Classification models

I would suggest you read section 5.1 of Introduction to Statistical Learning to get a full treatment of this topic

In classification methods, we are typically interested in using some observed characteristics of a case to predict a binary categorical outcome. This can be extended to a multi-category outcome, but the largest number of applications involve a 1/0 outcome.

In these examples, we will use the Demographic and Health Survey Model Data. These are based on the DHS survey, but are publicly available and are used to practice using the DHS data sets, but don’t represent a real country.

In this example, we will use the outcome of contraceptive choice (modern vs other/none) as our outcome.

library(haven)
dat<-url("https://github.com/coreysparks/data/blob/master/ZZIR62FL.DTA?raw=true")
model.dat<-read_dta(dat)

Here we recode some of our variables and limit our data to those women who are not currently pregnant and who are sexually active.

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
model.dat2<-model.dat%>%
  mutate(region = v024, 
         modcontra= ifelse(v364 ==1,1, 0),
         age = cut(v012, breaks = 5), 
         livchildren=v218,
         educ = v106,
         currpreg=v213,
         wealth = as.factor(v190),
         partnered = ifelse(v701<=1, 0, 1),
         work = ifelse(v731%in%c(0,1), 0, 1),
         knowmodern=ifelse(v301==3, 1, 0),
         age2=v012^2, 
         rural = ifelse(v025==2, 1,0),
         wantmore = ifelse(v605%in%c(1,2), 1, 0))%>%
  filter(currpreg==0, v536>0, v701!=9)%>% #notpreg, sex active
  dplyr::select(caseid, region, modcontra,age, age2,livchildren, educ, knowmodern, rural, wantmore, partnered,wealth, work)
knitr::kable(head(model.dat2))
caseid region modcontra age age2 livchildren educ knowmodern rural wantmore partnered wealth work
1 1 2 2 0 (28.6,35.4] 900 4 0 1 1 1 0 1 1
1 4 2 2 0 (35.4,42.2] 1764 2 0 1 1 0 0 3 1
1 4 3 2 0 (21.8,28.6] 625 3 1 1 1 0 0 3 1
1 5 1 2 0 (21.8,28.6] 625 2 2 1 1 1 0 2 1
1 6 2 2 0 (35.4,42.2] 1369 2 0 1 1 1 0 3 1
1 7 2 2 0 (15,21.8] 441 1 0 1 1 1 0 1 1

Cross-validation of predictive models

The term cross-validation refers to fitting a model on a subset of data and then testing it on another subset of the data. Typically this process is repeated several times.

The simplest way of doing this is to leave out a single observation, refit the model without it in the data, then predict its value using the rest of the data. This is called hold out cross-validation.

K-fold cross-validation is a process where you leave out a “group” of observations, it is as follows:

  1. Randomize the data
  2. Split the data into k groups, where k is an integer
  3. For each of the k groups,
    • Take one of the groups as a hold out test set
    • Use the other k-1 groups as training data
    • Fit a model using the data on the k-1 groups, and test it on the hold out group
    • Measure predictive accuracy of that model, and throw the model away!
  4. Summarize the model accuracy over the measured model accuracy metrics

A further method is called leave one out, or LOO cross-validation. This combines hold out and k-fold cross-validation.

Why?

By doing this, we can see how model accuracy is affected by particular individuals, and overall allows for model accuracy to be measured repeatedly so we can assess things such as model tuning parameters.

If you remember from last time, the Lasso analysis depended upon us choosing a good value for the penalty term \(\lambda\). In a cross-validation analysis, we can use the various resamplings of the data to examine the model’s accuracy sensitivity to alternative values of this parameter.

This evaluation can either be done systematically, along a grid, or using a random search.

Alternative accuracy measures

We talked last time about using model accuracy as a measure of overall fit. This was calculated using the observed and predicted values of our outcome. For classification model, another commonly used metric of model predictive power is the Receiver Operating Characteristics (ROC) curve. This is a probability curve, and is often accompanied by the area under the curve (AUC) measure, which summarizes the separability of the classes. Together they tell you how capable the model is of determining difference between the classes in the data. The higher the values of these, the better, and they are both bound on (0,1).

A nice description of these are found here.

Regression trees

Regression trees are a common technique used in classification problems. Regression or classification trees attempt to find optimal splits in the data so that the best classification of observations can be found. Chapter 8 of Introduction to Statistical Learning is a good place to start with this.

Regression trees generate a set of splitting rules, which classify the data into a set of classes, based on combinations of the predictors. regression partition

This example, from the text, shows a 3 region partition of data on baseball hitter data. The outcome here is salary in dollars. Region 1 is players who’ve played less than 4.5 years, they typically have lower salary. The other 2 regions consist of players who’ve played longer than 4.5 years, and who have either less than 117.5 or greater than 117.5 hits. Those with more hits have higher salary than those with lower hits.

The regions can be thought of as nodes (or leaves) on a tree.

Here is a regression tree for these data. The Nodes are the mean salary (in thousands) for players in that region. For example, if a player has less than 4.5 years experiences, and have less than 39.5 hits, their average salary is 676.5 thousand dollars.

