This smooth constructor implements simple linear effects. The columns of the design matrix are automatically scaled. The main advantage of this constructor is speed when used in the BAMLSS boosting algorithm boost. Optionally, a ridge penalty can be added, please see the example.

## Linear smooth constructor.
lin(...)

## For mgcv.
# S3 method for linear.smooth.spec
smooth.construct(object, data, knots, ...)

Arguments

...

For function lin() a formula of the type ~x1+x2+x3 that specifies the covariates that should be modeled.

object, data, knots

See smooth.construct.

Value

Function lin(), similar to function s a simple smooth specification object.

Examples

if (FALSE) ## Simulate data.
set.seed(123)
d <- GAMart()

## Estimate model.
f <- num ~ lin(~x1+x2+x3+fac,ridge=TRUE)

b <- bamlss(f, data = d)
#> AICc 328.2219 logPost -168.649 logLik -157.258 edf 6.7460 eps 1.5021 iteration   1
#> AICc 306.1394 logPost -159.383 logLik -146.058 edf 6.9002 eps 0.3385 iteration   2
#> AICc 295.5924 logPost -155.273 logLik -140.746 edf 6.9379 eps 0.2123 iteration   3
#> AICc 290.4959 logPost -153.454 logLik -138.183 edf 6.9519 eps 1.5925 iteration   4
#> AICc 288.0301 logPost -152.685 logLik -136.943 edf 6.9588 eps 0.0900 iteration   5
#> AICc 286.8211 logPost -152.380 logLik -136.335 edf 6.9626 eps 0.0490 iteration   6
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#> AICc 285.9018 logPost -152.247 logLik -135.871 edf 6.9663 eps 0.0311 iteration   8
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#> AICc 285.5040 logPost -152.305 logLik -135.670 edf 6.9689 eps 0.0007 iteration  18
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#> AICc 285.5001 logPost -152.308 logLik -135.668 edf 6.9689 eps 0.0001 iteration  23
#> AICc 285.5001 logPost -152.308 logLik -135.668 edf 6.9689 eps 0.0001 iteration  23
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#> |********************| 100%  0.00sec  2.98sec
#> .. not computing effect plot for term lin(~x1+x2+x3+fac), use predict() instead!

summary(b)
#> 
#> Call:
#> bamlss(formula = f, data = d)
#> ---
#> Family: gaussian 
#> Link function: mu = identity, sigma = log
#> *---
#> Formula mu:
#> ---
#> num ~ lin(~x1 + x2 + x3 + fac, ridge = TRUE)
#> -
#> Parametric coefficients:
#>                Mean    2.5%     50%   97.5% parameters
#> (Intercept) -0.1745 -0.2057 -0.1748 -0.1461     -0.185
#> -
#> Acceptance probability:
#>       Mean 2.5% 50% 97.5%
#> alpha    1    1   1     1
#> -
#> Smooth terms:
#>                          Mean 2.5% 50% 97.5% parameters
#> lin(~x1+x2+x3+fac).tau21  NaN   NA  NA    NA      0.058
#> lin(~x1+x2+x3+fac).alpha    1    1   1     1         NA
#> lin(~x1+x2+x3+fac).edf    NaN   NA  NA    NA      4.969
#> ---
#> Formula sigma:
#> ---
#> sigma ~ 1
#> -
#> Parametric coefficients:
#>               Mean   2.5%    50%  97.5% parameters
#> (Intercept) -1.127 -1.186 -1.128 -1.065     -1.148
#> -
#> Acceptance probability:
#>         Mean   2.5%    50% 97.5%
#> alpha 0.9815 0.8596 1.0000     1
#> ---
#> Sampler summary:
#> -
#> DIC = 293.9441 logLik = -145.9162 pd = 2.1116
#> runtime = 3.003
#> ---
#> Optimizer summary:
#> -
#> AICc = 285.5001 edf = 6.9689 logLik = -135.6683
#> logPost = -152.3082 nobs = 500 runtime = 0.267
#>