Smooth Generalized Normal Distribution

To begin, load the package.

library(smoothic)

Boston Housing Data

Perform automatic variable selection using a smooth information criterion.

fit <- smoothic(
  formula = lcmedv ~ .,
  data = bostonhouseprice2,
  family = "sgnd", # Smooth Generalized Normal Distribution
  model = "mpr" # model location and scale
)

Display the estimates and standard errors.

summary(fit)
#> Call:
#> smoothic(formula = lcmedv ~ ., data = bostonhouseprice2, family = "sgnd", 
#>     model = "mpr")
#> Family:
#> [1] "sgnd"
#> Model:
#> [1] "mpr"
#> 
#> Coefficients:
#>                      Estimate         SEE        Z    Pvalue    
#> intercept_0_beta   3.61136944  0.07097461  50.8826 < 2.2e-16 ***
#> crim_1_beta       -0.02087987  0.00510433  -4.0906 5.122e-05 ***
#> zn_2_beta                   0           0        0         0    
#> indus_3_beta                0           0        0         0    
#> rm_4_beta          0.23351548  0.01013492  23.0407 < 2.2e-16 ***
#> age_5_beta        -0.00106744  0.00033431  -3.1930 0.0009644 ***
#> rad_6_beta         0.00888114  0.00224680   3.9528 8.239e-05 ***
#> ptratio_7_beta    -0.02584035  0.00243260 -10.6225 < 2.2e-16 ***
#> lnox_8_beta       -0.28333271  0.08040520  -3.5238 0.0003415 ***
#> ldis_9_beta       -0.16080844  0.02245545  -7.1612 1.721e-10 ***
#> ltax_10_beta      -0.18360925  0.01598370 -11.4873 < 2.2e-16 ***
#> llstat_11_beta    -0.17173098  0.01643777 -10.4473 < 2.2e-16 ***
#> chast_12_beta      0.04881278  0.01980792   2.4643 0.0078328 ** 
#> intercept_0_alpha -9.65538752  2.34917955  -4.1101 4.795e-05 ***
#> crim_1_alpha       0.02269813  0.01564627   1.4507 0.0890931 .  
#> zn_2_alpha                  0           0        0         0    
#> indus_3_alpha     -0.03371923  0.02188524  -1.5407 0.0735639 .  
#> rm_4_alpha        -0.20051538  0.10084591  -1.9883 0.0264247 *  
#> age_5_alpha        0.00159679  0.00374685   0.4262 0.5363418    
#> rad_6_alpha        0.03381129  0.01746317   1.9361 0.0299475 *  
#> ptratio_7_alpha             0           0        0         0    
#> lnox_8_alpha      -0.65242459  0.83315211  -0.7831 0.3127381    
#> ldis_9_alpha      -1.04204621  0.27808068  -3.7473 0.0001648 ***
#> ltax_10_alpha      1.33390312  0.38883292   3.4305 0.0004596 ***
#> llstat_11_alpha             0           0        0         0    
#> chast_12_alpha              0           0        0         0    
#> nu_0               0.30581625  0.10335134   2.9590 0.0019454 ** 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Penalized Likelihood:
#> [1] 218.3393

fit$kappa # shape estimate
#> [1] 1.557733

Plot the standardized coefficient values with respect to the epsilon-telescope.

plot_paths(fit)

Plot the model-based conditional density curves.

plot_effects(fit,
             what = c("median", "ltax", "rm", "ldis"), # or "all" for all selected variables
             density_range = c(2.25, 3.75))