library(tree)
data(Hitters, package = "ISLR")
head(Hitters)
##                   AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun
## -Andy Allanson      293   66     1   30  29    14     1    293    66      1
## -Alan Ashby         315   81     7   24  38    39    14   3449   835     69
## -Alvin Davis        479  130    18   66  72    76     3   1624   457     63
## -Andre Dawson       496  141    20   65  78    37    11   5628  1575    225
## -Andres Galarraga   321   87    10   39  42    30     2    396   101     12
## -Alfredo Griffin    594  169     4   74  51    35    11   4408  1133     19
##                   CRuns CRBI CWalks League Division PutOuts Assists Errors
## -Andy Allanson       30   29     14      A        E     446      33     20
## -Alan Ashby         321  414    375      N        W     632      43     10
## -Alvin Davis        224  266    263      A        W     880      82     14
## -Andre Dawson       828  838    354      N        E     200      11      3
## -Andres Galarraga    48   46     33      N        E     805      40      4
## -Alfredo Griffin    501  336    194      A        W     282     421     25
##                   Salary NewLeague
## -Andy Allanson        NA         A
## -Alan Ashby        475.0         N
## -Alvin Davis       480.0         A
## -Andre Dawson      500.0         N
## -Andres Galarraga   91.5         N
## -Alfredo Griffin   750.0         A
fit1<-tree(Salary ~ Years+Hits, data=Hitters)
fit1
## node), split, n, deviance, yval
##       * denotes terminal node
## 
##  1) root 263 53320000  535.9  
##    2) Years < 4.5 90  6769000  225.8  
##      4) Hits < 39.5 5  3131000  676.5 *
##      5) Hits > 39.5 85  2564000  199.3  
##       10) Years < 3.5 58   309400  138.8 *
##       11) Years > 3.5 27  1586000  329.3 *
##    3) Years > 4.5 173 33390000  697.2  
##      6) Hits < 117.5 90  5312000  464.9  
##       12) Years < 6.5 26   644100  334.7 *
##       13) Years > 6.5 64  4048000  517.8 *
##      7) Hits > 117.5 83 17960000  949.2  
##       14) Hits < 185 76 13290000  914.3  
##         28) Years < 5.5 8    82790  622.5 *
##         29) Years > 5.5 68 12450000  948.7 *
##       15) Hits > 185 7  3571000 1328.0 *
plot(fit1); text(fit1, pretty=1)

The cut points are decided by minimizing the residual sums of squares for a particular region. So we identify regions of the predictor space, \(R_1, R_2, \dots, R_j\) so that

\[\sum_j \sum_{\in R_j} \left ( y_i - \hat{y_{R_j}} \right )^2\] where \(\hat{y_{R_j}}\) is the mean for a particular region j.

Often this process may over-fit the data, meaning it creates too complicated of a tree (too many terminal nodes). It’s possible to prune the tree to arrive at a simpler tree split that may be easier to interpret.

We can tune the tree depth parameter by cross-validation of the data, across different tree depths. In this case a depth of 3 is optimal.

cvt<-cv.tree(fit1)
plot(cvt$size, cvt$dev, type="b")

Then, we can prune the tree, to basically get the tree version of the figure from above

tree2<-prune.tree(fit1, best=3)
plot(tree2); text(tree2, pretty=1)

# plot(x=Hitters$Years, y=Hitters$Hits)
# abline(v=4.5,  col=3, lwd=3)
# abline(h=117.5, col=4, lwd=3)

Prediction works by assigning the mean value from a region to an observation who matches the decision rule. For example, let’s make up a player who has 6 years experience and 200 hits

new<-data.frame(Hits=200, Years=6)

pred<-predict(fit1, newdata = new)
pred
##      1 
## 1327.5

Classification trees

If our outcome is categorical, or binary, the tree will be a classification tree. Instead of the mean of a particular value being predicted, the classification tree predicts the value of the most common class at a particular terminal node. So in addition to the tree predicting the class at each node, it also gives the class proportions at each node. The classification error rate is the percent of of observations at a node that do not belong to the most common class.

\[Error = 1- max (\hat p_{mk})\] This is not a good method for growing trees, and instead either the Gini index or the entropy is measured at each node:

\[Gini = \sum_k \hat p_{mk}(1-\hat p_{mk})\] The Gini index is used as a measure of node purity, if a node only contains 1 class, it is considered pure

\[Entropy = D = - \sum_k \hat p_{mk} \text{log} \hat p_{mk}\]

Bagging and Random Forests

The example above is a single “tree”, if we did this type of analysis a large number of times, then we would end up with a forest of such trees.

Bagging is short for bootstrap aggragation. This is a general purpose procedure for reducing the variance in a statistical test, but it is also commonly used in regression tree contexts. How this works in this setting is the data are bootstrapped into a large number of training sets, each of the same size. The regression tree is fit to each of these large number of trees and not pruned. By averaging these bootstrapped trees, the accuracy is actually higher than for a single tree alone.

Random forests not only bag the trees, but at each iteration a different set of predictors is chosen from the data, so not only do we arrive at a more accurate bagged tree, but we can also get an idea of how important any particular variable is, based on its averaged Gini impurity across all the trees considered.

## Warning: Number of logged events: 651

simple example using PRB data - Regression tree

#set up training set identifier
train1<-sample(1:dim(prb2)[1], size = .75*dim(prb2)[1], replace=T)

fit<-tree(e0total~., data=prb2[train1,])
summary(fit)
## 
## Regression tree:
## tree(formula = e0total ~ ., data = prb2[train1, ])
## Variables actually used in tree construction:
## [1] "imr" "cdr"
## Number of terminal nodes:  7 
## Residual mean deviance:  6.536 = 973.9 / 149 
## Distribution of residuals:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  -7.783  -1.300   0.000   0.000   1.750   8.000
plot(fit); text(fit, pretty=1)

cv.fit<-cv.tree(fit)
plot(cv.fit$size, cv.fit$dev, type="b")

pt1<-prune.tree(fit, best=7)
plot(pt1); text(pt1, pretty=1)

Bagged regression tree from PRB data - 100 trees - 3 variables each

library(randomForest)
## randomForest 4.6-14
## Type rfNews() to see new features/changes/bug fixes.
## 
## Attaching package: 'randomForest'
## The following object is masked from 'package:dplyr':
## 
##     combine
set.seed(1115)
t1<-tuneRF(y=prb2$e0total, x=prb2[,c(-12,-23)], trace=T, stepFactor = 2, ntreeTry = 1000, plot=T)
## mtry = 7  OOB error = 7.802162 
## Searching left ...
## mtry = 4     OOB error = 9.75998 
## -0.2509328 0.05 
## Searching right ...
## mtry = 14    OOB error = 6.484249 
## 0.1689164 0.05 
## mtry = 21    OOB error = 5.758013 
## 0.112 0.05

t1 #gewt mtry
##    mtry OOBError
## 4     4 9.759980
## 7     7 7.802162
## 14   14 6.484249
## 21   21 5.758013
bag.1<-randomForest(e0total~., data=prb2[train1,-23], mtry=14, ntree=100,importance=T) #mtry = 3; choose 3 variables for each tree
bag.1
## 
## Call:
##  randomForest(formula = e0total ~ ., data = prb2[train1, -23],      mtry = 14, ntree = 100, importance = T) 
##                Type of random forest: regression
##                      Number of trees: 100
## No. of variables tried at each split: 14
## 
##           Mean of squared residuals: 5.190271
##                     % Var explained: 95.89
plot(bag.1)

