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Smooth Generalized Normal Distribution

Source: vignettes/sgnd-boston.Rmd
sgnd-boston.Rmd

To begin, load the package.

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  3.61593796  0.16559666 21.8358 < 2.2e-16 ***
#> crim_1_beta      -0.01986098  0.00514643 -3.8592 0.0001499 ***
#> zn_2_beta                  0           0       0         0    
#> indus_3_beta               0           0       0         0    
#> rm_4_beta         0.23415197  0.03167535  7.3922 1.603e-10 ***
#> age_5_beta       -0.00106351  0.00054909 -1.9368 0.0321328 *  
#> rad_6_beta        0.00875929  0.00244040  3.5893 0.0003525 ***
#> ptratio_7_beta   -0.02582467  0.00376890 -6.8520 1.738e-09 ***
#> lnox_8_beta      -0.27873614  0.11738902 -2.3745 0.0110743 *  
#> ldis_9_beta      -0.15881138  0.03060053 -5.1898 1.437e-06 ***
#> ltax_10_beta     -0.18546652  0.07450491 -2.4893 0.0082330 ** 
#> llstat_11_beta   -0.17101398  0.04888847 -3.4980 0.0004670 ***
#> chast_12_beta     0.05012851  0.01950965  2.5694 0.0066730 ** 
#> 
#> Scale:
#>                    Estimate        SE       Z    Pvalue    
#> intercept_0_alpha -9.650061  2.266987 -4.2568 4.019e-05 ***
#> crim_1_alpha       0.018699  0.016471  1.1352 0.1727296    
#> zn_2_alpha                0         0       0         0    
#> indus_3_alpha     -0.034072  0.025857 -1.3177 0.1216615    
#> rm_4_alpha        -0.180956  0.104532 -1.7311 0.0512618 .  
#> age_5_alpha               0         0       0         0    
#> rad_6_alpha        0.032101  0.018842  1.7037 0.0544038 .  
#> ptratio_7_alpha           0         0       0         0    
#> lnox_8_alpha              0         0       0         0    
#> ldis_9_alpha      -0.963366  0.229340 -4.2006 4.855e-05 ***
#> ltax_10_alpha      1.385008  0.403220  3.4349 0.0005663 ***
#> llstat_11_alpha           0         0       0         0    
#> chast_12_alpha            0         0       0         0    
#> 
#> Shape:
#>                   Estimate      SE      Z   Pvalue   
#> intercept_0_nu     0.28911 0.10669 2.7098 0.004573 **
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Kappa Estimate:
#> [1] 1.535242
#> Penalized Likelihood:
#> [1] 223.6369
#> IC Value:
#> [1] -447.2739

fit$kappa # shape estimate
#> [1] 1.535242

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

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))