Model Information

Model Information Methods

This page documents methods for extracting dimensional and scale information from fitted smooth models.

Summary Table

Function	Returns	Type
nobs()	Number of observations	integer
nparam()	Parameter counts	matrix
sigma()	Residual standard deviation	numeric
extractScale()	Scale parameter(s)	numeric/vector

For model type methods (modelType(), modelName(), errorType()), see Model-Specification.

For structural methods (orders(), lags()), see Orders-and-Lags.

For formula method, see Explanatory-Variables.

Basic Model Information

nobs()

Returns the number of observations used in model estimation.

R Usage

model <- adam(AirPassengers, "MMM", lags=12, h=12, holdout=TRUE)

# Number of observations
nobs(model)  # 132 (144 - 12 holdout)

Python Usage

from smooth import ADAM

model = ADAM(model="MMM", lags=12)
model.fit(y)

# Number of observations
n = model.nobs

Output

R: Returns an integer with the number of in-sample observations.

Python: Returns an int with the number of observations used for fitting.

Note

When holdout=TRUE, nobs() returns the number of in-sample observations (excluding holdout).

nparam()

Returns the number of estimated parameters in the model, broken down by category.

R Usage

model <- adam(AirPassengers, "MMM", lags=12)

# Number of estimated parameters
nparam(model)

Python Usage

from smooth import ADAM

model = ADAM(model="MMM", lags=12)
model.fit(y)

# Number of estimated parameters
n_params = model.nparam

Output

R: Returns the number of estimated parameters, with detailed breakdown available via model$nParam.

Python: Returns an int with the total number of estimated parameters.

Example

model <- adam(AirPassengers, "MAM", lags=12)
nparam(model)

The more detailed information about parameters can be accessed via:

model$nParam

Scale of the model

sigma()

Returns the residual standard deviation (scale parameter) of the model.

R Usage

model <- adam(AirPassengers, "MMM", lags=12)

# Residual standard deviation
sigma(model)

Python Usage

from smooth import ADAM

model = ADAM(model="MMM", lags=12)
model.fit(y)

# Residual standard deviation
scale = model.sigma

Output

R: Returns a numeric value with the residual standard deviation.

Python: Returns a float with the scale/standard error estimate.

Note

The scale of the sigma depends on the type of the error in the model. If it was the additive error, the scale will be in the original units. If it was the multiplicative one, sigma will have the interpretation closer to variability percents.

extractScale()

Extracts the scale parameter from the model, including time-varying scale if a Scale-Model was fitted.

R Usage

# Basic model
model <- adam(AirPassengers, "MMM", lags=12)
extractScale(model)  # Single value

# With scale model
scaleModel <- sm(model, model="MNM", lags=12)
fullModel <- implant(model, scaleModel)
extractScale(fullModel)  # Time series of scale values

See Also

• ADAM - Main ADAM function
• Model-Specification - Model type methods (modelType, modelName, errorType)
• Orders-and-Lags - orders() and lags() methods
• Explanatory-Variables - formula() method
• Coefficients-and-Parameters - Extracting parameters
• Visualisation-and-Output - Model output methods
• Scale-Model - Time-varying scale