importance(bag.1)
##                                     %IncMSE IncNodePurity
## continent                          3.848523     405.32174
## population.                        2.447108      47.23318
## cbr                                2.757050     444.96134
## cdr                               12.544770    2713.17272
## rate.of.natural.increase           2.419710     156.97416
## net.migration.rate                 1.669214      51.52248
## imr                               16.149632   11064.00964
## womandlifetimeriskmaternaldeath    5.211886    2608.32904
## tfr                                2.133800     179.19983
## percpoplt15                        2.913135     486.07099
## percpopgt65                        4.272992      65.84541
## percurban                          1.708796      32.93916
## percpopinurbangt750k               2.316377      43.63507
## percpop1549hivaids2007             4.479647     493.30197
## percmarwomcontraall                3.889310      69.80177
## percmarwomcontramodern             2.990570      51.66386
## percppundernourished0204           3.274408      42.50857
## motorvehper1000pop0005             2.482953      31.30377
## percpopwaccessimprovedwatersource  3.444429      35.62867
## gnippppercapitausdollars           7.252401     532.61671
## popdenspersqkm                     2.862772      64.64063
varImpPlot(bag.1, n.var = 10, type=1)

Classification tree for life expectancy - low or high

prb2$lowe0<-as.factor(ifelse(prb2$e0total

cv.fit<-cv.tree(fit)
cv.fit
## $size
## [1] 6 5 4 3 2 1
## 
## $dev
## [1] 141.5133 126.0102 117.9069  92.0370 113.7485 220.3056
## 
## $k
## [1]      -Inf  10.52553  10.71965  14.55516  28.17398 136.27366
## 
## $method
## [1] "deviance"
## 
## attr(,"class")
## [1] "prune"         "tree.sequence"
plot(cv.fit$size, cv.fit$dev, type="b")

pt1<-prune.tree(fit, best=cv.fit$size[which.min(cv.fit$dev)])
plot(pt1); text(pt1, pretty=1)

Random forest tree for PRB low life expectancy

#Tune to find best number of variables to try
t1<-tuneRF(y=prb2$e0total, x=prb2[,c(-12,-23)], trace=T, stepFactor = 2, ntreeTry = 1000, plot=T)
## mtry = 7  OOB error = 7.789191 
## Searching left ...
## mtry = 4     OOB error = 9.541584 
## -0.2249776 0.05 
## Searching right ...
## mtry = 14    OOB error = 6.142687 
## 0.2113831 0.05 
## mtry = 21    OOB error = 5.816884 
## 0.05303921 0.05

t1
##    mtry OOBError
## 4     4 9.541584
## 7     7 7.789191
## 14   14 6.142687
## 21   21 5.816884
y<-prb2$e0total[train1]
bag.2<-randomForest(y=y,x=prb2[train1,c(-12,-23)],  mtry=14, ntree=500,importance=T)
bag.2
## 
## Call:
##  randomForest(x = prb2[train1, c(-12, -23)], y = y, ntree = 500,      mtry = 14, importance = T) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 14
## 
##           Mean of squared residuals: 5.127008
##                     % Var explained: 95.94
plot(bag.2)

importance(bag.2,scale = T )
##                                     %IncMSE IncNodePurity
## continent                          8.113739     315.13346
## population.                        3.491805      47.75376
## cbr                                4.170075     237.33712
## cdr                               30.801400    2809.97899
## rate.of.natural.increase           6.466801     128.37004
## net.migration.rate                 3.123241      41.33661
## imr                               33.424467   10939.33769
## womandlifetimeriskmaternaldeath   11.242490    2433.13138
## tfr                                3.817190     126.53284
## percpoplt15                        6.053018     651.77864
## percpopgt65                        8.185953      79.82232
## percurban                          5.381906      35.32764
## percpopinurbangt750k               3.061482      48.14325
## percpop1549hivaids2007             9.939650     421.01757
## percmarwomcontraall                6.826742      58.17955
## percmarwomcontramodern             7.054051      51.61753
## percppundernourished0204           3.312644      47.19299
## motorvehper1000pop0005             3.973039      54.94647
## percpopwaccessimprovedwatersource  4.080611      82.97701
## gnippppercapitausdollars          15.504913     674.79257
## popdenspersqkm                     4.588320      58.80380
varImpPlot(bag.2, n.var = 10, type=2)

pred<-predict(bag.2, newdata=prb2[-train1,])
table(pred, prb2[-train1, "lowe0"])
##                   
## pred               high low
##   43.9116333333333    0   1
##   46.2554             0   1
##   46.6971666666667    0   1
##   46.8996666666667    0   1
##   48.5067             0   1
##   49.0209666666666    0   1
##   49.2719333333333    0   1
##   49.63               0   1
##   49.8501             0   1
##   49.9107666666667    0   1
##   50.2087666666666    0   1
##   50.3383             0   1
##   50.4601333333333    0   1
##   50.479              0   1
##   52.2138             0   1
##   52.9432333333333    0   1
##   52.9651             0   1
##   57.493              0   1
##   58.0111333333333    0   1
##   58.9252666666667    0   1
##   59.0438666666667    0   1
##   59.0600333333333    0   1
##   60.1836333333333    0   1
##   60.5708666666667    0   1
##   61.0191333333333    0   1
##   61.5247333333333    0   1
##   62.9420666666667    0   1
##   63.4492666666667    0   1
##   63.4620333333333    0   1
##   63.5176333333333    0   1
##   64.1848             0   1
##   64.6063666666666    0   1
##   66.7599             0   1
##   67.3326666666666    0   1
##   68.4877666666667    0   1
##   69.2124             0   1
##   69.5067666666667    1   0
##   69.8787             0   1
##   70.2796666666667    0   1
##   70.5176             0   1
##   70.5517333333333    1   0
##   70.7125             1   0
##   70.805              0   1
##   71.2856333333334    1   0
##   71.3414333333333    1   0
##   71.3880666666667    1   0
##   71.6605333333333    1   0
##   71.7564333333333    1   0
##   71.7668666666667    0   1
##   71.8388             1   0
##   71.8765             0   1
##   72.1625666666667    1   0
##   72.1743             1   0
##   72.2219             1   0
##   72.2382666666667    1   0
##   72.303              1   0
##   72.3485             0   1
##   72.4083666666667    0   1
##   72.6019             1   0
##   72.6527             1   0
##   72.8502             1   0
##   73.0262             0   1
##   73.0343333333333    1   0
##   73.0405666666667    1   0
##   73.0917666666667    1   0
##   73.1843             1   0
##   73.2967666666667    0   1
##   73.3403             1   0
##   73.3828333333333    1   0
##   73.4574666666667    0   1
##   73.6294             1   0
##   74.0595666666666    1   0
##   74.1802666666667    1   0
##   74.4077             1   0
##   74.4351333333333    1   0
##   74.5592666666666    1   0
##   74.8154333333333    1   0
##   74.8921             1   0
##   74.9333666666667    1   0
##   75.0284333333334    1   0
##   75.111              1   0
##   76.0959333333334    1   0
##   76.1659333333333    1   0
##   76.4618333333333    1   0
##   76.5154             1   0
##   77.3296666666667    1   0
##   78.1521666666667    1   0
##   78.5404             1   0
##   78.6370333333334    1   0
##   78.7316             1   0
##   78.8905             1   0
##   78.972              1   0
##   79.1079333333333    1   0
##   79.3042333333334    1   0
##   79.3422             1   0
##   79.3878333333333    1   0
##   79.5871333333333    1   0
##   79.7036666666667    1   0
##   80.1361666666667    1   0
mean(pred==prb2[-train1, "lowe0"]) #accuracy
## [1] 0

