Семинар 7. Классификация
Октябрь, 29, 2018
Шаманское заклинание для настройки глобальных опций отчёта:
library(tidyverse) # обработка данных, графики...
library(skimr) # описательные статистики
library(rio) # импорт фантастического количества форматов данных
library(broom) # метла превращает результаты оценивания моделей в таблички
library(Ecdat) # много-много разных наборов данных
library(ISLR) # ещё данные
library(sandwich) # оценка Var для гетероскедастичности
library(caret) # пакет для подбора параметров разных моделей
library(FFTrees) # быстрые деревья
library(margins) # для подсчёта предельных эффектов
library(rpart.plot) # для картинок деревьев
library(plotROC) # визуализация ROC-кривой
library(ggeffects) # графики для предельных эффектов
library(MLmetrics) # метрики качества
library(ranger) # строим деревьяИмпортируем набор данных по успеваемости студентов и смотрим на него :)
educ <- import('data/xAPI-Edu-Data.csv')
skim(educ)## Skim summary statistics
## n obs: 480
## n variables: 17
##
## Variable type: character
## variable missing complete n min max empty n_unique
## Class 0 480 480 1 1 0 3
## GradeID 0 480 480 4 4 0 10
## NationalITy 0 480 480 2 11 0 14
## ParentAnsweringSurvey 0 480 480 2 3 0 2
## ParentschoolSatisfaction 0 480 480 3 4 0 2
## PlaceofBirth 0 480 480 3 11 0 14
## Relation 0 480 480 3 6 0 2
## SectionID 0 480 480 1 1 0 3
## Semester 0 480 480 1 1 0 2
## StageID 0 480 480 10 12 0 3
## StudentAbsenceDays 0 480 480 7 7 0 2
## Topic 0 480 480 2 9 0 12
## gender 0 480 480 1 1 0 2
##
## Variable type: integer
## variable missing complete n mean sd p0 p25 p50 p75 p100
## AnnouncementsView 0 480 480 37.92 26.61 0 14 33 58 98
## Discussion 0 480 480 43.28 27.64 1 20 39 70 99
## VisITedResources 0 480 480 54.8 33.08 0 20 65 84 99
## raisedhands 0 480 480 46.77 30.78 0 15.75 50 75 100
## hist
## <U+2587><U+2586><U+2585><U+2585><U+2585><U+2583><U+2583><U+2582>
## <U+2587><U+2587><U+2587><U+2587><U+2583><U+2585><U+2585><U+2583>
## <U+2586><U+2583><U+2582><U+2581><U+2583><U+2583><U+2587><U+2587>
## <U+2587><U+2586><U+2583><U+2583><U+2583><U+2586><U+2586><U+2583>Данные взяты с kaggle.com. Целевая переменная — успеваемость студента, Class, принимает три значения, ‘H’ (high), ‘M’ (mid), ‘L’ (low). Остальные переменные — характеристики студента.
Для целей бинарной классификации объединяем две верхних категории в одну:
educ_logit <- mutate(educ, y = fct_collapse(Class, H = c('M', 'H')))И объявляем все текстовые переменные факторными:
educ_fct <- mutate_if(educ_logit, is.character, factor)Разделим выборку на две части, обучающую и тестовую. По тестовой мы сможем оценить качество прогнозов нашей модели.
Разбиение выборки на две части — это случаная операция, поэтому зададим на удачу зерно генератора случайных чисел.
Создадим вектор train_rows с номерами строк для обучающей части.
set.seed(777)
train_rows <- createDataPartition(educ_fct$y, p = 0.8, list = FALSE)И разделим выборку согласно вектору train_rows:
educ_train <- educ_fct[train_rows, ]
educ_test <- educ_fct[-train_rows, ]- Упражнение 1.
Разделите набор данных Default из пакета ISLR на обучающую и тестовую выборки так, чтобы в первую попало 70% всех наблюдений.
def <- Default
glimpse(def)## Observations: 10,000
## Variables: 4
## $ default <fct> No, No, No, No, No, No, No, No, No, No, No, No, No, No...
## $ student <fct> No, Yes, No, No, No, Yes, No, Yes, No, No, Yes, Yes, N...
## $ balance <dbl> 729.5265, 817.1804, 1073.5492, 529.2506, 785.6559, 919...
## $ income <dbl> 44361.625, 12106.135, 31767.139, 35704.494, 38463.496,...train_rows <- createDataPartition(def$default, p = 0.7, list = FALSE)
def_train <- def[train_rows, ]
def_test <- def[-train_rows, ]1 Логистическая регрессия
С помощью метода максимального правдоподобия оценивается модель
\[ y_i = \begin{cases} 1, \text{ если } y^*_i \geq 0; \\ 0, \text{ иначе.} \end{cases} \]
\[ y_i^* = \beta_1 + \beta_2 x_i + \beta_3 z_i + u_i, \] где \(u_i\) имеет специальное логистическое распределение.
Также модель можно записать в виде:
\[ \ln \frac{P(y_i = 1)}{P(y_i = 0)} = \beta_1 + \beta_2 x_i + \beta_3 z_i \]
Реализуем логистическую регрессию с помощью функции glm. Передадим ей набор данных educ_train, формулу и укажем специалный аргумент family = binomial(link = 'logit'). Сохраним результаты оценивания в переменную educ_lmodel и посмотрим на них.
educ_lmodel_glm <- glm(data = educ_train, y ~ gender + SectionID + raisedhands, family = binomial(link = 'logit'))
summary(educ_lmodel_glm)##
## Call:
## glm(formula = y ~ gender + SectionID + raisedhands, family = binomial(link = "logit"),
## data = educ_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8009 -0.4881 -0.1803 0.6427 3.2122
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.745737 0.365406 2.041 0.04127 *
## genderM 1.004068 0.335521 2.993 0.00277 **
## SectionIDB -0.348347 0.319917 -1.089 0.27621
## SectionIDC -0.702561 0.601374 -1.168 0.24270
## raisedhands -0.069383 0.008099 -8.567 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 445.18 on 384 degrees of freedom
## Residual deviance: 271.91 on 380 degrees of freedom
## AIC: 281.91
##
## Number of Fisher Scoring iterations: 6Какие коэффициенты значимы на уровне значимости \(\alpha = 0.01\)?
Упражнение 2.
Оцените вероятность не возврата кредита default в зависимости от всех остальных факторов в наборе данных def.
def_lmodel_glm <- glm(data = def_train, default ~ ., family = binomial(link = 'logit'))
summary(def_lmodel_glm)##
## Call:
## glm(formula = default ~ ., family = binomial(link = "logit"),
## data = def_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3813 -0.1512 -0.0623 -0.0237 3.6689
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.048e+01 5.612e-01 -18.668 <2e-16 ***
## studentYes -5.418e-01 2.778e-01 -1.950 0.0511 .
## balance 5.457e-03 2.626e-04 20.783 <2e-16 ***
## income 4.056e-06 9.549e-06 0.425 0.6710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2050.6 on 7000 degrees of freedom
## Residual deviance: 1145.3 on 6997 degrees of freedom
## AIC: 1153.3
##
## Number of Fisher Scoring iterations: 8Чтобы найти предельные эффекты, воспользуемся функцией margins из одноимённого пакета. Снова выведем результаты командой summary().
educ_margins <- margins(educ_lmodel_glm)
summary(educ_margins)## factor AME SE z p lower upper
## SectionIDB -0.0399 0.0364 -1.0964 0.2729 -0.1111 0.0314
## SectionIDC -0.0790 0.0648 -1.2194 0.2227 -0.2060 0.0480
## genderM 0.1173 0.0377 3.1130 0.0019 0.0434 0.1912
## raisedhands -0.0079 0.0005 -16.7717 0.0000 -0.0089 -0.0070По умолчанию считается средний предельный эффект. Если нужно подсчитать предельный эффект для конкретного наблюдения, например, для среднего, то можно воспользоваться опцией at.
