
For each threshold value that leads to a new splitting of the threshold
variables a threshold-GAM is applied: one smoothing function is applied
to only those observations where the threshold variable has been below the threshold
value for the given time step (year). A second smoothing function is applied to
observations where the threshold variable is above the prior defined threshold.
From the list of computed models the threshold-GAM with the lowest Generalized
Cross Validation (GCV) and its threshold value are selected and returned. For more
infos on threshold-GAMs see also the details section in test_interaction.
test_interaction and loocv_thresh_gam
which apply the function
# Using some models of the Baltic Sea demo data in this package test <- thresh_gam(model = model_gam_ex$model[[1]], ind_vec = ind_init_ex$ind_train[[1]], press_vec = ind_init_ex$press_train[[1]], t_var = ind_init_ex$press_train[[2]], name_t_var = "Ssum", k = 4, a = 0.2, b = 0.8)