More complicated example

using caret to create training and test sets.

We use an 80% training fraction

library(caret)
## Loading required package: lattice
## Loading required package: ggplot2
## 
## Attaching package: 'ggplot2'
## The following object is masked from 'package:randomForest':
## 
##     margin
set.seed(1115)
train<- createDataPartition(y = model.dat2$modcontra , p = .80, list=F)

dtrain<-model.dat2[train,]
## Warning: The `i` argument of ``[`()` can't be a matrix as of tibble 3.0.0.
## Convert to a vector.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.
dtest<-model.dat2[-train,]

Create design matrix

If we have a mixture of factor variables and continuous predictors in our analysis, it is best to set up the design matrix for our models before we run them. Many methods within caret won’t use factor variables correctly unless we set up the dummy variable representations first.

y<-dtrain$modcontra
y<-as.factor(ifelse(y==1, "mod", "notmod"))
x<-model.matrix(~factor(region)+factor(age)+livchildren+factor(rural)+factor(wantmore)+factor(educ)+partnered+factor(work)+factor(wealth), data=dtrain)
x<-data.frame(x)[,-1]

km1<-kmeans(x, centers = 2, nstart=10)
km1
## K-means clustering with 2 clusters of sizes 1669, 2460
## 
## Cluster means:
##   factor.region.2 factor.region.3 factor.region.4 factor.age..21.8.28.6.
## 1       0.2636309      0.09466747       0.2013182             0.07010186
## 2       0.2524390      0.16829268       0.1959350             0.36951220
##   factor.age..28.6.35.4. factor.age..35.4.42.2. factor.age..42.2.49.
## 1              0.3349311              0.3133613           0.27980827
## 2              0.2317073              0.1317073           0.08658537
##   livchildren factor.rural.1 factor.wantmore.1 factor.educ.1 factor.educ.2
## 1    5.173158      0.7177951         0.2822049     0.1084482    0.06411025
## 2    1.876423      0.6235772         0.7199187     0.1284553    0.17560976
##   factor.educ.3 partnered factor.work.1 factor.wealth.2 factor.wealth.3
## 1    0.01018574 0.2150989     0.8106651       0.2348712       0.2264829
## 2    0.03455285 0.3337398     0.7365854       0.2060976       0.2126016
##   factor.wealth.4 factor.wealth.5
## 1       0.1995207      0.08568005
## 2       0.2008130      0.16138211
## 
## Clustering vector:
##    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
##    1    2    2    2    1    2    1    2    1    2    1    2    2    2    2    1 
##   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32 
##    2    1    2    2    1    1    2    2    2    2    2    2    2    2    2    1 
##   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48 
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##    2    2    2    1    2    2    2    2    2    2    1    2    1    1    2    2 
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##    1    2    2    2    2    2    2    1    2    2    2    2    1    1    2    2 
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##  641  642  643  644  645  646  647  648  649  650  651  652  653  654  655  656 
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##    1    1    2    2    1    1    2    2    2    2    2    2    2    1    2    2 
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##    2    2    2    2    1    2    2    2    2    2    2    2    2    2    2    2 
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##  737  738  739  740  741  742  743  744  745  746  747  748  749  750  751  752 
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##  785  786  787  788  789  790  791  792  793  794  795  796  797  798  799  800 
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##  817  818  819  820  821  822  823  824  825  826  827  828  829  830  831  832 
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##  833  834  835  836  837  838  839  840  841  842  843  844  845  846  847  848 
##    1    2    2    2    2    1    2    1    1    1    1    1    2    2    2    1 
##  849  850  851  852  853  854  855  856  857  858  859  860  861  862  863  864 
##    2    2    1    2    1    2    2    2    1    2    2    2    2    2    2    2 
##  865  866  867  868  869  870  871  872  873  874  875  876  877  878  879  880 
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##  881  882  883  884  885  886  887  888  889  890  891  892  893  894  895  896 
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##    1    1    2    2    1    2    2    1    1    2    1    2    2    2    2    1 
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##    2    2    2    2    2    2    2    2    2    2    2    2    1    1    2    2 
##  945  946  947  948  949  950  951  952  953  954  955  956  957  958  959  960 
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##  961  962  963  964  965  966  967  968  969  970  971  972  973  974  975  976 
##    2    2    2    1    1    1    2    1    1    2    1    1    1    2    2    1 
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##    1    1    2    2    1    2    1    2    2    2    2    1    2    1    2    1 
##  993  994  995  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 
##    2    1    1    1    2    1    2    1    2    2    2    1    2    1    2    1 
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##    1    2    1    2    2    1    2    1    2    2    2    1    1    2    2    2 
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##    1    2    1    1    2    1    2    2    1    2    2    2    2    2    1    1 
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##    1    2    2    2    2    2    2    1    1    2    1    1    1    1    1    2 
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##    2    2    1    2    1    1    1    1    2    2    2    1    2    1    2    1 
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##    2    2    2    2    2    2    1    2    1    1    1    2    2    1    2    2 
## 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 
##    2    1    2    2    2    2    1    1    2    1    2    1    1    2    1    1 
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##    1    2    2    2    1    1    2    1    1    2    2    2    1    1    2    1 
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##    2    2    2    1    2    1    2    2    2    2    1    2    1    1    1    1 
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##    1    2    2    2    1    2    2    2    2    2    1    2    2    1    1    1 
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##    1    1    1    2    2    2    1    2    1    2    2    1    1    2    2    1 
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##    1    2    2    2    1    2    2    2    2    2    2    1    2    2    2    2 
## 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 
##    1    1    2    2    1    2    1    1    1    2    2    2    1    1    1    1 
## 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 
##    2    1    2    2    1    1    2    2    2    1    2    2    1    2    2    2 
## 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 
##    2    2    1    2    1    2    2    1    1    1    2    2    1    1    1    2 
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##    1    1    2    2    2    2    1    2    1    1    1    2    2    2    2    1 
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##    1    1    2    1    1    2    1    2    2    2    2    2    2    2    2    2 
## 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 
##    1    1    2    2    2    2    2    2    2    2    2    2    2    1    1    1 
## 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 
##    1    1    1    2    1    2    1    2    1    2    2    2    1    2    2    1 
## 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 
##    1    1    2    2    2    2    2    2    2    2    2    1    1    2    2    2 
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 
##    1    2    1    2    2    1    2    2    1    2    2    2    1    1    2    1 
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##    2    2    1    2    1    2    2    1    1    1    2    2    2    1    1    2 
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 
##    2    2    2    1    2    2    2    2    1    2    2    1    1    1    2    1 
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 
##    1    2    2    2    1    1    2    2    1    2    2    2    2    2    2    2 
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 
