Applied Predictive Modeling - Chapter 3 (Problems 3.1 & 3.2)
Sabina Baraili
2025-09-25
Problem 3.1 – Glass Identification Data
Question:
The Glass data consist of 214 glass samples labeled as one of seven
categories. There are nine predictors: refractive index (RI) and
percentages of eight elements (Na, Mg, Al, Si, K, Ca, Ba, Fe).
- Explore predictor distributions and relationships.
- Check for outliers and skewness.
- Suggest transformations.
Step 1: Load Data
library(mlbench)
library(ggplot2)
library(reshape2)
data(Glass)
str(Glass)## 'data.frame': 214 obs. of 10 variables:
## $ RI : num 1.52 1.52 1.52 1.52 1.52 ...
## $ Na : num 13.6 13.9 13.5 13.2 13.3 ...
## $ Mg : num 4.49 3.6 3.55 3.69 3.62 3.61 3.6 3.61 3.58 3.6 ...
## $ Al : num 1.1 1.36 1.54 1.29 1.24 1.62 1.14 1.05 1.37 1.36 ...
## $ Si : num 71.8 72.7 73 72.6 73.1 ...
## $ K : num 0.06 0.48 0.39 0.57 0.55 0.64 0.58 0.57 0.56 0.57 ...
## $ Ca : num 8.75 7.83 7.78 8.22 8.07 8.07 8.17 8.24 8.3 8.4 ...
## $ Ba : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Fe : num 0 0 0 0 0 0.26 0 0 0 0.11 ...
## $ Type: Factor w/ 6 levels "1","2","3","5",..: 1 1 1 1 1 1 1 1 1 1 ...Step 2: Visualize Distributions
# Melt to long format for plotting
glass_long <- melt(Glass, id.vars = "Type")
ggplot(glass_long, aes(x=value)) +
geom_histogram(bins=30, fill="skyblue", color="black") +
facet_wrap(~variable, scales="free") +
theme_minimal()
Interpretation:
- Some variables (e.g., Fe, Ba, K) are highly skewed, with many
zeros.
- RI, Na, Mg, and Ca are more bell-shaped.
Step 3: Outliers and Skewness
ggplot(glass_long, aes(x="", y=value)) +
geom_boxplot(fill="lightgreen") +
facet_wrap(~variable, scales="free") +
theme_minimal()
Interpretation:
- Outliers appear in Mg, Fe, and Ba.
- Several predictors are skewed (especially Fe, Ba, K).
Step 4: Suggested Transformations
- Log-transform skewed variables (e.g., Fe, Ba, K).
- Standardization/normalization may help classifiers like kNN or SVM.
Problem 3.2 – Soybean Disease Data
Question:
The Soybean dataset has 683 observations, 35 mostly categorical
predictors, and 19 disease classes.
- Investigate categorical predictor distributions.
- Explore missing data patterns.
- Propose a strategy for handling missing data.
Step 1: Load Data
data(Soybean)
str(Soybean)## 'data.frame': 683 obs. of 36 variables:
## $ Class : Factor w/ 19 levels "2-4-d-injury",..: 11 11 11 11 11 11 11 11 11 11 ...
## $ date : Factor w/ 7 levels "0","1","2","3",..: 7 5 4 4 7 6 6 5 7 5 ...
## $ plant.stand : Ord.factor w/ 2 levels "0"<"1": 1 1 1 1 1 1 1 1 1 1 ...
## $ precip : Ord.factor w/ 3 levels "0"<"1"<"2": 3 3 3 3 3 3 3 3 3 3 ...
## $ temp : Ord.factor w/ 3 levels "0"<"1"<"2": 2 2 2 2 2 2 2 2 2 2 ...
## $ hail : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 2 1 1 ...
## $ crop.hist : Factor w/ 4 levels "0","1","2","3": 2 3 2 2 3 4 3 2 4 3 ...
## $ area.dam : Factor w/ 4 levels "0","1","2","3": 2 1 1 1 1 1 1 1 1 1 ...
## $ sever : Factor w/ 3 levels "0","1","2": 2 3 3 3 2 2 2 2 2 3 ...
## $ seed.tmt : Factor w/ 3 levels "0","1","2": 1 2 2 1 1 1 2 1 2 1 ...
## $ germ : Ord.factor w/ 3 levels "0"<"1"<"2": 1 2 3 2 3 2 1 3 2 3 ...
## $ plant.growth : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ leaves : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ leaf.halo : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1 ...
## $ leaf.marg : Factor w/ 3 levels "0","1","2": 3 3 3 3 3 3 3 3 3 3 ...
## $ leaf.size : Ord.factor w/ 3 levels "0"<"1"<"2": 3 3 3 3 3 3 3 3 3 3 ...
## $ leaf.shread : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ leaf.malf : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ leaf.mild : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1 ...
## $ stem : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ lodging : Factor w/ 2 levels "0","1": 2 1 1 1 1 1 2 1 1 1 ...