Предельные эффекты тоже можно визуализировать! Эта функция реализована в пакете ggeffects и называетя ggpredict. Ей нужно передать оценённую модель и указать переменные для визуализации в аргументе terms.
pred_educ_vis <- ggpredict(educ_lmodel_glm, terms = c('raisedhands', 'gender'))
pred_educ_vis <- plot(pred_educ_vis)- Упражнение 3.
Оцените предельные эффекты для модели def_lmodel_glm. Визуализируйте предельный эффекта для баланса кредитной карты balance отдельно для студентов student и всех остальных.
def_margins <- margins(def_lmodel_glm)
summary(def_margins)## factor AME SE z p lower upper
## balance 0.0001 0.0000 20.7360 0.0000 0.0001 0.0001
## income 0.0000 0.0000 0.4241 0.6715 -0.0000 0.0000
## studentYes -0.0115 0.0057 -2.0232 0.0431 -0.0227 -0.0004pred_def_vis <- ggpredict(def_lmodel_glm, terms = c('balance', 'student'))
plot(pred_def_vis)
Оценивать логистическую модель также можно с помощью пакета caret. Изменения минимальные:
educ_lmodel <- train(data = educ_train, y ~ gender + SectionID + raisedhands, family = binomial(link = 'logit'), method = 'glm')
summary(educ_lmodel)##
## Call:
## NULL
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8009 -0.4881 -0.1803 0.6427 3.2122
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.745737 0.365406 2.041 0.04127 *
## genderM 1.004068 0.335521 2.993 0.00277 **
## SectionIDB -0.348347 0.319917 -1.089 0.27621
## SectionIDC -0.702561 0.601374 -1.168 0.24270
## raisedhands -0.069383 0.008099 -8.567 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 445.18 on 384 degrees of freedom
## Residual deviance: 271.91 on 380 degrees of freedom
## AIC: 281.91
##
## Number of Fisher Scoring iterations: 6- Упражнение 4.
Оцените заново логистическую регессию по набору данных def с помощью функций пакета caret.
def_lmodel <- train(data = def_train, default ~ ., family = binomial(link = 'logit'), method = 'glm')
summary(def_lmodel)##
## Call:
## NULL
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3813 -0.1512 -0.0623 -0.0237 3.6689
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.048e+01 5.612e-01 -18.668 <2e-16 ***
## studentYes -5.418e-01 2.778e-01 -1.950 0.0511 .
## balance 5.457e-03 2.626e-04 20.783 <2e-16 ***
## income 4.056e-06 9.549e-06 0.425 0.6710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2050.6 on 7000 degrees of freedom
## Residual deviance: 1145.3 on 6997 degrees of freedom
## AIC: 1153.3
##
## Number of Fisher Scoring iterations: 8Посторим прогнозы модели для тестовых данных educ_test. Для этого будем использовать функцию predict, которой передадим оценённую модель educ_lmodel. В переменной educ_predz уже будут лежать предсказанные классы. Чтобы получить их вероятности, нужно добавить аргумент type = 'prob'.
educ_pred <- predict(educ_lmodel, newdata = educ_test)
head(educ_pred)## [1] L H L H H L
## Levels: H Leduc_prob <- predict(educ_lmodel, newdata = educ_test, type = 'prob')
head(educ_prob)## H L
## 25 0.1975849 0.8024151
## 31 0.8432553 0.1567447
## 37 0.3001891 0.6998109
## 45 0.8240289 0.1759711
## 50 0.7801183 0.2198817
## 55 0.2855258 0.7144742- Упражнение 5.
Постройте прогнозы для тестовой выборки def_test. Сохраните как предсказанные классы, так и их вероятности.
def_pred <- predict(def_lmodel, newdata = def_test)
head(def_pred)## [1] No No No No No No
## Levels: No Yesdef_prob <- predict(def_lmodel, newdata = def_test, type = 'prob')
head(def_prob)## No Yes
## 2 0.9985137 0.0014863447
## 3 0.9888977 0.0111023380
## 4 0.9994151 0.0005848639
## 5 0.9976080 0.0023920164
## 6 0.9974519 0.0025481033
## 13 0.9998847 0.0001152535Теперь мы можем посмотреть на матрицу ошибок и узнать, насколько хорошую модель мы оецнили. Для этого будем использовть функцию confusionMatrix из пакета caret. В качестве аргумента data нужно указать предсказанные значения, а в reference — правильные ответы.
confusionMatrix(data = educ_pred, reference = educ_test$y)## Confusion Matrix and Statistics
##
## Reference
## Prediction H L
## H 65 8
## L 5 17
##
## Accuracy : 0.8632
## 95% CI : (0.7774, 0.9251)
## No Information Rate : 0.7368
## P-Value [Acc > NIR] : 0.002303
##
## Kappa : 0.633
## Mcnemar's Test P-Value : 0.579100
##
## Sensitivity : 0.9286
## Specificity : 0.6800
## Pos Pred Value : 0.8904
## Neg Pred Value : 0.7727
## Prevalence : 0.7368
## Detection Rate : 0.6842
## Detection Prevalence : 0.7684
## Balanced Accuracy : 0.8043
##
## 'Positive' Class : H
## - Упражнение 6.
Составьте матрицу ошибок для прогнозов модели def_lmodel.
confusionMatrix(data = def_pred, reference = def_test$default)## Confusion Matrix and Statistics
##
## Reference
## Prediction No Yes
## No 2891 67
## Yes 9 32
##
## Accuracy : 0.9747
## 95% CI : (0.9684, 0.98)
## No Information Rate : 0.967
## P-Value [Acc > NIR] : 0.008743
##
## Kappa : 0.4464
## Mcnemar's Test P-Value : 6.22e-11
##
## Sensitivity : 0.9969
## Specificity : 0.3232
## Pos Pred Value : 0.9773
## Neg Pred Value : 0.7805
## Prevalence : 0.9670
## Detection Rate : 0.9640
## Detection Prevalence : 0.9863
## Balanced Accuracy : 0.6601
##
## 'Positive' Class : No
## Чтобы получичть и другие метрики качества для нашей модели, будем использовать функции twoClassSummary() и prSummary(). Первая возвращает значения ROC, специфичности и чувствительности.
Чувствительность (полнота) показывает долю правильно распознанных объектов отрицательного класса. \[ TPR = TP / (TP + FN) = recall = sensitivity \]
Специфичность показывает долю правильно распознанных объектов положительного класса. \[ FPR = FP / (FP + TN) = 1 - specificity \]
ROC — это площадь под кривой, построенной в осях доли правильных положительных ответов и доли неправильных положительных ответов в зависимости от значения порога для попадания в положительный класс.
Вторая функция возвращает AUC, полноту, точность и F-меру.
AUC — это площадь под кривой, построенной в осях точность-полнота. Точность — это доля объектов на самом деле принадлежащих к положительному классу среди всех объектов, которых модель отнесла к положительному классу. \[ precision = TP / (TP + FP) \]
А F-мера — это среднее гармоническое между точностью и полнотой.