##    2    1    1    2    1    1    2    1    2    1    1    2    2    1    2    1 
## 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 
##    2    1    2    2    2    2    2    1    2    2    2    1    1    1    2    2 
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##    1    1    1    2    2    1    2    1    2    1    2    2    1    2    2    2 
## 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 
##    1    1    2    2    2    2    1    1    2    2    2    2    2    2    2    2 
## 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 
##    2    2    2    2    2    2    2    1    1    1    2    1    1    1    1    1 
## 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 
##    2    2    2    2    1    1    2    2    2    1    2    1    2    2    1    1 
## 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 
##    2    2    1    2    2    2    2    2    2    1    2    2    2    2    2    2 
## 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 
##    2    2    2    2    1    2    1    1    2    1    1    2    2    2    1    2 
## 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 
##    2    2    1    2    1    1    2    2    1    1    2    2    2    2    2    2 
## 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 
##    2    2    2    1    1    1    1    1    2    1    1    2    2    2    1    2 
## 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 
##    2    2    1    2    1    2    1    2    2    2    1    1    1    2    2    2 
## 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 
##    2    2    2    2    1    1    1    1    2    2    2    2    2    2    2    1 
## 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 
##    1    1    2    1    2    2    1    2    2    2    2    1    2    1    2    2 
## 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 
##    2    2    1    2    2    2    2    2    2    2    2    1    1    2    2    1 
## 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 
##    2    2    1    2    2    1    2    2    1    2    2    2    2    1    2    1 
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##    2    1    2    2    2    2    2    1    2    2    1    1    2    2    2    2 
## 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 
##    2    2    2    2    2    1    1    2    2    2    1    2    1    2    1    2 
## 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 
##    2    1    2    2    2    2    2    2    1    1    2    2    2    2    2    2 
## 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 
##    2    2    2    1    2    2    1    1    2    1    2    1    1    2    2    1 
## 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 
##    2    2    1    2    2    1    1    1    2    2    2    2    2    2    1    2 
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##    1    2    2    1    1    1    2    1    2    2    2    1    1    1    2    1 
## 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 
##    2    1    2    2    2    1    1    1    2    2    1    1    1    1    2    1 
## 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 
##    2    2    2    1    2    1    2    1    1    1    1    2    2    2    2    1 
## 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 
##    1    2    1    1    1    2    2    2    2    2    1    1    1    2    1    2 
## 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 
##    2    2    1    1    2    1    1    2    1    2    1    1    2    2    2    2 
## 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 
##    2    2    2    2    2    2    1    2    1    1    2    2    2    2    1    2 
## 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 
##    1    1    2    1    1    1    2    2    2    1    1    2    2    1    2    1 
## 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 
##    1    1    1    2    1    2    2    2    1    2    1    1    1    2    2    1 
## 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 
##    1    2    2    1    1    2    1    2    2    1    2    2    1    1    1    1 
## 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 
##    2    1    1    1    1    2    2    2    2    1    1    1    1    1    2    2 
## 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 
##    2    2    1    1    2    2    1    2    2    2    2    1    1    1    2    2 
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##    1    1    2    1    2    2    1    2    2    1    2    1    2    1    2    2 
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##    1    2    2    2    1    2    2    1    2    2    2    1    2    1    1    2 
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## 3745 3746 3747 3748 3749 3750 3751 3752 3753 3754 3755 3756 3757 3758 3759 3760 
##    2    2    1    1    2    2    2    2    1    1    2    2    2    2    2    2 
## 3761 3762 3763 3764 3765 3766 3767 3768 3769 3770 3771 3772 3773 3774 3775 3776 
##    2    2    1    2    1    1    2    2    1    2    2    1    2    2    2    2 
## 3777 3778 3779 3780 3781 3782 3783 3784 3785 3786 3787 3788 3789 3790 3791 3792 
##    2    1    1    2    1    2    2    1    1    1    2    2    2    1    2    1 
## 3793 3794 3795 3796 3797 3798 3799 3800 3801 3802 3803 3804 3805 3806 3807 3808 
##    2    2    1    1    1    1    1    2    2    1    2    1    2    2    1    2 
## 3809 3810 3811 3812 3813 3814 3815 3816 3817 3818 3819 3820 3821 3822 3823 3824 
##    1    1    1    1    2    1    1    1    2    2    2    2    1    2    1    1 
## 3825 3826 3827 3828 3829 3830 3831 3832 3833 3834 3835 3836 3837 3838 3839 3840 
##    1    2    2    1    1    2    2    2    2    2    1    1    2    1    2    2 
## 3841 3842 3843 3844 3845 3846 3847 3848 3849 3850 3851 3852 3853 3854 3855 3856 
##    2    1    1    2    2    2    2    2    2    2    1    2    2    1    2    2 
## 3857 3858 3859 3860 3861 3862 3863 3864 3865 3866 3867 3868 3869 3870 3871 3872 
##    2    2    2    2    1    2    2    1    1    1    1    2    1    2    1    2 
## 3873 3874 3875 3876 3877 3878 3879 3880 3881 3882 3883 3884 3885 3886 3887 3888 
##    1    2    2    2    2    1    2    2    1    1    1    2    1    2    1    2 
## 3889 3890 3891 3892 3893 3894 3895 3896 3897 3898 3899 3900 3901 3902 3903 3904 
##    1    1    1    1    1    1    2    2    1    1    1    2    2    2    2    2 
## 3905 3906 3907 3908 3909 3910 3911 3912 3913 3914 3915 3916 3917 3918 3919 3920 
##    1    2    2    1    2    2    1    2    2    1    2    1    2    2    2    2 
## 3921 3922 3923 3924 3925 3926 3927 3928 3929 3930 3931 3932 3933 3934 3935 3936 
##    2    2    2    1    1    2    2    2    2    1    2    2    1    1    1    2 
## 3937 3938 3939 3940 3941 3942 3943 3944 3945 3946 3947 3948 3949 3950 3951 3952 
##    1    2    1    2    1    2    1    1    2    1    2    2    1    2    1    1 
## 3953 3954 3955 3956 3957 3958 3959 3960 3961 3962 3963 3964 3965 3966 3967 3968 
##    1    2    2    1    1    1    2    1    1    2    2    2    1    2    1    2 
## 3969 3970 3971 3972 3973 3974 3975 3976 3977 3978 3979 3980 3981 3982 3983 3984 
##    1    1    1    1    2    1    1    1    2    1    2    1    2    1    1    2 
## 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 
##    2    1    2    1    2    2    2    2    2    2    1    1    2    1    2    2 
## 4001 4002 4003 4004 4005 4006 4007 4008 4009 4010 4011 4012 4013 4014 4015 4016 
##    2    2    2    1    1    1    1    1    1    2    1    2    1    2    1    2 
## 4017 4018 4019 4020 4021 4022 4023 4024 4025 4026 4027 4028 4029 4030 4031 4032 
##    1    1    1    1    2    1    2    2    2    2    2    2    2    1    1    1 
## 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045 4046 4047 4048 
##    2    1    2    2    2    2    2    2    1    2    1    2    1    1    1    1 
## 4049 4050 4051 4052 4053 4054 4055 4056 4057 4058 4059 4060 4061 4062 4063 4064 
##    2    2    1    2    1    1    2    1    1    2    2    2    2    1    2    2 
## 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 4079 4080 
##    2    2    1    1    2    2    2    1    1    2    1    2    2    2    1    1 
## 4081 4082 4083 4084 4085 4086 4087 4088 4089 4090 4091 4092 4093 4094 4095 4096 
##    1    2    2    1    2    2    2    2    1    1    1    1    1    2    1    2 
## 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 4110 4111 4112 
##    1    2    1    2    2    2    2    2    1    1    1    1    1    2    2    2 
## 4113 4114 4115 4116 4117 4118 4119 4120 4121 4122 4123 4124 4125 4126 4127 4128 
##    2    1    1    2    2    2    2    2    1    2    1    1    1    1    2    1 
## 4129 
##    2 
## 
## Within cluster sum of squares by cluster:
## [1] 6942.451 9338.897
##  (between_SS / total_SS =  40.8 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"
dtrain$cluster<- km1$cluster

