Corey Sparks R blog

I post regularly on various R topics, mostly involving data on people

Demography Informal Methods Seminar - Classification and Regression Trees

Written on June 30, 2020

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.

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

## 
## 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
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.

##                   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
## 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 *

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.

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

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

##      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

## 
## 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

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

## 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
## 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

##    mtry OOBError
## 4     4 9.759980
## 7     7 7.802162
## 14   14 6.484249
## 21   21 5.758013
## 
## 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

##                                     %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

Classification tree for life expectancy - low or high

## $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"

Random forest tree for PRB low life expectancy

## 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

##    mtry OOBError
## 4     4 9.541584
## 7     7 7.789191
## 14   14 6.142687
## 21   21 5.816884
## 
## 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

##                                     %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

##                   
## 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
## [1] 0

More complicated example

using caret to create training and test sets.

We use an 80% training fraction

## Loading required package: lattice
## Loading required package: ggplot2
## 
## Attaching package: 'ggplot2'
## The following object is masked from 'package:randomForest':
## 
##     margin
## 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.

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.

## 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 
##    1    2    1    2    1    1    1    1    1    1    1    2    1    2    2    2 
##   49   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64 
##    2    1    1    1    2    2    2    1    1    2    2    1    2    1    2    2 
##   65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80 
##    2    2    2    2    2    2    1    2    2    1    1    1    2    2    1    2 
##   81   82   83   84   85   86   87   88   89   90   91   92   93   94   95   96 
##    2    2    1    2    1    1    2    2    2    1    1    2    1    2    2    1 
##   97   98   99  100  101  102  103  104  105  106  107  108  109  110  111  112 
##    2    1    2    2    2    2    2    1    1    2    2    1    1    2    1    2 
##  113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128 
##    2    1    2    1    1    1    1    2    2    1    1    2    2    1    2    1 
##  129  130  131  132  133  134  135  136  137  138  139  140  141  142  143  144 
##    2    2    2    2    2    1    1    2    2    2    2    2    2    2    2    1 
##  145  146  147  148  149  150  151  152  153  154  155  156  157  158  159  160 
##    2    2    2    2    1    1    1    1    2    1    1    2    2    2    1    2 
##  161  162  163  164  165  166  167  168  169  170  171  172  173  174  175  176 
##    2    2    2    2    1    1    2    1    2    2    2    2    1    2    1    2 
##  177  178  179  180  181  182  183  184  185  186  187  188  189  190  191  192 
##    1    2    2    1    1    2    2    2    2    2    2    2    2    2    2    1 
##  193  194  195  196  197  198  199  200  201  202  203  204  205  206  207  208 
##    2    2    1    2    1    2    2    2    1    2    2    1    2    2    2    1 
##  209  210  211  212  213  214  215  216  217  218  219  220  221  222  223  224 
##    2    2    2    2    2    1    2    1    2    2    2    2    2    2    2    2 
##  225  226  227  228  229  230  231  232  233  234  235  236  237  238  239  240 
##    2    1    2    1    2    2    2    1    2    2    2    1    2    1    1    1 
##  241  242  243  244  245  246  247  248  249  250  251  252  253  254  255  256 
##    1    2    2    2    2    2    2    2    1    2    1    2    2    2    2    2 
##  257  258  259  260  261  262  263  264  265  266  267  268  269  270  271  272 
##    1    2    2    2    2    1    1    1    2    2    2    2    2    2    2    1 
##  273  274  275  276  277  278  279  280  281  282  283  284  285  286  287  288 
##    2    2    1    1    1    1    2    1    2    1    2    2    2    2    2    1 
##  289  290  291  292  293  294  295  296  297  298  299  300  301  302  303  304 
##    1    1    1    1    2    2    2    1    2    2    2    1    2    2    1    2 
##  305  306  307  308  309  310  311  312  313  314  315  316  317  318  319  320 
##    2    2    2    1    2    1    2    2    1    2    2    2    2    2    2    2 
##  321  322  323  324  325  326  327  328  329  330  331  332  333  334  335  336 
##    1    2    2    2    1    2    2    1    2    1    1    1    2    1    2    2 
##  337  338  339  340  341  342  343  344  345  346  347  348  349  350  351  352 
##    2    1    2    2    1    1    1    1    2    2    1    2    2    1    2    1 
##  353  354  355  356  357  358  359  360  361  362  363  364  365  366  367  368 
##    2    1    1    2    2    2    2    2    2    2    2    1    2    1    2    2 
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##    1    2    1    2    1    2    2    2    2    2    1    1    2    1    2    1 
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##    2    1    2    2    2    2    2    1    2    2    1    1    2    2    2    2 
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##    2    2    2    2    1    1    2    2    2    2    1    1    1    2    1    2 
##  417  418  419  420  421  422  423  424  425  426  427  428  429  430  431  432 
##    2    2    1    1    1    2    2    1    2    1    1    1    2    2    2    1 
##  433  434  435  436  437  438  439  440  441  442  443  444  445  446  447  448 
##    2    1    1    1    2    1    1    1    1    2    2    2    1    2    1    2 
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##    1    1    2    2    2    2    1    2    1    2    2    1    2    2    2    2 
##  465  466  467  468  469  470  471  472  473  474  475  476  477  478  479  480 
##    2    2    2    2    2    2    1    2    2    1    2    2    2    1    2    2 
##  481  482  483  484  485  486  487  488  489  490  491  492  493  494  495  496 
##    2    1    2    2    2    2    2    1    1    1    2    1    1    2    1    2 
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##    2    2    2    1    1    2    2    2    1    1    1    2    2    2    1    2 
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##  529  530  531  532  533  534  535  536  537  538  539  540  541  542  543  544 
##    2    2    1    2    2    1    1    2    2    1    1    2    1    2    2    2 
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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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##    1    1    2    2    1    1    2    2    2    2    2    2    2    1    2    2 
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##  705  706  707  708  709  710  711  712  713  714  715  716  717  718  719  720 
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##  737  738  739  740  741  742  743  744  745  746  747  748  749  750  751  752 
