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:
#> 
#> Location:
#>                     Estimate          SE       Z    Pvalue    
#> intercept_0_beta  3.61484896  0.09473284 38.1584 < 2.2e-16 ***
#> crim_1_beta      -0.02083915  0.00525492 -3.9656 9.521e-05 ***
#> zn_2_beta                  0           0       0         0    
#> indus_3_beta               0           0       0         0    
#> rm_4_beta         0.23370359  0.01233188 18.9512 < 2.2e-16 ***
#> age_5_beta       -0.00105836  0.00035072 -3.0177 0.0018230 ** 
#> rad_6_beta        0.00893513  0.00236064  3.7850 0.0001725 ***
#> ptratio_7_beta   -0.02602475  0.00280413 -9.2809 1.070e-14 ***
#> lnox_8_beta      -0.28290631  0.08344519 -3.3903 0.0006006 ***
#> ldis_9_beta      -0.16020525  0.02301161 -6.9619 7.788e-10 ***
#> ltax_10_beta     -0.18402351  0.02603465 -7.0684 4.848e-10 ***
#> llstat_11_beta   -0.17194746  0.02055909 -8.3636 1.094e-12 ***
#> chast_12_beta     0.04804492  0.01958231  2.4535 0.0086759 ** 
#> 
#> Scale:
#>                    Estimate        SE       Z    Pvalue    
#> intercept_0_alpha -9.652431  2.293223 -4.2091 4.194e-05 ***
#> crim_1_alpha       0.021396  0.015921  1.3439 0.1139337    
#> zn_2_alpha                0         0       0         0    
#> indus_3_alpha     -0.033849  0.022387 -1.5120 0.0806782 .  
#> rm_4_alpha        -0.205594  0.102716 -2.0016 0.0268356 *  
#> age_5_alpha               0         0       0         0    
#> rad_6_alpha        0.033704  0.017691  1.9052 0.0337295 *  
#> ptratio_7_alpha           0         0       0         0    
#> lnox_8_alpha      -0.478042  0.817158 -0.5850 0.4314891    
#> ldis_9_alpha      -1.049942  0.269546 -3.8952 0.0001204 ***
#> ltax_10_alpha      1.375999  0.391715  3.5128 0.0004103 ***
#> llstat_11_alpha           0         0       0         0    
#> chast_12_alpha            0         0       0         0    
#> 
#> Shape:
#>                   Estimate      SE      Z   Pvalue   
#> intercept_0_nu     0.29520 0.10618 2.7801 0.003585 **
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Kappa Estimate:
#> [1] 1.54339
#> Penalized Likelihood:
#> [1] 221.1142
#> IC Value:
#> [1] -442.2284

fit$kappa # shape estimate
#> [1] 1.54339

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