summary(glm(modcontra~factor(cluster), family = binomial, data=dtrain))
## 
## Call:
## glm(formula = modcontra ~ factor(cluster), family = binomial, 
##     data = dtrain)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.6581  -0.6581  -0.5908  -0.5908   1.9139  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      -1.41958    0.06181  -22.96   <2e-16 ***
## factor(cluster)2 -0.23744    0.08272   -2.87   0.0041 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 3818.3  on 4128  degrees of freedom
## Residual deviance: 3810.2  on 4127  degrees of freedom
## AIC: 3814.2
## 
## Number of Fisher Scoring iterations: 4
head(x)
##   factor.region.2 factor.region.3 factor.region.4 factor.age..21.8.28.6.
## 1               1               0               0                      0
## 2               1               0               0                      1
## 3               1               0               0                      0
## 4               1               0               0                      0
## 5               1               0               0                      0
## 6               1               0               0                      0
##   factor.age..28.6.35.4. factor.age..35.4.42.2. factor.age..42.2.49.
## 1                      1                      0                    0
## 2                      0                      0                    0
## 3                      0                      1                    0
## 4                      0                      0                    1
## 5                      1                      0                    0
## 6                      0                      0                    0
##   livchildren factor.rural.1 factor.wantmore.1 factor.educ.1 factor.educ.2
## 1           4              1                 1             0             0
## 2           3              1                 0             1             0
## 3           2              1                 1             0             0
## 4           2              1                 1             0             0
## 5           4              1                 1             0             0
## 6           1              1                 1             1             0
##   factor.educ.3 partnered factor.work.1 factor.wealth.2 factor.wealth.3
## 1             0         0             1               0               0
## 2             0         0             1               0               1
## 3             0         0             1               0               1
## 4             0         0             1               0               0
## 5             0         0             1               0               0
## 6             0         0             1               0               0
##   factor.wealth.4 factor.wealth.5
## 1               0               0
## 2               0               0
## 3               0               0
## 4               1               0
## 5               0               0
## 6               0               0
table(y)
## y
##    mod notmod 
##    719   3410
prop.table(table(y))
## y
##       mod    notmod 
## 0.1741342 0.8258658
xtest<-model.matrix(~factor(region)+factor(age)+livchildren+factor(rural)+factor(wantmore)+factor(educ)+partnered+factor(work)+factor(wealth), data=dtest)
xtest<-xtest[,-1]
xtest<-data.frame(xtest)

yt<-dtest$modcontra
yt<-as.factor(ifelse(yt==1, "mod", "notmod"))
prop.table(table(yt))
## yt
##       mod    notmod 
## 0.2102713 0.7897287

Set up caret for repeated 10 fold cross-validation

To set up the training controls for a caret model, we typically have to specify the type of re-sampling method, the number of resamplings, the number of repeats (if you’re doing repeated sampling). Here we will do a 10 fold cross-validation, 10 is often recommended as a choice for k based on experimental sensitivity analysis.