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##  753  754  755  756  757  758  759  760  761  762  763  764  765  766  767  768 
##    2    1    2    2    2    2    2    2    2    2    2    2    2    2    2    1 
##  769  770  771  772  773  774  775  776  777  778  779  780  781  782  783  784 
##    2    2    1    2    1    2    1    2    2    1    1    1    1    2    2    2 
##  785  786  787  788  789  790  791  792  793  794  795  796  797  798  799  800 
##    1    1    2    2    2    2    2    1    2    2    2    2    2    2    2    2 
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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 
##    2    2    2    2    2    2    2    1    2    2    1    2    2    2    1    2 
##  881  882  883  884  885  886  887  888  889  890  891  892  893  894  895  896 
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##  913  914  915  916  917  918  919  920  921  922  923  924  925  926  927  928 
##    1    1    2    2    1    2    2    1    1    2    1    2    2    2    2    1 
##  929  930  931  932  933  934  935  936  937  938  939  940  941  942  943  944 
##    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 
##    2    2    2    2    2    2    2    1    1    2    2    2    2    2    2    1 
##  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 
## 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 
##    1    2    2    2    2    2    2    1    1    2    1    1    1    1    1    2 
## 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 
##    2    2    1    2    1    1    1    1    2    2    2    1    2    1    2    1 
## 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 
##    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 
## 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 
##    1    2    2    2    1    1    2    1    1    2    2    2    1    1    2    1 
## 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 
##    2    2    2    1    2    1    2    2    2    2    1    2    1    1    1    1 
## 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 
##    1    2    2    2    1    2    2    2    2    2    1    2    2    1    1    1 
## 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 
##    1    1    1    2    2    2    1    2    1    2    2    1    1    2    2    1 
## 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 
##    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 
## 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 
##    1    1    2    2    2    2    1    2    1    1    1    2    2    2    2    1 
## 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 
##    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 
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 
##    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 
## 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 
##    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 
## 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 
##    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 
## 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 
##    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 
## 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 
##    2    2    2    2    1    2    2    2    2    2    2    2    2    1    2    2 
## 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 
##    2    2    1    1    1    2    2    2    2    2    2    2    1    2    2    2 
## 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 
##    1    1    2    1    2    2    1    2    2    1    2    1    2    1    2    2 
## 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 
##    1    2    1    2    1    1    1    1    2    2    2    1    2    2    2    2 
## 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 
##    2    1    1    2    2    2    2    2    2    2    2    2    1    1    1    2 
## 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 
##    1    2    1    2    2    1    1    1    1    2    2    1    2    1    2    1 
## 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 
##    1    2    2    2    1    2    2    1    2    2    2    1    2    1    1    2 
## 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 
##    2    2    1    2    2    2    1    1    2    1    2    2    2    2    2    2 
## 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 
##    2    2    1    2    2    1    2    2    2    2    2    2    2    2    2    1 
## 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 
##    2    1    1    1    2    1    2    1    2    2    1    2    1    2    2    2 
## 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 
##    2    1    2    2    2    2    2    1    2    2    1    2    2    2    2    2 
## 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 
##    1    1    1    1    2    2    1    2    1    2    2    2    1    1    1    1 
## 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 
##    2    2    1    1    2    2    1    2    2    1    1    2    1    2    2    1 
## 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 
##    2    1    2    2    1    1    2    1    2    1    1    2    2    1    2    1 
## 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 
##    2    2    2    2    2    2    1    1    1    2    2    2    2    2    2    1 
## 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 
##    2    2    1    2    1    2    1    1    2    1    1    2    1    1    2    2 
## 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 
##    1    1    1    2    2    1    2    2    2    1    1    2    1    1    2    1 
## 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 
##    2    2    1    2    2    2    2    2    2    2    1    2    1    1    1    1 
## 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 
##    2    2    2    2    1    1    2    2    2    2    2    1    1    2    2    2 
## 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 
##    2    1    1    2    1    2    1    2    1    1    1    2    1    1    2    2 
## 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 
##    2    2    1    1    2    1    1    2    1    2    2    2    1    1    2    1 
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##    2    1    2    2    1    1    1    1    2    2    2    1    1    2    1    2 
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## 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"
## 
## 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
##   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
## y
##    mod notmod 
##    719   3410
## y
##       mod    notmod 
## 0.1741342 0.8258658
## 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

Train regression classification models using caret

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

## 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.
## Loading required package: rpart

## 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

## 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             
## 
## 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

## 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

## 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             
## 
## 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

## 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.
## 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             
## 
## 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:

## Type 'citation("pROC")' for a citation.
## 
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
## 
##     cov, smooth, var
## Setting levels: control = mod, case = notmod
## Setting direction: controls > cases

## 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
## Setting levels: control = mod, case = notmod
## Setting direction: controls > cases
## Area under the curve: 0.6774