DATA624 HW4
Benson T
2025-02-27
3.1
The UC Irvine Machine Learning Repository 6 contains a dataset 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.
The data can be accessed via:
library(mlbench)
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 ...- Using visualizations, explore the predictor variables to understand their distributions as well as the relationships between predictors.
Glass_long <- pivot_longer(Glass, cols = c(RI, Na, Mg, Al, Si, K, Ca, Ba, Fe),
names_to = "Predictor", values_to = "Value")
ggplot(Glass_long, aes(x = Value)) +
geom_histogram(fill = "lightblue", color = "black", bins = 20) +
facet_wrap(~ Predictor, scales = "free", ncol = 3) +
theme_minimal() +
labs(title = "Histograms of Glass Predictors")
ggplot(Glass_long, aes(y = Value)) +
geom_boxplot(fill = "lightblue") +
facet_wrap(~ Predictor, scales = "free", ncol = 3) +
theme_minimal() +
labs(title = "Boxplots of Glass Predictors")
- Do there appear to be any outliers in the data? Are any predictors skewed?
- Skewness: Al, Ba, Ca, Fe, Mg, Na, Rl, and Si
- Outliers: Al, Ba, Ca, Fe, K, Na, Rl, and Si
- Are there any relevant transformations of one or more predictors that might improve the classification model?
Transformation type:
- Yeo-Johnson:
- Reduces skewness: It transforms non-normal data into a distribution that is more symmetric and Gaussian-like, which is ideal for many statistical models.(Can handle zero or negative value)
- Stabilizes variance: It can reduce heteroscedasticity in the data, making it more suitable for regression or classification models.
- Box-Cox Transformation:
- Reduces skewness: It transforms right-skewed data into a more symmetric, Gaussian-like distribution, making it easier for statistical models to handle.(Cant handle zero or negative value)
- Stabilizes variance: It reduces heteroscedasticity, improving the assumptions of models like linear regression.
- Log Transformation:
- Reduces right skewness: It’s particularly effective for data with a long right tail, compressing large values and expanding small ones, resulting in a more symmetric distribution.(cant handle zero or negative value)
- Stabilizes variance: It can reduce heteroscedasticity, especially in data where variance increases with the mean.
In the Data(Glass), I tries to apply Yeo-Johnson Transformation. After applied Yeo-Johnson Transformation: - Symmetric: Al, Ca, Na, Ri, and Si - Skewness: Ba, Fe, Mg, and K - Outliers: Al, Ba, Ca, Fe, Na, Rl, and Si
The Yeo-Johnson transformation has likely imporved the model by normalizing the data.
Glass_transformed <- Glass
for (pred in c("Ba", "Fe", "K")) {
if (any(Glass[[pred]] <= 0)) {
Glass_transformed[[pred]] <- Glass[[pred]] + 0.1
}
bc_trans <- BoxCoxTrans(Glass_transformed[[pred]])
Glass_transformed[[pred]] <- predict(bc_trans, Glass_transformed[[pred]])
}
preproc <- preProcess(Glass[, 1:9], method = c("YeoJohnson", "center", "scale"))
transformed_data <- predict(preproc, Glass[, 1:9])
post_skewness <- apply(transformed_data, 2, e1071::skewness)
print(post_skewness)## RI Na Mg Al Si
## 1.6027150827 -0.0088476749 -0.8770969306 0.0002128329 -0.7202392108
## K Ca Ba Fe
## -0.0708227694 -0.2063893005 3.3686799688 1.7298107096transformed_long <- as.data.frame(transformed_data) %>%
pivot_longer(cols = everything(), names_to = "Predictor", values_to = "Value")
ggplot(transformed_long, aes(x = Value)) +
geom_histogram(fill = "lightgreen", color = "black", bins = 20) +
facet_wrap(~ Predictor, scales = "free", ncol = 3) +
theme_minimal() +
labs(title = "Histograms of Transformed Glass Predictors")
ggplot(transformed_long, aes(y = Value)) +
geom_boxplot(fill = "lightgreen") +
facet_wrap(~ Predictor, scales = "free", ncol = 3) +
theme_minimal() +
labs(title = "Boxplots of Glass Predictors")
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.
