amlps.object {blapsr}

Object resulting from the fit of an additive partial linear model.

Description

An object returned by the amlps function consists in a list with various components related to the fit of an additive partial linear model with the Laplace-P-spline approach.

Value

An amlps object has the following elements:

formula

The formula of the additive model.

n

Sample size.

q

Total number of smooth terms.

K

Number of B-spline basis functions used for the fit.

penalty.order

Chosen penalty order.

latfield.dim

The dimension of the latent field. This is equal to the sum of the number of B-spline coefficients and the number of regression parameters related to the covariates in the linear part.

linear.coeff

Estimated linear regression coefficients. This is a matrix containing the posterior point estimate, standard deviation and lower/upper bounds of the credible interval.

spline.estim

The estimated B-spline coefficients. This is a list with q vectors of size K-1 representing the estimated B-spline amplitudes for each smooth term.

edf

Estimated effective degrees of freedom for each latent field variable.

Approx.signif

A matrix returning the observed test statistic and p-value for the approximate significance of smooth terms.

EDf

The estimated effective degrees of freedom of the smooth terms.

EDfHPD.95

95% HPD interval for the degrees of freedom of the smooth terms.

ED

The estimated degrees of freedom of the additive model.

sd.error

The estimated standard deviation of the error.

vmap

The maximum a posteriori of the (log) posterior penalty vector.

Cov.vmap

Covariance matrix of the (log) posterior penalty vector evaluated at vmap.

pen.family

The family of the posterior distribution for v. It is either "skew-normal" or "gaussian".

pendist.params

The parameterization for the posterior distribution of v. If the posterior of v belongs to the skew-normal family, then pendist.params is a matrix with as many rows as the number of smooth terms q. Each row contains the location, scale and shape parameter of the skew-normal distribution. If the posterior of v belongs to the Gaussian family, then pendist.params is a vector of length q, corresponding to vmap.

Covmaximum

The covariance matrix of the latent field evaluated at vmap.

latmaximum

The latent field vector evaluated at vmap.

fitted.values

The fitted response values.

residuals

The response residuals.

r2.adj

The adjusted r-squared of the model indicating the proportion of the data variance explained by the model fit.

data

The data frame.

Author(s)

Oswaldo Gressani [e-mail].

See Also

amlps, print.amlps, plot.amlps