Однако обе функции требуют, чтобы во данных были столбцы с вероятностями классов под названиями самих этих классов, истинные ответы под названием obs, и бинарные предсказания, названные как pred. Поэтому создадим отдельную таблицу educ_test_set со всеми результатами оценивания.
educ_test_set <- data.frame(H = educ_prob$H,
L = educ_prob$L,
pred = educ_pred,
obs = educ_test$y)
glimpse(educ_test_set)## Observations: 95
## Variables: 4
## $ H <dbl> 0.1975849, 0.8432553, 0.3001891, 0.8240289, 0.7801183, 0....
## $ L <dbl> 0.802415134, 0.156744738, 0.699810922, 0.175971069, 0.219...
## $ pred <fct> L, H, L, H, H, L, H, L, L, H, L, L, H, H, L, H, H, H, H, ...
## $ obs <fct> L, H, L, H, H, L, H, L, L, H, H, L, H, H, L, H, L, H, L, ...twoClassSummary(educ_test_set, lev = levels(educ_test_set$obs)) # don't work with tibble## ROC Sens Spec
## 0.9037143 0.9285714 0.6800000prSummary(educ_test_set, lev = levels(educ_test_set$obs)) # нужен пакет MLmetrics## AUC Precision Recall F
## 0.9300243 0.8904110 0.9285714 0.9090909- Упражнение 7.
Выведите характеристики модели def_lmodel с помощью функций twoClassSummary() и prSummary().
def_test_set <- data.frame(No = def_prob$No,
Yes = def_prob$Yes,
pred = def_pred,
obs = def_test$default)
twoClassSummary(def_test_set, lev = levels(def_test_set$obs))## ROC Sens Spec
## 0.9607524 0.9968966 0.3232323prSummary(def_test_set, lev = levels(def_test_set$obs))## AUC Precision Recall F
## 0.9982003 0.9773496 0.9968966 0.9870263Почти все метрики можно визуализировать! Но для примера мы построим ROC-кривую. Для этого вдобавок к базовому cлою ggplot мы будем использовать слой geom_roc из пакета plotROC. В эстетиках нужно указать аргументы d — истинные значения — и m — метки класса 1. Если добавить аргумент color, то можно получить разные ROC-кривые по категориям какой-нибудь переменной.
ggplot(educ_test_set, aes(d = obs, m = L)) +
geom_roc(n.cuts = 0)
educ_test_set <- mutate(educ_test_set, gender = educ_test$gender)
ggplot(educ_test_set, aes(d = obs, m = L, color = gender)) +
geom_roc(n.cuts = 0)
- Упражнение 8.
Визуализируйте ROC-кривую для прогнозов модели def_lmodel. Сначала общую, а затем отдельно для студентов и всех остальных.
ggplot(def_test_set, aes(d = obs, m = Yes)) +
geom_roc(n.cuts = 0)
def_test_set <- mutate(def_test_set, stud = def_test$student)
ggplot(def_test_set, aes(d = obs, m = Yes, color = stud)) +
geom_roc(n.cuts = 0)
2 На природу, к деревьям и в лес!
Бинарные деревья очень легко интепретируются при приемлемом качестве прогнозов.
Алгоритмы построения дерева отличаются деталями:
- по какому критерию делить веточку на две?
- когда остановить процесс деления веточек?
- следует ли обрезать дерево после окончания деления?
- как обрабатывать пропущенные значений?
tree_model <- train(y ~ . - Class, data = educ_test,
method = 'rpart2',
na.action = na.omit)## note: only 2 possible values of the max tree depth from the initial fit.
## Truncating the grid to 2 .Картинка дерева:
rpart.plot(tree_model$finalModel)
Описание дерева:
summary(tree_model)## Call:
## (function (formula, data, weights, subset, na.action = na.rpart,
## method, model = FALSE, x = FALSE, y = TRUE, parms, control,
## cost, ...)
## {
## Call <- match.call()
## if (is.data.frame(model)) {
## m <- model
## model <- FALSE
## }
## else {
## indx <- match(c("formula", "data", "weights", "subset"),
## names(Call), nomatch = 0)
## if (indx[1] == 0)
## stop("a 'formula' argument is required")
## temp <- Call[c(1, indx)]
## temp$na.action <- na.action
## temp[[1]] <- quote(stats::model.frame)
## m <- eval.parent(temp)
## }
## Terms <- attr(m, "terms")
## if (any(attr(Terms, "order") > 1))
## stop("Trees cannot handle interaction terms")
## Y <- model.response(m)
## wt <- model.weights(m)
## if (any(wt < 0))
## stop("negative weights not allowed")
## if (!length(wt))
## wt <- rep(1, nrow(m))
## offset <- model.offset(m)
## X <- rpart.matrix(m)
## nobs <- nrow(X)
## nvar <- ncol(X)
## if (missing(method)) {
## method <- if (is.factor(Y) || is.character(Y))
## "class"
## else if (inherits(Y, "Surv"))
## "exp"
## else if (is.matrix(Y))
## "poisson"
## else "anova"
## }
## if (is.list(method)) {
## mlist <- method
## method <- "user"
## init <- if (missing(parms))
## mlist$init(Y, offset, wt = wt)
## else mlist$init(Y, offset, parms, wt)
## keep <- rpartcallback(mlist, nobs, init)
## method.int <- 4
## parms <- init$parms
## }
## else {
## method.int <- pmatch(method, c("anova", "poisson", "class",
## "exp"))
## if (is.na(method.int))
## stop("Invalid method")
## method <- c("anova", "poisson", "class", "exp")[method.int]
## if (method.int == 4)
## method.int <- 2
## init <- if (missing(parms))
## get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, , wt)
## else get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, parms, wt)
## ns <- asNamespace("rpart")
## if (!is.null(init$print))
## environment(init$print) <- ns
## if (!is.null(init$summary))
## environment(init$summary) <- ns
## if (!is.null(init$text))
## environment(init$text) <- ns
## }
## Y <- init$y
## xlevels <- .getXlevels(Terms, m)
## cats <- rep(0, ncol(X))
## if (!is.null(xlevels))
## cats[match(names(xlevels), colnames(X))] <- unlist(lapply(xlevels,
## length))
## extraArgs <- list(...)
## if (length(extraArgs)) {
## controlargs <- names(formals(rpart.control))
## indx <- match(names(extraArgs), controlargs, nomatch = 0)
## if (any(indx == 0))
## stop(gettextf("Argument %s not matched", names(extraArgs)[indx ==
## 0]), domain = NA)
## }
## controls <- rpart.control(...)
## if (!missing(control))
## controls[names(control)] <- control
## xval <- controls$xval
## if (is.null(xval) || (length(xval) == 1 && xval == 0) ||
## method == "user") {
## xgroups <- 0
## xval <- 0
## }
## else if (length(xval) == 1) {
## xgroups <- sample(rep(1:xval, length = nobs), nobs, replace = FALSE)
## }
## else if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else {
## if (!is.null(attr(m, "na.action"))) {
## temp <- as.integer(attr(m, "na.action"))
## xval <- xval[-temp]
## if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else stop("Wrong length for 'xval'")
## }
## else stop("Wrong length for 'xval'")
## }
## if (missing(cost))
## cost <- rep(1, nvar)
## else {
## if (length(cost) != nvar)
## stop("Cost vector is the wrong length")
## if (any(cost <= 0))
## stop("Cost vector must be positive")
## }
## tfun <- function(x) if (is.matrix(x))
## rep(is.ordered(x), ncol(x))
## else is.ordered(x)
## labs <- sub("^`(.*)`$", "\\1", attr(Terms, "term.labels"))
## isord <- unlist(lapply(m[labs], tfun))
## storage.mode(X) <- "double"
## storage.mode(wt) <- "double"
## temp <- as.double(unlist(init$parms))
## if (!length(temp))
## temp <- 0
## rpfit <- .Call(C_rpart, ncat = as.integer(cats * (!isord)),
## method = as.integer(method.int), as.double(unlist(controls)),
## temp, as.integer(xval), as.integer(xgroups), as.double(t(init$y)),
## X, wt, as.integer(init$numy), as.double(cost))
## nsplit <- nrow(rpfit$isplit)
## ncat <- if (!is.null(rpfit$csplit))
## nrow(rpfit$csplit)
## else 0
## if (nsplit == 0)
## xval <- 0
## numcp <- ncol(rpfit$cptable)
## temp <- if (nrow(rpfit$cptable) == 3)
## c("CP", "nsplit", "rel error")
## else c("CP", "nsplit", "rel error", "xerror", "xstd")
## dimnames(rpfit$cptable) <- list(temp, 1:numcp)
## tname <- c("<leaf>", colnames(X))
## splits <- matrix(c(rpfit$isplit[, 2:3], rpfit$dsplit), ncol = 5,
## dimnames = list(tname[rpfit$isplit[, 1] + 1], c("count",
## "ncat", "improve", "index", "adj")))
## index <- rpfit$inode[, 2]
## nadd <- sum(isord[rpfit$isplit[, 1]])
## if (nadd > 0) {
## newc <- matrix(0, nadd, max(cats))
## cvar <- rpfit$isplit[, 1]
## indx <- isord[cvar]
## cdir <- splits[indx, 2]
## ccut <- floor(splits[indx, 4])
## splits[indx, 2] <- cats[cvar[indx]]
## splits[indx, 4] <- ncat + 1:nadd
## for (i in 1:nadd) {
## newc[i, 1:(cats[(cvar[indx])[i]])] <- -as.integer(cdir[i])
## newc[i, 1:ccut[i]] <- as.integer(cdir[i])
## }
## catmat <- if (ncat == 0)
## newc
## else {
## cs <- rpfit$csplit
## ncs <- ncol(cs)
## ncc <- ncol(newc)
## if (ncs < ncc)
## cs <- cbind(cs, matrix(0, nrow(cs), ncc - ncs))
## rbind(cs, newc)
## }
## ncat <- ncat + nadd
## }
## else catmat <- rpfit$csplit
## if (nsplit == 0) {
## frame <- data.frame(row.names = 1, var = "<leaf>", n = rpfit$inode[,
## 5], wt = rpfit$dnode[, 3], dev = rpfit$dnode[, 1],
## yval = rpfit$dnode[, 4], complexity = rpfit$dnode[,
## 2], ncompete = 0, nsurrogate = 0)
## }
## else {
## temp <- ifelse(index == 0, 1, index)
## svar <- ifelse(index == 0, 0, rpfit$isplit[temp, 1])
## frame <- data.frame(row.names = rpfit$inode[, 1], var = tname[svar +
## 1], n = rpfit$inode[, 5], wt = rpfit$dnode[, 3],
## dev = rpfit$dnode[, 1], yval = rpfit$dnode[, 4],
## complexity = rpfit$dnode[, 2], ncompete = pmax(0,
## rpfit$inode[, 3] - 1), nsurrogate = rpfit$inode[,
## 4])
## }
## if (method.int == 3) {
## numclass <- init$numresp - 2
## nodeprob <- rpfit$dnode[, numclass + 5]/sum(wt)
## temp <- pmax(1, init$counts)
## temp <- rpfit$dnode[, 4 + (1:numclass)] %*% diag(init$parms$prior/temp)
## yprob <- temp/rowSums(temp)
## yval2 <- matrix(rpfit$dnode[, 4 + (0:numclass)], ncol = numclass +
## 1)
## frame$yval2 <- cbind(yval2, yprob, nodeprob)
## }
## else if (init$numresp > 1)
## frame$yval2 <- rpfit$dnode[, -(1:3), drop = FALSE]
## if (is.null(init$summary))
## stop("Initialization routine is missing the 'summary' function")
## functions <- if (is.null(init$print))
## list(summary = init$summary)
## else list(summary = init$summary, print = init$print)
## if (!is.null(init$text))
## functions <- c(functions, list(text = init$text))
## if (method == "user")
## functions <- c(functions, mlist)
## where <- rpfit$which
## names(where) <- row.names(m)
## ans <- list(frame = frame, where = where, call = Call, terms = Terms,
## cptable = t(rpfit$cptable), method = method, parms = init$parms,
## control = controls, functions = functions, numresp = init$numresp)
## if (nsplit)
## ans$splits = splits
## if (ncat > 0)
## ans$csplit <- catmat + 2
## if (nsplit)
## ans$variable.importance <- importance(ans)
## if (model) {
## ans$model <- m
## if (missing(y))
## y <- FALSE
## }
## if (y)
## ans$y <- Y
## if (x) {
## ans$x <- X
## ans$wt <- wt
## }
## ans$ordered <- isord
## if (!is.null(attr(m, "na.action")))
## ans$na.action <- attr(m, "na.action")
## if (!is.null(xlevels))
## attr(ans, "xlevels") <- xlevels
## if (method == "class")
## attr(ans, "ylevels") <- init$ylevels
## class(ans) <- "rpart"
## ans
## })(formula = .outcome ~ ., data = list(genderM = c(1, 0, 1, 0,
## 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0,
## 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1,
## 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1,
## 1, 1, 0, 0, 0, 1, 0), NationalITyIran = c(0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0), NationalITyIraq = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0), NationalITyJordan = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
## 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0,
## 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1),
## NationalITyKW = c(1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0), NationalITyLybia = c(0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), NationalITyMorocco = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), NationalITyPalestine = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0), NationalITySaudiArabia = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), NationalITySyria = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), NationalITyTunis = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), NationalITyUSA = c(0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), NationalITylebanon = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), NationalITyvenzuela = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthIran = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthIraq = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthJordan = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1,
## 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1), PlaceofBirthKuwaIT = c(1,
## 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthLybia = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthMorocco = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthPalestine = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0), PlaceofBirthSaudiArabia = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthSyria = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthTunis = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthUSA = c(0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthlebanon = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), PlaceofBirthvenzuela = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), StageIDMiddleSchool = c(1,
## 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), StageIDlowerlevel = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-04` = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-05` = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-06` = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-07` = c(1,
## 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-08` = c(0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), `GradeIDG-09` = c(0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-10` = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-11` = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), `GradeIDG-12` = c(0,
## 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), SectionIDB = c(1,
## 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0,
## 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1,
## 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), SectionIDC = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicBiology = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicChemistry = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1), TopicEnglish = c(0,
## 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicFrench = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicGeology = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0), TopicHistory = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicIT = c(1,
## 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicMath = c(0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicQuran = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicScience = c(0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), TopicSpanish = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), SemesterS = c(0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1,
## 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
## 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1), RelationMum = c(0,
## 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1,
## 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1,
## 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0), raisedhands = c(0,
## 35, 8, 33, 29, 12, 70, 11, 12, 50, 20, 4, 80, 14, 1, 12,
## 25, 25, 55, 12, 100, 100, 80, 10, 100, 70, 22, 70, 10, 75,
## 83, 22, 67, 27, 70, 17, 96, 72, 87, 5, 73, 72, 22, 70, 69,
## 59, 10, 69, 10, 79, 22, 90, 82, 72, 74, 41, 51, 81, 62, 18,
## 32, 22, 65, 55, 50, 30, 27, 80, 75, 16, 40, 35, 14, 20, 7,
## 10, 20, 80, 5, 10, 70, 88, 39, 35, 53, 74, 84, 85, 90, 77,
## 25, 79, 89, 85, 5), VisITedResources = c(2, 80, 6, 33, 39,
## 50, 69, 2, 0, 90, 80, 8, 90, 60, 7, 26, 27, 29, 33, 10, 80,
## 85, 90, 10, 75, 50, 51, 82, 2, 71, 75, 51, 31, 41, 81, 61,
## 61, 83, 81, 3, 84, 80, 20, 40, 76, 97, 17, 34, 17, 84, 20,
## 62, 31, 41, 71, 39, 79, 79, 64, 17, 14, 34, 59, 79, 90, 10,
## 20, 77, 80, 90, 87, 92, 97, 3, 9, 94, 88, 88, 9, 12, 83,
## 90, 71, 80, 88, 62, 77, 89, 86, 82, 82, 91, 96, 88, 4), AnnouncementsView = c(3,
## 50, 4, 30, 50, 8, 35, 2, 6, 29, 33, 10, 55, 11, 6, 7, 0,
## 40, 6, 20, 95, 85, 55, 15, 50, 33, 48, 3, 13, 72, 62, 42,
## 42, 49, 39, 42, 42, 12, 22, 2, 77, 58, 18, 2, 82, 42, 12,
## 12, 12, 82, 6, 80, 52, 46, 56, 35, 85, 91, 72, 26, 32, 15,
## 74, 44, 83, 20, 33, 63, 15, 15, 50, 29, 15, 9, 11, 40, 31,
## 51, 19, 29, 29, 86, 40, 34, 9, 49, 79, 22, 85, 74, 52, 49,
## 45, 79, 5), Discussion = c(70, 70, 22, 90, 77, 30, 30, 8,
## 13, 60, 33, 60, 19, 75, 10, 40, 69, 17, 9, 16, 90, 70, 19,
## 19, 70, 41, 10, 73, 53, 53, 53, 40, 14, 14, 84, 14, 94, 90,
## 70, 10, 81, 66, 6, 16, 94, 70, 40, 17, 14, 37, 26, 60, 25,
## 27, 37, 39, 89, 85, 84, 34, 29, 9, 83, 43, 13, 5, 35, 83,
## 20, 11, 41, 33, 14, 3, 10, 11, 28, 39, 98, 93, 33, 81, 26,
## 22, 33, 43, 68, 61, 10, 79, 20, 22, 92, 70, 8), ParentAnsweringSurveyYes = c(1,
## 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0,
## 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1,
## 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1,
## 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1,
## 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0), ParentschoolSatisfactionGood = c(1,
## 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0,
## 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0), `StudentAbsenceDaysUnder-7` = c(0,
## 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1,
## 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0,
## 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0), .outcome = c(2,
## 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2,
## 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1,
## 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2)), control = list(
## minsplit = 20, minbucket = 7, cp = 0.01, maxcompete = 4,
## maxsurrogate = 5, usesurrogate = 2, surrogatestyle = 0, maxdepth = 3,
## xval = 0))
## n= 95
##
## CP nsplit rel error
## 1 0.64 0 1.00
## 2 0.16 1 0.36
## 3 0.01 3 0.04
##
## Variable importance
## VisITedResources raisedhands
## 32 15
## AnnouncementsView Discussion
## 14 12
## StudentAbsenceDaysUnder-7 NationalITyKW
## 8 6
## ParentschoolSatisfactionGood PlaceofBirthKuwaIT
## 6 5
## GradeIDG-11 TopicScience
## 1 1
##
## Node number 1: 95 observations, complexity param=0.64
## predicted class=H expected loss=0.2631579 P(node) =1
## class counts: 70 25
## probabilities: 0.737 0.263
## left son=2 (79 obs) right son=3 (16 obs)
## Primary splits:
## VisITedResources < 13 to the right, improve=20.89274, (0 missing)
## AnnouncementsView < 21 to the right, improve=19.03174, (0 missing)
## raisedhands < 13 to the right, improve=15.92105, (0 missing)
## StudentAbsenceDaysUnder-7 < 0.5 to the right, improve=14.91254, (0 missing)
## Discussion < 10.5 to the right, improve=11.73166, (0 missing)
## Surrogate splits:
## raisedhands < 11.5 to the right, agree=0.926, adj=0.562, (0 split)
## Discussion < 8.5 to the right, agree=0.863, adj=0.187, (0 split)
## AnnouncementsView < 5.5 to the right, agree=0.853, adj=0.125, (0 split)
##
## Node number 2: 79 observations, complexity param=0.16
## predicted class=H expected loss=0.1139241 P(node) =0.8315789
## class counts: 70 9
## probabilities: 0.886 0.114
## left son=4 (59 obs) right son=5 (20 obs)
## Primary splits:
## StudentAbsenceDaysUnder-7 < 0.5 to the right, improve=6.049367, (0 missing)
## AnnouncementsView < 20 to the right, improve=5.093265, (0 missing)
## VisITedResources < 55 to the right, improve=4.429367, (0 missing)
## Discussion < 18 to the right, improve=4.201351, (0 missing)
## ParentschoolSatisfactionGood < 0.5 to the right, improve=3.175174, (0 missing)
## Surrogate splits:
## Discussion < 9.5 to the right, agree=0.785, adj=0.15, (0 split)
## GradeIDG-11 < 0.5 to the left, agree=0.772, adj=0.10, (0 split)
## TopicScience < 0.5 to the left, agree=0.772, adj=0.10, (0 split)
## VisITedResources < 18.5 to the right, agree=0.772, adj=0.10, (0 split)
## AnnouncementsView < 2.5 to the right, agree=0.772, adj=0.10, (0 split)
##
## Node number 3: 16 observations
## predicted class=L expected loss=0 P(node) =0.1684211
## class counts: 0 16
## probabilities: 0.000 1.000
##
## Node number 4: 59 observations
## predicted class=H expected loss=0 P(node) =0.6210526
## class counts: 59 0
## probabilities: 1.000 0.000
##
## Node number 5: 20 observations, complexity param=0.16
## predicted class=H expected loss=0.45 P(node) =0.2105263
## class counts: 11 9
## probabilities: 0.550 0.450
## left son=10 (12 obs) right son=11 (8 obs)
## Primary splits:
## AnnouncementsView < 22 to the right, improve=8.066667, (0 missing)
## ParentschoolSatisfactionGood < 0.5 to the right, improve=6.627273, (0 missing)
## Discussion < 18.5 to the right, improve=6.515385, (0 missing)
## PlaceofBirthKuwaIT < 0.5 to the left, improve=4.900000, (0 missing)
## VisITedResources < 56.5 to the right, improve=4.361538, (0 missing)
## Surrogate splits:
## NationalITyKW < 0.5 to the left, agree=0.85, adj=0.625, (0 split)
## Discussion < 18.5 to the right, agree=0.85, adj=0.625, (0 split)
## ParentschoolSatisfactionGood < 0.5 to the right, agree=0.85, adj=0.625, (0 split)
## PlaceofBirthKuwaIT < 0.5 to the left, agree=0.80, adj=0.500, (0 split)
## VisITedResources < 36.5 to the right, agree=0.80, adj=0.500, (0 split)
##
## Node number 10: 12 observations
## predicted class=H expected loss=0.08333333 P(node) =0.1263158
## class counts: 11 1
## probabilities: 0.917 0.083
##
## Node number 11: 8 observations
## predicted class=L expected loss=0 P(node) =0.08421053
## class counts: 0 8
## probabilities: 0.000 1.000- Упражнение 9.
Постройте дерево для набора данных def, визуализируйте результат и нарисуйте картинку.