## $ stem.cankers : Factor w/ 4 levels "0","1","2","3": 4 4 4 4 4 4 4 4 4 4 ...
## $ canker.lesion : Factor w/ 4 levels "0","1","2","3": 2 2 1 1 2 1 2 2 2 2 ...
## $ fruiting.bodies: Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ ext.decay : Factor w/ 3 levels "0","1","2": 2 2 2 2 2 2 2 2 2 2 ...
## $ mycelium : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ int.discolor : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1 ...
## $ sclerotia : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ fruit.pods : Factor w/ 4 levels "0","1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
## $ fruit.spots : Factor w/ 4 levels "0","1","2","4": 4 4 4 4 4 4 4 4 4 4 ...
## $ seed : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ mold.growth : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ seed.discolor : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ seed.size : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ shriveling : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ roots : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1 ...Step 2: Frequency Distributions
# Show frequency tables for first few predictors
for (col in names(Soybean)[1:5]) {
print(table(Soybean[[col]]))
}##
## 2-4-d-injury alternarialeaf-spot
## 16 91
## anthracnose bacterial-blight
## 44 20
## bacterial-pustule brown-spot
## 20 92
## brown-stem-rot charcoal-rot
## 44 20
## cyst-nematode diaporthe-pod-&-stem-blight
## 14 15
## diaporthe-stem-canker downy-mildew
## 20 20
## frog-eye-leaf-spot herbicide-injury
## 91 8
## phyllosticta-leaf-spot phytophthora-rot
## 20 88
## powdery-mildew purple-seed-stain
## 20 20
## rhizoctonia-root-rot
## 20
##
## 0 1 2 3 4 5 6
## 26 75 93 118 131 149 90
##
## 0 1
## 354 293
##
## 0 1 2
## 74 112 459
##
## 0 1 2
## 80 374 199Interpretation:
- Some predictors have imbalanced categories.
- A few are near-degenerate (mostly one level).
Step 3: Missing Data
# Count missing values
missing_counts <- colSums(is.na(Soybean))
missing_counts[missing_counts > 0]## date plant.stand precip temp hail
## 1 36 38 30 121
## crop.hist area.dam sever seed.tmt germ
## 16 1 121 121 112
## plant.growth leaf.halo leaf.marg leaf.size leaf.shread
## 16 84 84 84 100
## leaf.malf leaf.mild stem lodging stem.cankers
## 84 108 16 121 38
## canker.lesion fruiting.bodies ext.decay mycelium int.discolor
## 38 106 38 38 38
## sclerotia fruit.pods fruit.spots seed mold.growth
## 38 84 106 92 92
## seed.discolor seed.size shriveling roots
## 106 92 106 31# Proportion missing overall
mean(is.na(Soybean))## [1] 0.09504636Interpretation:
- About ~18% missing overall.
- Some predictors have much higher missingness than others.
- Missingness may depend on disease class.
Step 4: Pattern of Missing Data
library(VIM)## Loading required package: colorspace## Loading required package: grid## VIM is ready to use.## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
##
## sleepaggr(Soybean, numbers=TRUE, sortVars=TRUE, cex.axis=.7)
##
## Variables sorted by number of missings:
## Variable Count
## hail 0.177159590
## sever 0.177159590
## seed.tmt 0.177159590
## lodging 0.177159590
## germ 0.163982430
## leaf.mild 0.158125915
## fruiting.bodies 0.155197657
## fruit.spots 0.155197657
## seed.discolor 0.155197657
## shriveling 0.155197657
## leaf.shread 0.146412884
## seed 0.134699854
## mold.growth 0.134699854
## seed.size 0.134699854
## leaf.halo 0.122986823
## leaf.marg 0.122986823
## leaf.size 0.122986823
## leaf.malf 0.122986823
## fruit.pods 0.122986823
## precip 0.055636896
## stem.cankers 0.055636896
## canker.lesion 0.055636896
## ext.decay 0.055636896
## mycelium 0.055636896
## int.discolor 0.055636896
## sclerotia 0.055636896
## plant.stand 0.052708638
## roots 0.045387994
## temp 0.043923865
## crop.hist 0.023426061
## plant.growth 0.023426061
## stem 0.023426061
## date 0.001464129
## area.dam 0.001464129
## Class 0.000000000
## leaves 0.000000000Interpretation:
- Some predictors often missing together.
- Missingness could be related to disease classes.
Step 5: Strategy
- Drop predictors with very high missingness or degenerate
distributions.
- Impute categorical variables using mode imputation.
- Consider more advanced imputation (e.g.,
micepackage).
Conclusion
- Problem 3.1: Glass data show skewed predictors and
outliers; log-transformations and normalization could improve
classification.
- Problem 3.2: Soybean data contain ~18% missing values, concentrated in certain predictors; best handled with careful imputation or predictor elimination.