Data 624 Assignment 4: Kuhn and Johnson book Applied Predictive Modeling Chapter 3 Exercise 3.1, 3.2
Chanice Mckenzie
#3.1 The UC Irvine Machine Learning Repository6 contains a data set related to glass identification. The data consist of 214 glass samples labeled as one of seven class categories. There are nine predictors, including the refractive index and percentages of eight elements: Na, Mg, Al, Si, K, Ca, Ba, and Fe.
#(a) Using visualizations, explore the predictor variables to understand their distributions as well as the relationships between predictors.
pairs(Glass)
#visual distributions
Glass |>
pivot_longer(-Type) |>
ggplot(aes(x = value)) +
geom_histogram(bins = 20, fill = "blue", color = "white") +
facet_wrap(~ name, scales = "free") +
theme_minimal()
#boxplots
Glass |>
pivot_longer(-Type) |>
ggplot(aes(y = value)) +
geom_boxplot() +
facet_wrap(~ name, scales = "free") +
theme_minimal()
#correlation
cor(Glass[, -10]) ## RI Na Mg Al Si K
## RI 1.0000000000 -0.19188538 -0.122274039 -0.40732603 -0.54205220 -0.289832711
## Na -0.1918853790 1.00000000 -0.273731961 0.15679367 -0.06980881 -0.266086504
## Mg -0.1222740393 -0.27373196 1.000000000 -0.48179851 -0.16592672 0.005395667
## Al -0.4073260341 0.15679367 -0.481798509 1.00000000 -0.00552372 0.325958446
## Si -0.5420521997 -0.06980881 -0.165926723 -0.00552372 1.00000000 -0.193330854
## K -0.2898327111 -0.26608650 0.005395667 0.32595845 -0.19333085 1.000000000
## Ca 0.8104026963 -0.27544249 -0.443750026 -0.25959201 -0.20873215 -0.317836155
## Ba -0.0003860189 0.32660288 -0.492262118 0.47940390 -0.10215131 -0.042618059
## Fe 0.1430096093 -0.24134641 0.083059529 -0.07440215 -0.09420073 -0.007719049
## Ca Ba Fe
## RI 0.8104027 -0.0003860189 0.143009609
## Na -0.2754425 0.3266028795 -0.241346411
## Mg -0.4437500 -0.4922621178 0.083059529
## Al -0.2595920 0.4794039017 -0.074402151
## Si -0.2087322 -0.1021513105 -0.094200731
## K -0.3178362 -0.0426180594 -0.007719049
## Ca 1.0000000 -0.1128409671 0.124968219
## Ba -0.1128410 1.0000000000 -0.058691755
## Fe 0.1249682 -0.0586917554 1.000000000#(b) Do there appear to be any outliers in the data? Are any predictors skewed?
#Several predictors exhibit skewness, particularly Ba and Fe, which contain many near-zero observations and a few larger values. K also appears right-skewed. These distributions suggest the presence of potential outliers
#(c) Are there any relevant transformations of one or more predictors that might improve the classification model?
library(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## liftglass_predictors <- Glass[, -10]
trans <- preProcess(glass_predictors,
method = c("YeoJohnson", "center", "scale", "pca"))#Ba, Fe, and K exhibit substantial right skewness, Yeo-Johnson transformation would help reduce skewness and stabilize variance. Additionally, centering and scaling the predictors would improve performance for models sensitive to differences in scale
library(mlbench)
data(Soybean)
??soybean#3.2 The soybean data can also be found at the UC Irvine Machine Learning Repository. Data were collected to predict disease in 683 soybeans. The 35 predictors are mostly categorical and include information on the environmental conditions (e.g., temperature, precipitation) and plant conditions (e.g., left spots, mold growth). The outcome labels consist of 19 distinct classes.
