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Shape AIC for Nominal Variables

Shape AIC for Nominal Variables

This vignette demonstrates how to compute the Shape AIC for nominal variables using the shape_aic function from the nomiShape package. Shape AIC quantifies the goodness-of-fit of different shape models to the distribution of a nominal variable.

Computing Shape AIC

# Example usage of shape_aic
shape_aic(categories, "animal")
#>         Shape      AIC   DeltaAIC
#> 1     Uniform 1198.948    0.00000
#> 2  Triangular 1267.201   68.25385
#> 3 Exponential 1994.144  795.19640
#> 4      Normal 2897.166 1698.21859
# Example usage of shape_aic
shape_aic(categories2, "animal")
#>         Shape      AIC   DeltaAIC
#> 1  Triangular 1137.919   0.000000
#> 2 Exponential 1140.017   2.098416
#> 3     Uniform 1198.948  61.028672
#> 4      Normal 1986.456 848.536855
# Example usage of shape_aic
shape_aic(categories3, "animal")
#>         Shape       AIC DeltaAIC
#> 1 Exponential  822.6242   0.0000
#> 2      Normal  961.7948 139.1706
#> 3  Triangular  981.4556 158.8314
#> 4     Uniform 1198.9476 376.3234
# Example usage of shape_aic
shape_aic(starwars, "species")
#>         Shape      AIC   DeltaAIC
#> 1 Exponential 555.1934   0.000000
#> 2  Triangular 559.2814   4.088026
#> 3     Uniform 599.4124  44.218957
#> 4      Normal 781.9204 226.727018
# approximate rate from top counts
obs <- sort(table(starwars$species), decreasing = TRUE)
ranks <- seq_along(obs)
rate_est <- -coef(lm(log(obs + 1e-6) ~ ranks))[2]  # linear fit in log-space
rate_est
#>      ranks 
#> 0.03724241
shape_aic(starwars, "species")
#>         Shape      AIC   DeltaAIC
#> 1 Exponential 555.1934   0.000000
#> 2  Triangular 559.2814   4.088026
#> 3     Uniform 599.4124  44.218957
#> 4      Normal 781.9204 226.727018
shape_aic (starwars,"species") 
#>         Shape      AIC   DeltaAIC
#> 1 Exponential 555.1934   0.000000
#> 2  Triangular 559.2814   4.088026
#> 3     Uniform 599.4124  44.218957
#> 4      Normal 781.9204 226.727018
shape_aic (mpg,"manufacturer") 
#>         Shape      AIC   DeltaAIC
#> 1 Exponential 1163.754   0.000000
#> 2  Triangular 1167.389   3.634591
#> 3     Uniform 1267.367 103.613256
#> 4      Normal 1744.504 580.749726

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