The other things we specify are:

  • repeats - These are the number of times we wish to repeat the cross-validation, typically 3 or more is used
  • classProbs = TRUE - this is necessary to assess accuracy in the confusion matrix
  • search = “random” is used if you want to randomly search along the values of the tuning parameter
  • sampling - Here we can specify alternative sampling methods to account for unbalanced outcomes
  • SummaryFunction=twoClassSummary - keeps information on the two classes of the outcome
  • savePredictions = T - have the process save all the predicted values throughout the process, we need this for the ROC curves
fitctrl <- trainControl(method="repeatedcv", 
                        number=10, 
                        repeats=5,
                        classProbs = TRUE,
                     search="random", #randomly search on different values of the tuning parameters
                     sampling = "down", #optional, but good for unbalanced outcomes like this one
                     summaryFunction=twoClassSummary,
                     savePredictions = "all")

Train regression classification models using caret

Here we fit a basic regression classification tree using the rpart() function

fitctrl <- trainControl(method="cv", 
                        number=10, 
                        #repeats=5,
                        classProbs = TRUE,
                     search="random",
                     sampling = "down",
                     summaryFunction=twoClassSummary,
                     savePredictions = "all")

rp1<-caret::train(y=y, x=x, 
           metric="ROC",
           method ="rpart",
          tuneLength=20, #try 20 random values of the tuning parameters
           trControl=fitctrl,
          preProcess=c("center", "scale"))

rp1
## CART 
## 
## 4129 samples
##   19 predictor
##    2 classes: 'mod', 'notmod' 
## 
## Pre-processing: centered (19), scaled (19) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 3716, 3716, 3716, 3716, 3716, 3716, ... 
## Addtional sampling using down-sampling prior to pre-processing
## 
## Resampling results across tuning parameters:
## 
##   cp            ROC        Sens       Spec     
##   0.0000000000  0.6387339  0.5883216  0.6005865
##   0.0002781641  0.6398112  0.5910994  0.6002933
##   0.0003477051  0.6393265  0.5938772  0.5979472
##   0.0004636069  0.6378236  0.5883216  0.6011730
##   0.0013908206  0.6414247  0.6202269  0.5944282
##   0.0018544274  0.6447474  0.6453052  0.6093842
## 
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.001854427.
library(rpart.plot)
## Loading required package: rpart
plot(rp1)

#plot(rp1$finalModel)
prp(rp1$finalModel,type=4, extra = 4, 
    main="Classification tree for using modern contraception")

varImp(rp1)
## rpart variable importance
## 
##                        Overall
## livchildren            100.000
## partnered               79.283
## factor.age..28.6.35.4.  60.287
## factor.rural.1          54.849
## factor.educ.2           37.668
## factor.age..21.8.28.6.  33.258
## factor.region.3         32.785
## factor.wantmore.1       25.272
## factor.region.2         22.304
## factor.work.1           21.409
## factor.age..42.2.49.    20.856
## factor.region.4         19.453
## factor.wealth.4         17.237
## factor.wealth.3          9.969
## factor.age..35.4.42.2.   8.871
## factor.wealth.2          6.085
## factor.educ.1            5.067
## factor.wealth.5          3.287
## factor.educ.3            0.000
plot(varImp(rp1), top=10)

##Accuracy on training set
pred1<-predict(rp1, newdata=x)
confusionMatrix(data = pred1,reference = y, positive = "mod" )
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  mod notmod
##     mod     496   1186
##     notmod  223   2224
##                                           
##                Accuracy : 0.6588          
##                  95% CI : (0.6441, 0.6732)
##     No Information Rate : 0.8259          
##     P-Value [Acc > NIR] : 1               
##                                           
##                   Kappa : 0.2238          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.6898          
##             Specificity : 0.6522          
##          Pos Pred Value : 0.2949          
##          Neg Pred Value : 0.9089          
##              Prevalence : 0.1741          
##          Detection Rate : 0.1201          
##    Detection Prevalence : 0.4074          
##       Balanced Accuracy : 0.6710          
##                                           
##        'Positive' Class : mod             
## 
predt1<-predict(rp1, newdata=xtest)
confusionMatrix(data = predt1, yt, positive = "mod" )
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction mod notmod
##     mod    132    302
##     notmod  85    513
##                                           
##                Accuracy : 0.625           
##                  95% CI : (0.5947, 0.6546)
##     No Information Rate : 0.7897          
##     P-Value [Acc > NIR] : 1               
##                                           
##                   Kappa : 0.1739          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.6083          
##             Specificity : 0.6294          
##          Pos Pred Value : 0.3041          
##          Neg Pred Value : 0.8579          
##              Prevalence : 0.2103          
##          Detection Rate : 0.1279          
##    Detection Prevalence : 0.4205          
##       Balanced Accuracy : 0.6189          
##                                           
##        'Positive' Class : mod             
## 

Bagged tree model

fitctrl <- trainControl(method="cv", 
                        number=10, 
                        #repeats=5,
                        classProbs = TRUE,
                     search="random",
                     sampling = "down",
                     summaryFunction=twoClassSummary,
                     savePredictions = "all")

bt1<-caret::train(y=y, x=x, 
           metric="ROC",
           method ="treebag",
          tuneLength=20, #try 20 random values of the tuning parameters
           trControl=fitctrl,
          preProcess=c("center", "scale"))

print(bt1)
## Bagged CART 
## 
## 4129 samples
##   19 predictor
##    2 classes: 'mod', 'notmod' 
## 
## Pre-processing: centered (19), scaled (19) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 3716, 3716, 3716, 3716, 3716, 3716, ... 
## Addtional sampling using down-sampling prior to pre-processing
## 
## Resampling results:
## 
##   ROC        Sens       Spec     
##   0.6289611  0.6132238  0.5721408
plot(varImp(bt1))