table(Soybean$plant.stand)##
## 0 1
## 354 293table(Soybean$precip)##
## 0 1 2
## 74 112 459table(Soybean$temp)##
## 0 1 2
## 80 374 199prop.table(table(Soybean$plant.stand))##
## 0 1
## 0.5471406 0.4528594summary(Soybean)## Class date plant.stand precip temp
## brown-spot : 92 5 :149 0 :354 0 : 74 0 : 80
## alternarialeaf-spot: 91 4 :131 1 :293 1 :112 1 :374
## frog-eye-leaf-spot : 91 3 :118 NA's: 36 2 :459 2 :199
## phytophthora-rot : 88 2 : 93 NA's: 38 NA's: 30
## anthracnose : 44 6 : 90
## brown-stem-rot : 44 (Other):101
## (Other) :233 NA's : 1
## hail crop.hist area.dam sever seed.tmt germ plant.growth
## 0 :435 0 : 65 0 :123 0 :195 0 :305 0 :165 0 :441
## 1 :127 1 :165 1 :227 1 :322 1 :222 1 :213 1 :226
## NA's:121 2 :219 2 :145 2 : 45 2 : 35 2 :193 NA's: 16
## 3 :218 3 :187 NA's:121 NA's:121 NA's:112
## NA's: 16 NA's: 1
##
##
## leaves leaf.halo leaf.marg leaf.size leaf.shread leaf.malf leaf.mild
## 0: 77 0 :221 0 :357 0 : 51 0 :487 0 :554 0 :535
## 1:606 1 : 36 1 : 21 1 :327 1 : 96 1 : 45 1 : 20
## 2 :342 2 :221 2 :221 NA's:100 NA's: 84 2 : 20
## NA's: 84 NA's: 84 NA's: 84 NA's:108
##
##
##
## stem lodging stem.cankers canker.lesion fruiting.bodies ext.decay
## 0 :296 0 :520 0 :379 0 :320 0 :473 0 :497
## 1 :371 1 : 42 1 : 39 1 : 83 1 :104 1 :135
## NA's: 16 NA's:121 2 : 36 2 :177 NA's:106 2 : 13
## 3 :191 3 : 65 NA's: 38
## NA's: 38 NA's: 38
##
##
## mycelium int.discolor sclerotia fruit.pods fruit.spots seed
## 0 :639 0 :581 0 :625 0 :407 0 :345 0 :476
## 1 : 6 1 : 44 1 : 20 1 :130 1 : 75 1 :115
## NA's: 38 2 : 20 NA's: 38 2 : 14 2 : 57 NA's: 92
## NA's: 38 3 : 48 4 :100
## NA's: 84 NA's:106
##
##
## mold.growth seed.discolor seed.size shriveling roots
## 0 :524 0 :513 0 :532 0 :539 0 :551
## 1 : 67 1 : 64 1 : 59 1 : 38 1 : 86
## NA's: 92 NA's:106 NA's: 92 NA's:106 2 : 15
## NA's: 31
##
##
## nearZeroVar(Soybean)## [1] 19 26 28#(a) Investigate the frequency distributions for the categorical predictors. Are any of the distributions degenerate in the ways discussed earlier in this chapter?
#Several categorical predictors exhibit highly imbalanced frequency distributions, with some levels occurring much more frequently than others. In certain variables, one category dominates the majority of observations, suggesting near-zero variance. These degenerate predictors may provide little discriminatory information and could negatively affect some classification models.
#(b) Roughly 18 % of the data are missing. Are there particular predictors that are more likely to be missing? Is the pattern of missing data related to the classes?
sum(is.na(Soybean$plant.stand))## [1] 36table(Soybean$Class, is.na(Soybean$plant.stand))##
## FALSE TRUE
## 2-4-d-injury 0 16
## alternarialeaf-spot 91 0
## anthracnose 44 0
## bacterial-blight 20 0
## bacterial-pustule 20 0
## brown-spot 92 0
## brown-stem-rot 44 0
## charcoal-rot 20 0
## cyst-nematode 0 14
## diaporthe-pod-&-stem-blight 9 6
## diaporthe-stem-canker 20 0
## downy-mildew 20 0
## frog-eye-leaf-spot 91 0
## herbicide-injury 8 0
## phyllosticta-leaf-spot 20 0
## phytophthora-rot 88 0
## powdery-mildew 20 0
## purple-seed-stain 20 0
## rhizoctonia-root-rot 20 0sum(is.na(Soybean)) / length(Soybean)## [1] 64.91667Several predictors contain substantial missing data. The amount of missingness varies across predictors, indicating that some variables are more prone to missing values than others. When comparing missing values by class, there appears to be variation in missingness across outcome categories, suggesting that the missing data pattern may not be completely random.
#(c) Develop a strategy for handling missing data, either by eliminating predictors or imputation.
preProc_soy <- preProcess(Soybean, method = c("knnImpute"))## Warning in pre_process_options(method, column_types): The following
## pre-processing methods were eliminated: 'knnImpute', 'center', 'scale'Soybean_imputed <- predict(preProc_soy, Soybean)#A reasonable strategy would involve removing predictors with excessive missingness and applying imputation to the remaining variables. For categorical predictors, mode imputation or k-nearest neighbors imputation could be appropriate