The data can be loaded via:
library(mlbench)
data(Soybean)
## See ?Soybean for details- Investigate the frequency distributions for the categorical predictors. Are any of the distributions degenerate in the ways discussed earlier in this chapter?
- Frequent ratio greater than 20 can indicate a near zero variance.
- Low percent unique is suggest the preditor has very low unique level.
- While frequent ratio is high and low in percent unique, the predictor is flagged as near zero variance.
- When near zero variance is flag, the predictor is consider degenerate.
Based on the table, the predictors leaf.mild, mycelium, and sclerotia have been flagged as near-zero variance, meaning they have extremely low variability in their values.
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 ...predictors <- Soybean[, -1]
categorical_predictors <- predictors[, sapply(predictors, is.factor)]
nzv <- nearZeroVar(categorical_predictors, saveMetrics = TRUE)
print(nzv)## freqRatio percentUnique zeroVar nzv
## date 1.137405 1.0248902 FALSE FALSE
## plant.stand 1.208191 0.2928258 FALSE FALSE
## precip 4.098214 0.4392387 FALSE FALSE
## temp 1.879397 0.4392387 FALSE FALSE
## hail 3.425197 0.2928258 FALSE FALSE
## crop.hist 1.004587 0.5856515 FALSE FALSE
## area.dam 1.213904 0.5856515 FALSE FALSE
## sever 1.651282 0.4392387 FALSE FALSE
## seed.tmt 1.373874 0.4392387 FALSE FALSE
## germ 1.103627 0.4392387 FALSE FALSE
## plant.growth 1.951327 0.2928258 FALSE FALSE
## leaves 7.870130 0.2928258 FALSE FALSE
## leaf.halo 1.547511 0.4392387 FALSE FALSE
## leaf.marg 1.615385 0.4392387 FALSE FALSE
## leaf.size 1.479638 0.4392387 FALSE FALSE
## leaf.shread 5.072917 0.2928258 FALSE FALSE
## leaf.malf 12.311111 0.2928258 FALSE FALSE
## leaf.mild 26.750000 0.4392387 FALSE TRUE
## stem 1.253378 0.2928258 FALSE FALSE
## lodging 12.380952 0.2928258 FALSE FALSE
## stem.cankers 1.984293 0.5856515 FALSE FALSE
## canker.lesion 1.807910 0.5856515 FALSE FALSE
## fruiting.bodies 4.548077 0.2928258 FALSE FALSE
## ext.decay 3.681481 0.4392387 FALSE FALSE
## mycelium 106.500000 0.2928258 FALSE TRUE
## int.discolor 13.204545 0.4392387 FALSE FALSE
## sclerotia 31.250000 0.2928258 FALSE TRUE
## fruit.pods 3.130769 0.5856515 FALSE FALSE
## fruit.spots 3.450000 0.5856515 FALSE FALSE
## seed 4.139130 0.2928258 FALSE FALSE
## mold.growth 7.820896 0.2928258 FALSE FALSE
## seed.discolor 8.015625 0.2928258 FALSE FALSE
## seed.size 9.016949 0.2928258 FALSE FALSE
## shriveling 14.184211 0.2928258 FALSE FALSE
## roots 6.406977 0.4392387 FALSE FALSEflagged_predictors <- rownames(nzv[nzv$nzv == TRUE, ])
print(flagged_predictors)## [1] "leaf.mild" "mycelium" "sclerotia"- Roughly 18% of the data are missing. Are there particular predictors that are more likely to be missing? Is the pattern of missing data related to the classes?