##Accuracy on training set
pred1<-predict(bt1, newdata=x)
confusionMatrix(data = pred1,reference = y, positive = "mod" )
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  mod notmod
##     mod     646   1201
##     notmod   73   2209
##                                           
##                Accuracy : 0.6915          
##                  95% CI : (0.6771, 0.7055)
##     No Information Rate : 0.8259          
##     P-Value [Acc > NIR] : 1               
##                                           
##                   Kappa : 0.3374          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.8985          
##             Specificity : 0.6478          
##          Pos Pred Value : 0.3498          
##          Neg Pred Value : 0.9680          
##              Prevalence : 0.1741          
##          Detection Rate : 0.1565          
##    Detection Prevalence : 0.4473          
##       Balanced Accuracy : 0.7731          
##                                           
##        'Positive' Class : mod             
## 
predt1<-predict(bt1, newdata=xtest)
confusionMatrix(data = predt1,yt, positive = "mod" )
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction mod notmod
##     mod    135    329
##     notmod  82    486
##                                           
##                Accuracy : 0.6017          
##                  95% CI : (0.5711, 0.6318)
##     No Information Rate : 0.7897          
##     P-Value [Acc > NIR] : 1               
##                                           
##                   Kappa : 0.1541          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.6221          
##             Specificity : 0.5963          
##          Pos Pred Value : 0.2909          
##          Neg Pred Value : 0.8556          
##              Prevalence : 0.2103          
##          Detection Rate : 0.1308          
##    Detection Prevalence : 0.4496          
##       Balanced Accuracy : 0.6092          
##                                           
##        'Positive' Class : mod             
## 

Random forest model using caret

library(rpart)
rf1<-caret::train(y=y, x=x, 
           data=dtrain,
           metric="ROC",
           method ="rf",
          tuneLength=20, #try 20 random values of the tuning parameters
           trControl=fitctrl, 
          preProcess=c("center", "scale"))

rf1
## Random Forest 
## 
## 4129 samples
##   19 predictor
##    2 classes: 'mod', 'notmod' 
## 
## Pre-processing: centered (19), scaled (19) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 3716, 3716, 3716, 3716, 3716, 3716, ... 
## Addtional sampling using down-sampling prior to pre-processing
## 
## Resampling results across tuning parameters:
## 
##   mtry  ROC        Sens       Spec     
##    1    0.6737048  0.5508803  0.6994135
##    2    0.6727308  0.6023670  0.6571848
##    3    0.6770178  0.6357003  0.6357771
##    5    0.6598504  0.6286189  0.5958944
##    6    0.6531281  0.6091549  0.6011730
##    7    0.6432423  0.6091549  0.5909091
##    8    0.6339576  0.6147692  0.5809384
##    9    0.6425341  0.6426252  0.5809384
##   11    0.6283912  0.6258998  0.5733138
##   13    0.6313454  0.6271127  0.5759531
##   15    0.6371863  0.6439750  0.5712610
## 
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 3.
##Accuracy on training set
predrf1<-predict(rf1, newdata=x)
confusionMatrix(data = predrf1,y, positive = "mod" )
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  mod notmod
##     mod     529    972
##     notmod  190   2438
##                                           
##                Accuracy : 0.7186          
##                  95% CI : (0.7046, 0.7323)
##     No Information Rate : 0.8259          
##     P-Value [Acc > NIR] : 1               
##                                           
##                   Kappa : 0.3154          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.7357          
##             Specificity : 0.7150          
##          Pos Pred Value : 0.3524          
##          Neg Pred Value : 0.9277          
##              Prevalence : 0.1741          
##          Detection Rate : 0.1281          
##    Detection Prevalence : 0.3635          
##       Balanced Accuracy : 0.7254          
##                                           
##        'Positive' Class : mod             
## 
predgl1<-predict(rf1, newdata=xtest)
confusionMatrix(data = predgl1,yt, positive = "mod" )
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction mod notmod
##     mod    129    266
##     notmod  88    549
##                                           
##                Accuracy : 0.657           
##                  95% CI : (0.6271, 0.6859)
##     No Information Rate : 0.7897          
##     P-Value [Acc > NIR] : 1               
##                                           
##                   Kappa : 0.2061          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.5945          
##             Specificity : 0.6736          
##          Pos Pred Value : 0.3266          
##          Neg Pred Value : 0.8619          
##              Prevalence : 0.2103          
##          Detection Rate : 0.1250          
##    Detection Prevalence : 0.3828          
##       Balanced Accuracy : 0.6340          
##                                           
##        'Positive' Class : mod             
## 

We see that by down sampling the more common level of the outcome, we end up with much more balanced accuracy in terms of specificity and sensitivity.

You see that the best fitting model is much more complicated than the previous one. Each node box displays the classification, the probability of each class at that node (i.e. the probability of the class conditioned on the node) and the percentage of observations used at that node. From here.

ROC curve

The ROC curve can be shown for the model:

library(pROC)
## Type 'citation("pROC")' for a citation.
## 
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var
# Select a parameter setting
mycp<-rf1$pred$mtry==rf1$bestTune$mtry
selectedIndices <- mycp==T
# Plot:
plot.roc(rf1$pred$obs[selectedIndices], rf1$pred$mod[selectedIndices], grid=T)
## Setting levels: control = mod, case = notmod
## Setting direction: controls > cases

#Value of ROC and AUC
roc(rf1$pred$obs[selectedIndices],  rf1$pred$mod[selectedIndices])
## Setting levels: control = mod, case = notmod
## Setting direction: controls > cases
## 
## Call:
## roc.default(response = rf1$pred$obs[selectedIndices], predictor = rf1$pred$mod[selectedIndices])
## 
## Data: rf1$pred$mod[selectedIndices] in 719 controls (rf1$pred$obs[selectedIndices] mod) > 3410 cases (rf1$pred$obs[selectedIndices] notmod).
## Area under the curve: 0.6774
auc(rf1$pred$obs[selectedIndices],  rf1$pred$mod[selectedIndices])
## Setting levels: control = mod, case = notmod
## Setting direction: controls > cases
## Area under the curve: 0.6774