DALSM {DALSM}

Fit a double additive location-scale model (DALSM) with a flexible error distribution

Description

Fit a location-scale regression model with a flexible error distribution and additive terms in location (=mean) and dispersion (= log(sd)) using Laplace P-splines from potentially right- and interval-censored response data.

Usage

DALSM(y, formula1,formula2, data,
       K1=10, K2=10, pen.order1=2, pen.order2=2,
       b.tau=1e-4, lambda1.min=1, lambda2.min=1,
       phi.0=NULL,psi1.0=NULL,psi2.0=NULL,lambda1.0=NULL,lambda2.0=NULL,
       REML=FALSE, diag.only=TRUE, Normality=FALSE, sandwich=TRUE,
       K.error=20, rmin=NULL,rmax=NULL,
       ci.level=.95, iterlim=50,verbose=FALSE)

Arguments

y

n-vector of responses or (nx2)-matrix/data.frame when interval-censoring (with the 2 elements giving the interval bounds) or right-censoring (when the element in the 2nd column equals Inf).

formula1

model formula for location (i.e. for the conditional mean).

formula2

model formula for dispersion (i.e. for the log of the conditional standard deviation).

data

data frame containing the model covariates.

K1

(optional) number of B-splines to describe a given additive term in the location submodel (default: 10).

K2

(optional) number of B-splines to describe a given additive term in the dispersion submodel (default: 10).

pen.order1

(optional) penalty order for the additive terms in the location submodel (default: 2).

pen.order2

(optional) penalty order for the additive terms in the dispersion submodel (default: 2).

b.tau

(optional) prior on penalty parameter \tau is Gamma(1,b.tau=1e-4) (for additive terms) (default: 1e-4).

lambda1.min

(optional) minimal value for the penalty parameters in the additive model for location (default: 1.0).

lambda2.min

(optional) minimal value for penalty parameters in the additive model for log-dispersion (default: 1.0).

phi.0

(optional) initial values for the spline parameters in the log-hazard of the standardized error distribution.

psi1.0

(optional) initial values for the location submodel parameters.

psi2.0

(optional) initial values for the dispersion submodel parameters.

lambda1.0

(optional) initial value for the J1 penalty parameters of the additive terms in the location submodel.

lambda2.0

(optional) initial value for the J2 penalty parameters of the additive terms in the dispersion submodel.

REML

(optional) logical indicating if a REML correction is desired to estimate the dispersion parameters (default: FALSE).

diag.only

(optional) logical indicating if only the diagonal of the Hessian needs to be corrected during REML (default: TRUE).

Normality

(optional) logical indicating if Normality is assumed for the error term (default: FALSE).

sandwich

(optional) logical indicating if sandwich variance estimators are needed for the regression parameters for a NP error distribution (when Normality=FALSE) ; it is forced to be TRUE when Normality=TRUE.

K.error

(optional) number of B-splines to approximate the log of the error hazard on (rmin,rmax) (default: 20).

rmin

(optional) minimum value for the support of the standardized error distribution (default: min(y)-sd(y)).

rmax

(optional) maximum value for the support of the standardized error distribution (default: max(y)+sd(y)).

ci.level

(optional) nominal level for the reported credible intervals (default: .95).

iterlim

(optional) maximum number of iterations (after which the algorithm is interrupted with a non-convergence diagnostic) (default: 50).

verbose

(optional) logical indicating whether estimation step details should be displayed (default: FALSE).

Value

An object of class DASLM containing several components from the fit, see DALSM.object for details. A summary can be printed using print.DALSM or plotted using plot.DALSM.

Author(s)

Philippe Lambert [e-mail]

References

Lambert, P. (2021). Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data. Computational Statistics and Data Analysis, 161: 107250. <doi:10.1016/j.csda.2021.107250>

See Also

DALSM.object, print.DALSM, plot.DALSM.

Examples

require(DALSM)
data(DALSM_IncomeData)
resp = DALSM_IncomeData[,1:2]
fit = DALSM(y=resp,
            formula1 = ~twoincomes+s(age)+s(eduyrs),
            formula2 = ~twoincomes+s(age)+s(eduyrs),
            data = DALSM_IncomeData)
print(fit)
plot(fit)