HW4_624 Predictive Analytics
Karim Hammoud
Do problems 3.1 and 3.2 in the Kuhn and Johnson book Applied Predictive Modeling.
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.
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 ...(a) Using visualizations, explore the predictor variables to understand their distributions as well as the relationships between predictors.
x <- Glass[,1:9]
par(mfrow=c(3,3))
for (i in 1:ncol(x)) {
hist(x[, i], xlab = names(x[i]), main = paste(names(x)[i]), col = "skyblue3")
}
pairs(x, main ="matrix")
Histograms above show RI, Na, AI, and Si have more of a normal distribution, while the others don’t show any normality. In the matrix of the scatterplot most of the variables don’t have strong correlation; maybe only RI and Ca do show a positive relationship.
(b) Do there appear to be any outliers in the data? Are any predictors skewed?
Here I am going to run the boxplot to check if there is any outlines, and how the data is skewed.
x <- Glass[,1:9]
par(mfrow = c(3,3))
for (i in 1:ncol(x)){
boxplot(x[,i], ylab=names(x[i]), horizontal = T, col= "skyblue3")
}
par(mfrow = c(3,3))
for (i in 1:ncol(x)) {
d <- density(x[,i], na.rm = TRUE)
plot(d, main = paste(names(x[i])))
polygon(d, col="steelblue")
}
From the boxplots we can see outliers in each variable except in Mg, there are an extereme outliers in K and BA, most of the vairables are skewed, Mg is left skewed, while Ca, Ba, Fe, K are right skewed.
(c) Are there any relevant transformations of one or more predictors that might improve the classification model?
To reduce skewness, he Box-Cox method uses a maximum likelihood estimation to determine the transformation parameter \(\lambda\). This can be used to improve the overall classification model.
Using the BoxCox to transform the data
transform <- function(x){
y <- BoxCox(x, lambda = BoxCox.lambda(x, lower=0))
}
x1 <- as.data.frame(sapply(x, transform))
head(x1)## RI Na Mg Al Si K Ca Ba
## 1 0.4193782 2.613147 3.489966 0.09697182 4.273981 -2.5764727 2.169150 -11.30597
## 2 0.4171403 2.631311 2.599979 0.32523264 4.287131 -0.7171316 2.058049 -11.30597
## 3 0.4161976 2.605049 2.549980 0.46731972 4.290700 -0.9140172 2.051643 -11.30597
## 4 0.4171732 2.581111 2.689978 0.26673561 4.285479 -0.5522072 2.106661 -11.30597
## 5 0.4170151 2.585643 2.619979 0.22369983 4.291933 -0.5866341 2.088243 -11.30597
## 6 0.4160525 2.548797 2.609979 0.52706793 4.290426 -0.4400241 2.088243 -11.30597
## Fe
## 1 -7.605525
## 2 -7.605525
## 3 -7.605525
## 4 -7.605525
## 5 -7.605525
## 6 -1.234520Visualize the transformation
x1 %>%
gather() %>%
ggplot(aes(value))+
geom_histogram()+
facet_wrap(~key, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
The skewness of variables was changed as a result of applying the box-cox transformation.
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 environmen- tal 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
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 ...(a) Investigate the frequency distributions for the categorical predictors. Are any of the distributions degenerate in the ways discussed earlier in this chapter?
x <- Soybean[,2:36]
par(mfrow=c(3,6))
for (i in 1:ncol(x)){
smoothScatter(x[ ,i], ylab = names(x[i]))
}
library(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## lift## The following objects are masked from 'package:fabletools':
##
## MAE, RMSEnearZeroVar(x, names = TRUE, saveMetrics=T)## 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 FALSEThere are few variables the have unique values in the Smoothed Density Scatterplots. mycelium and sclerotia could possibly be degenerate due to the low frequencies in some of thier values. The variables leaf.mild and int.discolor appear to show near-zero variance as well. I ran the nearZeroVar() function on the data shows that only mycelium, sclerotia, and leaf.mild have near-zero variance (“nzv”). but it doesn’t show that any variable has zero variance (“zeroVar”).
(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?
Using the aggr function I will plots and calculates the amount of missing values in each variable.
aggr(Soybean, prop = c(T, T), bars=T, numbers=T, sortVars=T)
##
## 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 0.000000000The bar chart shows the proportion of missing data per variable with a grid with the proportion of missing data for variable combinations. there are few variables have over 15% missing values, there are over 82% not missing values accross all variables.
Soybean %>%
mutate(Total = n()) %>%
filter(!complete.cases(.)) %>%
group_by(Class) %>%
mutate(Missing = n(), Proportion=Missing/Total) %>%
select(Class, Missing, Proportion) %>%
unique()## # A tibble: 5 × 3
## # Groups: Class [5]
## Class Missing Proportion
## <fct> <int> <dbl>
## 1 phytophthora-rot 68 0.0996
## 2 diaporthe-pod-&-stem-blight 15 0.0220
## 3 cyst-nematode 14 0.0205
## 4 2-4-d-injury 16 0.0234
## 5 herbicide-injury 8 0.0117From the list the majority of the missing values are in the phytophthora-rot class which has nearly 10% incomplete cases. The are only four more, out of the eighteen other, variables with incomplete cases. The pattern of missing data is related to the classes.
(c) Develop a strategy for handling missing data, either by eliminating predictors or imputation.
MIMCA function/package to impute multiple dataset for the missing values.
library(missMDA)
res <- MIMCA(Soybean, ncp=1,nboot=2)
str(res)## List of 3
## $ res.MI :List of 2
## ..$ nboot=1:'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 : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## .. ..$ precip : Factor w/ 3 levels "0","1","2": 3 3 3 3 3 3 3 3 3 3 ...
## .. ..$ temp : 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 : 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 : 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 ...
## ..$ nboot=2:'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 : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## .. ..$ precip : Factor w/ 3 levels "0","1","2": 3 3 3 3 3 3 3 3 3 3 ...
## .. ..$ temp : 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 : 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 : 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 ...
## $ res.imputeMCA: num [1:683, 1:118] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:683] "1" "2" "3" "4" ...
## .. ..$ : chr [1:118] "2-4-d-injury" "alternarialeaf-spot" "anthracnose" "bacterial-blight" ...
## $ call :List of 8
## ..$ X :'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 ...
## ..$ nboot : num 2
## ..$ ncp : num 1
## ..$ coeff.ridge: num 1
## ..$ threshold : num 1e-06
## ..$ seed : NULL
## ..$ maxiter : num 1000
## ..$ tab.disj : num [1:683, 1:118, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "class")= chr [1:2] "MIMCA" "list"It looks there are no missing data left in the data. The aggr function used in (b) now shows no missing data in any variable.