def_tree <- train(data = def_train, default ~ ., method = 'rpart2')
rpart.plot(def_tree$finalModel)
summary(def_tree)## Call:
## (function (formula, data, weights, subset, na.action = na.rpart,
## method, model = FALSE, x = FALSE, y = TRUE, parms, control,
## cost, ...)
## {
## Call <- match.call()
## if (is.data.frame(model)) {
## m <- model
## model <- FALSE
## }
## else {
## indx <- match(c("formula", "data", "weights", "subset"),
## names(Call), nomatch = 0)
## if (indx[1] == 0)
## stop("a 'formula' argument is required")
## temp <- Call[c(1, indx)]
## temp$na.action <- na.action
## temp[[1]] <- quote(stats::model.frame)
## m <- eval.parent(temp)
## }
## Terms <- attr(m, "terms")
## if (any(attr(Terms, "order") > 1))
## stop("Trees cannot handle interaction terms")
## Y <- model.response(m)
## wt <- model.weights(m)
## if (any(wt < 0))
## stop("negative weights not allowed")
## if (!length(wt))
## wt <- rep(1, nrow(m))
## offset <- model.offset(m)
## X <- rpart.matrix(m)
## nobs <- nrow(X)
## nvar <- ncol(X)
## if (missing(method)) {
## method <- if (is.factor(Y) || is.character(Y))
## "class"
## else if (inherits(Y, "Surv"))
## "exp"
## else if (is.matrix(Y))
## "poisson"
## else "anova"
## }
## if (is.list(method)) {
## mlist <- method
## method <- "user"
## init <- if (missing(parms))
## mlist$init(Y, offset, wt = wt)
## else mlist$init(Y, offset, parms, wt)
## keep <- rpartcallback(mlist, nobs, init)
## method.int <- 4
## parms <- init$parms
## }
## else {
## method.int <- pmatch(method, c("anova", "poisson", "class",
## "exp"))
## if (is.na(method.int))
## stop("Invalid method")
## method <- c("anova", "poisson", "class", "exp")[method.int]
## if (method.int == 4)
## method.int <- 2
## init <- if (missing(parms))
## get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, , wt)
## else get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, parms, wt)
## ns <- asNamespace("rpart")
## if (!is.null(init$print))
## environment(init$print) <- ns
## if (!is.null(init$summary))
## environment(init$summary) <- ns
## if (!is.null(init$text))
## environment(init$text) <- ns
## }
## Y <- init$y
## xlevels <- .getXlevels(Terms, m)
## cats <- rep(0, ncol(X))
## if (!is.null(xlevels))
## cats[match(names(xlevels), colnames(X))] <- unlist(lapply(xlevels,
## length))
## extraArgs <- list(...)
## if (length(extraArgs)) {
## controlargs <- names(formals(rpart.control))
## indx <- match(names(extraArgs), controlargs, nomatch = 0)
## if (any(indx == 0))
## stop(gettextf("Argument %s not matched", names(extraArgs)[indx ==
## 0]), domain = NA)
## }
## controls <- rpart.control(...)
## if (!missing(control))
## controls[names(control)] <- control
## xval <- controls$xval
## if (is.null(xval) || (length(xval) == 1 && xval == 0) ||
## method == "user") {
## xgroups <- 0
## xval <- 0
## }
## else if (length(xval) == 1) {
## xgroups <- sample(rep(1:xval, length = nobs), nobs, replace = FALSE)
## }
## else if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else {
## if (!is.null(attr(m, "na.action"))) {
## temp <- as.integer(attr(m, "na.action"))
## xval <- xval[-temp]
## if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else stop("Wrong length for 'xval'")
## }
## else stop("Wrong length for 'xval'")
## }
## if (missing(cost))
## cost <- rep(1, nvar)
## else {
## if (length(cost) != nvar)
## stop("Cost vector is the wrong length")
## if (any(cost <= 0))
## stop("Cost vector must be positive")
## }
## tfun <- function(x) if (is.matrix(x))
## rep(is.ordered(x), ncol(x))
## else is.ordered(x)
## labs <- sub("^`(.*)`$", "\\1", attr(Terms, "term.labels"))
## isord <- unlist(lapply(m[labs], tfun))
## storage.mode(X) <- "double"
## storage.mode(wt) <- "double"
## temp <- as.double(unlist(init$parms))
## if (!length(temp))
## temp <- 0
## rpfit <- .Call(C_rpart, ncat = as.integer(cats * (!isord)),
## method = as.integer(method.int), as.double(unlist(controls)),
## temp, as.integer(xval), as.integer(xgroups), as.double(t(init$y)),
## X, wt, as.integer(init$numy), as.double(cost))
## nsplit <- nrow(rpfit$isplit)
## ncat <- if (!is.null(rpfit$csplit))
## nrow(rpfit$csplit)
## else 0
## if (nsplit == 0)
## xval <- 0
## numcp <- ncol(rpfit$cptable)
## temp <- if (nrow(rpfit$cptable) == 3)
## c("CP", "nsplit", "rel error")
## else c("CP", "nsplit", "rel error", "xerror", "xstd")
## dimnames(rpfit$cptable) <- list(temp, 1:numcp)
## tname <- c("<leaf>", colnames(X))
## splits <- matrix(c(rpfit$isplit[, 2:3], rpfit$dsplit), ncol = 5,
## dimnames = list(tname[rpfit$isplit[, 1] + 1], c("count",
## "ncat", "improve", "index", "adj")))
## index <- rpfit$inode[, 2]
## nadd <- sum(isord[rpfit$isplit[, 1]])
## if (nadd > 0) {
## newc <- matrix(0, nadd, max(cats))
## cvar <- rpfit$isplit[, 1]
## indx <- isord[cvar]
## cdir <- splits[indx, 2]
## ccut <- floor(splits[indx, 4])
## splits[indx, 2] <- cats[cvar[indx]]
## splits[indx, 4] <- ncat + 1:nadd
## for (i in 1:nadd) {
## newc[i, 1:(cats[(cvar[indx])[i]])] <- -as.integer(cdir[i])
## newc[i, 1:ccut[i]] <- as.integer(cdir[i])
## }
## catmat <- if (ncat == 0)
## newc
## else {
## cs <- rpfit$csplit
## ncs <- ncol(cs)
## ncc <- ncol(newc)
## if (ncs < ncc)
## cs <- cbind(cs, matrix(0, nrow(cs), ncc - ncs))
## rbind(cs, newc)
## }
## ncat <- ncat + nadd
## }
## else catmat <- rpfit$csplit
## if (nsplit == 0) {
## frame <- data.frame(row.names = 1, var = "<leaf>", n = rpfit$inode[,
## 5], wt = rpfit$dnode[, 3], dev = rpfit$dnode[, 1],
## yval = rpfit$dnode[, 4], complexity = rpfit$dnode[,
## 2], ncompete = 0, nsurrogate = 0)
## }
## else {
## temp <- ifelse(index == 0, 1, index)
## svar <- ifelse(index == 0, 0, rpfit$isplit[temp, 1])
## frame <- data.frame(row.names = rpfit$inode[, 1], var = tname[svar +
## 1], n = rpfit$inode[, 5], wt = rpfit$dnode[, 3],
## dev = rpfit$dnode[, 1], yval = rpfit$dnode[, 4],
## complexity = rpfit$dnode[, 2], ncompete = pmax(0,
## rpfit$inode[, 3] - 1), nsurrogate = rpfit$inode[,
## 4])
## }
## if (method.int == 3) {
## numclass <- init$numresp - 2
## nodeprob <- rpfit$dnode[, numclass + 5]/sum(wt)
## temp <- pmax(1, init$counts)
## temp <- rpfit$dnode[, 4 + (1:numclass)] %*% diag(init$parms$prior/temp)
## yprob <- temp/rowSums(temp)
## yval2 <- matrix(rpfit$dnode[, 4 + (0:numclass)], ncol = numclass +
## 1)
## frame$yval2 <- cbind(yval2, yprob, nodeprob)
## }
## else if (init$numresp > 1)
## frame$yval2 <- rpfit$dnode[, -(1:3), drop = FALSE]
## if (is.null(init$summary))
## stop("Initialization routine is missing the 'summary' function")
## functions <- if (is.null(init$print))
## list(summary = init$summary)
## else list(summary = init$summary, print = init$print)
## if (!is.null(init$text))
## functions <- c(functions, list(text = init$text))
## if (method == "user")
## functions <- c(functions, mlist)
## where <- rpfit$which
## names(where) <- row.names(m)
## ans <- list(frame = frame, where = where, call = Call, terms = Terms,
## cptable = t(rpfit$cptable), method = method, parms = init$parms,
## control = controls, functions = functions, numresp = init$numresp)
## if (nsplit)
## ans$splits = splits
## if (ncat > 0)
## ans$csplit <- catmat + 2
## if (nsplit)
## ans$variable.importance <- importance(ans)
## if (model) {
## ans$model <- m
## if (missing(y))
## y <- FALSE
## }
## if (y)
## ans$y <- Y
## if (x) {
## ans$x <- X
## ans$wt <- wt
## }
## ans$ordered <- isord
## if (!is.null(attr(m, "na.action")))
## ans$na.action <- attr(m, "na.action")
## if (!is.null(xlevels))
## attr(ans, "xlevels") <- xlevels
## if (method == "class")
## attr(ans, "ylevels") <- init$ylevels
## class(ans) <- "rpart"
## ans
## })(formula = .outcome ~ ., data = list(studentYes = c(0, 0, 1,
## 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0,
## 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0,
## 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,
## 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1,