Yes, there are likely particular predictors more likely to be missing. (~15% ~18%) (hail, sever, seed.tmt, lodging, germ, leaf.mild, fruiting.bodies, fruit.spots, seed.discolor, shriveling)
Yes, the pattern is strongly related to the disease classes. (2 4 d injury, Cyst nematode, Diapother pod & stem blight, Herbicide injury, and Phytophthora rot)
missing_pct <- colSums(is.na(predictors)) / nrow(predictors) * 100
print(missing_pct[order(missing_pct, decreasing = TRUE)])## hail sever seed.tmt lodging germ
## 17.7159590 17.7159590 17.7159590 17.7159590 16.3982430
## leaf.mild fruiting.bodies fruit.spots seed.discolor shriveling
## 15.8125915 15.5197657 15.5197657 15.5197657 15.5197657
## leaf.shread seed mold.growth seed.size leaf.halo
## 14.6412884 13.4699854 13.4699854 13.4699854 12.2986823
## leaf.marg leaf.size leaf.malf fruit.pods precip
## 12.2986823 12.2986823 12.2986823 12.2986823 5.5636896
## stem.cankers canker.lesion ext.decay mycelium int.discolor
## 5.5636896 5.5636896 5.5636896 5.5636896 5.5636896
## sclerotia plant.stand roots temp crop.hist
## 5.5636896 5.2708638 4.5387994 4.3923865 2.3426061
## plant.growth stem date area.dam leaves
## 2.3426061 2.3426061 0.1464129 0.1464129 0.0000000missing_by_class <- tapply(rowSums(is.na(predictors)), Soybean$Class, mean) / ncol(predictors) * 100
print(missing_by_class[order(missing_by_class, decreasing = TRUE)])## 2-4-d-injury cyst-nematode
## 80.35714 68.57143
## herbicide-injury phytophthora-rot
## 57.14286 39.41558
## diaporthe-pod-&-stem-blight alternarialeaf-spot
## 33.71429 0.00000
## anthracnose bacterial-blight
## 0.00000 0.00000
## bacterial-pustule brown-spot
## 0.00000 0.00000
## brown-stem-rot charcoal-rot
## 0.00000 0.00000
## diaporthe-stem-canker downy-mildew
## 0.00000 0.00000
## frog-eye-leaf-spot phyllosticta-leaf-spot
## 0.00000 0.00000
## powdery-mildew purple-seed-stain
## 0.00000 0.00000
## rhizoctonia-root-rot
## 0.00000- Develop a strategy for handling missing data, either by eliminating predictors or imputation.
- Removes nzv predictors (leaf.mild, mycelium, sclerotia)
- Remove high-missingness predictors (> 15%)
- Using MICE with predictive mean matching
By using multiple cleaning methods and imputation with MICE to reduce missing data, to remove missing data and impute remaining values using predictive mean matching. It help simplifies the dataset and ensures robust predictive modeling with minimizing bias and enhancing accuracy.
response <- Soybean[, 1]
nzv_predictors <- rownames(nzv[nzv$nzv == TRUE, ])
clean_predictors <- predictors[, !names(predictors) %in% nzv_predictors]
high_missing <- names(missing_pct[missing_pct > 15])
clean_predictors <- clean_predictors[, !names(clean_predictors) %in% high_missing]
imp <- mice(clean_predictors, m = 5, method = "pmm", seed = 123)##
## iter imp variable
## 1 1 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 1 2 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 1 3 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 1 4 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 1 5 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 2 1 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 2 2 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 2 3 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 2 4 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 2 5 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 3 1 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 3 2 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 3 3 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 3 4 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 3 5 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 4 1 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 4 2 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 4 3 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 4 4 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 4 5 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 5 1 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 5 2 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 5 3 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 5 4 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots
## 5 5 date plant.stand precip temp crop.hist area.dam plant.growth leaf.halo leaf.marg leaf.size leaf.shread leaf.malf stem stem.cankers canker.lesion ext.decay int.discolor fruit.pods seed mold.growth seed.size roots## Warning: Number of logged events: 515imputed_predictors <- complete(imp)
imputed_soybean <- cbind(response, imputed_predictors)
str(imputed_soybean)## 'data.frame': 683 obs. of 24 variables:
## $ response : 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 ...
## $ 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 ...
## $ 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 ...
## $ stem : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ 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 ...
## $ ext.decay : Factor w/ 3 levels "0","1","2": 2 2 2 2 2 2 2 2 2 2 ...
## $ int.discolor : Factor w/ 3 levels "0","1","2": 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 ...
## $ 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.size : 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 ...print(colSums(is.na(imputed_soybean)) / nrow(imputed_soybean) * 100)## response date plant.stand precip temp
## 0 0 0 0 0
## crop.hist area.dam plant.growth leaves leaf.halo
## 0 0 0 0 0
## leaf.marg leaf.size leaf.shread leaf.malf stem
## 0 0 0 0 0
## stem.cankers canker.lesion ext.decay int.discolor fruit.pods
## 0 0 0 0 0
## seed mold.growth seed.size roots
## 0 0 0 0