## 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
## 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1,
## 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0,
## 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0,
## 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0,
## 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,
## 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,
## 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1,
## 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0,
## 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1,
## 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1,
## 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,
## 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1,
## 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
## 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
## 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0,
## 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0,
## 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1,
## 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,
## 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0,
## 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1,
## 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0,
## 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0,
## 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
## 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1,
## 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
## 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1,
## 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1,
## 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0,
## 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0,
## 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0,
## 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
## 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1,
## 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1,
## 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0,
## 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1,
## 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
## 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0,
## 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
## 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0,
## 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0,
## 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
## 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,
## 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0,
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## 0, 1, 0, 0, 1), balance = c(729.526495207286, 825.513330517201,
## 808.667504297266, 1161.05785403132, 0, 0, 1220.58375300377, 0,
## 527.540184074571, 485.936864171729, 228.952549642572, 954.261792773545,
## 1055.95660472904, 641.984388848021, 773.211724534176, 642.999738515429,
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## 692.034167065432, 351.45347152301, 742.627620785597, 653.118400123388,
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## 582.188700706555, 598.461392123585, 1486.99812160021, 943.796338713762,
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## 836.300071623191, 967.48268368178, 1258.18521914431, 1239.80169908455,
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## 888.613272550212, 1284.38636050636, 712.276351280275, 1290.62016864921,
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## 966.280287968092, 171.559115959856, 1482.48030006315, 640.662751732473,
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## 1304.91429931829, 256.471227559815, 1153.60499815384, 782.883029663905,
## 444.264906175272, 504.02837873803, 850.096116596461, 1412.23872130317,
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## 548.037783442488, 1257.05522168594, 687.683759014873, 957.68483377014,
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## 1549.04275451742, 862.656656416651, 1259.14941789257, 703.277787102737,
## 1082.39149734589, 910.449023533628, 353.778226008973, 1716.59541824424,
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## 1056.92735252411, 979.224424632862, 847.818706253068, 781.77128476306,
## 402.488886825952, 204.740181714577, 2022.67464324227, 748.937063784024,
## 838.275687752419, 386.016049290846, 812.399296525647, 1809.92656439359,
## 1328.18380411907, 1464.93604882699, 1200.56513764739, 870.734579925775,
## 1200.84739001594, 1428.83204736141, 0, 359.458866537597, 729.047433497618,
## 1042.80491991389, 367.466012183201, 737.70535394131, 56.9675603504705,
## 1165.49113814696, 1642.81999663825, 944.173560017781, 370.375186777666,
## 773.915226576855, 817.249811262394, 1060.71621967666, 986.40061892638,
## 717.341926951688, 1328.89272521776, 673.468191056081, 218.639297043088,
## 1218.16696582374, 13.5168025503509, 1351.84972233302, 107.282083049617,
## 1020.06724048864, 754.420612920964, 289.489575693364, 198.038409229701,
## 697.563808989791, 502.324783467779, 1459.68708304516, 716.998722689295,
## 1037.97270501782, 673.016117196098, 371.921784701252, 1061.44156214448,
## 1672.63924830477, 883.702645600325, 373.780330004006, 1287.79518693788,
## 510.613846954321, 775.630168716812, 1152.98288688657, 1675.27885173207,
## 739.901759396798, 226.417696514023, 1217.32171213419, 639.820558249208,
## 2.2876109529974, 419.637347665869, 1700.59991348658, 311.82458686811,
## 442.830222252675, 728.81496006121, 278.877902520137, 758.702327534491,
## 1890.16741147529, 0, 1075.86377237476, 864.039743518541, 947.634932740896,
## 267.303727744013, 13.67938266968, 1353.09384569505, 480.32126391483,
## 478.572055604816, 221.690461893355, 1361.45843240672, 977.848095602787,
## 1184.42524488153, 1118.70103943078, 1119.09724476071, 776.349979307366,
## 1268.37951467727, 0, 366.786957314063, 747.561036377875, 1787.285143726,
## 1929.44698025845, 856.357368420521, 1101.14970709405, 704.184519980701,
## 1126.2230230127, 649.773318564214, 977.657620997298, 1383.5663330639,
## 1095.46573957961, 1089.3717909992, 605.220968306144, 1033.88539901665,
## 1604.72055375478, 826.327025939312, 1176.14682328504, 1275.02319938737,
## 1290.28314005644, 1133.47419931933, 837.412566855277, 1134.16627849803,
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## 1524.29040044934, 777.023737418038, 1394.79581919528, 0, 62.5715751601826,
## 722.788038958828, 293.184772853638, 645.36685722913, 767.439505481761,
## 491.879747053414, 0, 0, 509.155164105994, 965.587370085486, 403.49720580419,
## 0, 742.290015884451, 1110.10045653192, 771.551295297819, 624.338891497583,
## 797.084335731408, 415.99250259786, 538.232681166002, 1181.93470239963,
## 104.443215077792, 564.209478577945, 804.53940215468, 1028.95364023327,
## 748.746583667659, 452.802228898258, 761.064098290519, 380.950200559961,
## 1602.84960709395, 0, 1082.74797626804, 779.657300310476, 994.158712170624,
## 442.56330169432, 1717.07159258608, 497.33495411576, 1149.68065499451,
## 1465.21016364328, 565.317604157056, 922.137890502439, 175.59938060484,
## 1024.94681888114, 750.410484208866, 790.870027432839, 112.327872497541,
## 738.394487315734, 721.808132499821, 680.820718973428, 815.406570873487,
## 1042.50711204107, 663.249868122172, 1478.61854506445, 337.756753994278,
## 0, 1516.31768923235, 790.590582117334, 1763.57908789461, 1280.41844842492,
## 345.467636476389, 197.989403751685, 1770.96944052649, 238.814643857072,
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## 758.465501261611, 908.931458644613, 558.518342410987, 1819.24233339211,
## 1110.68174400549, 723.243374669993, 972.031864031495, 696.014430649643,
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## 1115.82062964092, 601.163260610188, 1097.60003894511, 1321.44305286527,
## 1052.39326016205, 687.951701062434, 566.460512626349, 955.1353421032,
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## 839.915458349589, 913.505872937903, 49.2096658960132, 465.062888613853,
## 0, 732.264267594484, 588.991056252216, 863.140717831164, 857.575733973881,
## 891.155427066673, 918.122205965447, 421.40084342513, 731.3934721696,
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## 197.538321479143, 585.708088259361, 1947.02240116176, 196.9384595398,
## 591.863619018556, 1008.29161867619, 1052.22747774062, 331.680526736089,
## 913.107203974466, 1060.80742927021, 1184.36072325231, 1024.57823828863,
## 540.279044842846, 565.138987531877, 482.98219522045, 950.350093348717,
## 1551.02346886055, 981.596275086756, 1442.12980525117, 1060.33586008787,
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## 1312.86572975147, 1212.58956759787, 1504.29017813787, 1233.34360465673,
## 843.493455075409, 1173.55981500254, 1195.59028306582, 1202.88312357915,
## 24.8718234850631, 1521.17239555469, 1160.22179270323, 638.691982603121,
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## 1172.45949910584, 548.272863944776, 1752.88378856299, 555.920680160548,
## 1560.93175219903, 839.883556561924, 1112.8179784831, 940.590874822012,
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## 793.820465702134, 879.675617944934, 1237.64742197945, 1174.71648266832,
## 794.137787843789, 0, 1227.16110689129, 1902.61299103773, 450.305390754806,
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## 259.237577825768, 1143.69257803243, 0, 919.077555018396, 94.9324758740624,
## 197.910716505068, 624.91008800743, 138.252251807784, 1030.92756438288,
## 1130.05678744088, 795.541223505837, 1503.59623846768, 436.135012404984,
## 800.705593268976, 1881.04995231902, 1445.45802967522, 1166.10023562566,
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## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)), control = list(minsplit = 20,
## minbucket = 7, cp = 0.01, maxcompete = 4, maxsurrogate = 5,
## usesurrogate = 2, surrogatestyle = 0, maxdepth = 2, xval = 0))
## n= 7001
##
## CP nsplit rel error
## 1 0.08974359 0 1.0000000
## 2 0.01000000 2 0.8205128
##
## Variable importance
## balance
## 100
##
## Node number 1: 7001 observations, complexity param=0.08974359
## predicted class=No expected loss=0.0334238 P(node) =1
## class counts: 6767 234
## probabilities: 0.967 0.033
## left son=2 (6693 obs) right son=3 (308 obs)
## Primary splits:
## balance < 1700.586 to the left, improve=103.9433000, (0 missing)
## income < 26439.41 to the right, improve= 0.8238736, (0 missing)
## studentYes < 0.5 to the left, improve= 0.7464346, (0 missing)
##
## Node number 2: 6693 observations
## predicted class=No expected loss=0.01494098 P(node) =0.9560063
## class counts: 6593 100
## probabilities: 0.985 0.015
##
## Node number 3: 308 observations, complexity param=0.08974359
## predicted class=No expected loss=0.4350649 P(node) =0.04399372
## class counts: 174 134
## probabilities: 0.565 0.435
## left son=6 (226 obs) right son=7 (82 obs)
## Primary splits:
## balance < 1971.915 to the left, improve=23.034800, (0 missing)
## income < 48861.49 to the left, improve= 3.042984, (0 missing)
## studentYes < 0.5 to the right, improve= 1.582551, (0 missing)
##
## Node number 6: 226 observations
## predicted class=No expected loss=0.3185841 P(node) =0.0322811
## class counts: 154 72
## probabilities: 0.681 0.319
##
## Node number 7: 82 observations
## predicted class=Yes expected loss=0.2439024 P(node) =0.01171261
## class counts: 20 62
## probabilities: 0.244 0.756Предсказываем с помощью дерева на тестовой выборке:
educ_tree <- mutate(educ_test,
yhat = predict(tree_model, educ_test, na.action = na.pass))
confusionMatrix(educ_tree$yhat, educ_tree$y)## Confusion Matrix and Statistics
##
## Reference
## Prediction H L
## H 70 1
## L 0 24
##
## Accuracy : 0.9895
## 95% CI : (0.9427, 0.9997)
## No Information Rate : 0.7368
## P-Value [Acc > NIR] : 8.785e-12
##
## Kappa : 0.9725
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 1.0000
## Specificity : 0.9600
## Pos Pred Value : 0.9859
## Neg Pred Value : 1.0000
## Prevalence : 0.7368
## Detection Rate : 0.7368
## Detection Prevalence : 0.7474
## Balanced Accuracy : 0.9800
##
## 'Positive' Class : H
## - Упражнение 10.
Постройте прогнозы с помощью дерева на тестовой выборке def_test и оцените его качество, посмотрев на матрицу ошибок.
def_tree_pred <- mutate(def_test,
yhat = predict(def_tree, def_test))
confusionMatrix(def_tree_pred$yhat, def_tree_pred$y)## Confusion Matrix and Statistics
##
## Reference
## Prediction No Yes
## No 2963 0
## Yes 0 36
##
## Accuracy : 1
## 95% CI : (0.9988, 1)
## No Information Rate : 0.988
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 1
## Mcnemar's Test P-Value : NA
##
## Sensitivity : 1.000
## Specificity : 1.000
## Pos Pred Value : 1.000
## Neg Pred Value : 1.000
## Prevalence : 0.988
## Detection Rate : 0.988
## Detection Prevalence : 0.988
## Balanced Accuracy : 1.000
##
## 'Positive' Class : No
## Пакет caret представляет собой общий интерфейс ко многим моделям, однако некоторые модели он ещё не поддерживает. Например, быстрые и стройные, fast and frugal, деревья.
Быстрые деревья нужны, например, в медицине, чтобы создавать быстрые и простые рекомендации для спасения жизни.
Мы применим их для спасения неуспевающих студентов :) Увы, пакет принимает на вход только 0/1 в зависимой переменной, поэтому заменим названия категорий на числа:
educ_train2 <- mutate(educ_train, ybin = ifelse(y == 'H', 1, 0)) %>%
select(-Class)И построим картинку для быстрого и стройного дерева:
fftree_model <- FFTrees(formula = ybin ~ .,
data = educ_train2)
plot(fftree_model)
- Упражнение 11.
Используйте быстрые и стройные деревья для набора данных def_train. Помните, что целевая переменная в нём закодирована как ‘Yes’ и ‘No’.
def_train2 <- mutate(def_train, defaultbin = ifelse(default == 'Yes', 1, 0))
def_fftree <- FFTrees(formula = defaultbin ~ .,
data = def_train2)
plot(def_fftree)
3 Случайный лес
В алгоритме случайного леса мы
Выращиваем целый лес, скажем 500, деревьев.
Строим прогноз с помощью каждого дерева.
Агрегируем прогнозы деревьев. Можно в качестве итогового прогноза выбрать ту категорию, за которую проголосовало большинство деревьев. Можно оценить вероятности категорий, взяв процент деревьев, проголосовавших за ту или иную категорию.
Деревья оказываются не идеальными копиями друг друга по двум причинам:
Каждое дерево обучается на случайной выборке из исходной выборки. Обычно для каждого дерева берут подвыборку с повторениями из исходной выборки, так чтобы размер подвыборки равнялся размеру исходной выборки.
При каждом делении каждой ветки на две части происходит предварительный случайный отбор переменных. Скажем, из исходных 100 переменных, каждый раз случайно отбирается 10, а затем из этих 10 выбирается наилучшая, по которой ветвь и делится на две ветви.
У идеи есть куча вариантов исполнения, отличающихся деталями:
- критерием деления ветви на две;
- критерием остановки деления дерева;
- количеством предварительно отбираемых переменных перед каждым делением;
- количество деревьев;
Посмотрим на все вариации случайного леса, которые перебрал ranger.
ranger_model <- train(y ~ . - Class, data = educ_test,
method = 'ranger',
na.action = na.omit,
importance = 'impurity')
ranger_model## Random Forest
##
## 95 samples
## 17 predictors
## 2 classes: 'H', 'L'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 95, 95, 95, 95, 95, 95, ...
## Resampling results across tuning parameters:
##
## mtry splitrule Accuracy Kappa
## 2 gini 0.8084263 0.2857475
## 2 extratrees 0.7826656 0.1681609
## 31 gini 0.9328760 0.8013875
## 31 extratrees 0.9455940 0.8392984
## 60 gini 0.9082172 0.7402034
## 60 extratrees 0.9317405 0.7995645
##
## Tuning parameter 'min.node.size' was held constant at a value of 1
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were mtry = 31, splitrule =
## extratrees and min.node.size = 1.plot(ranger_model)
И более подробно про наилучшую:
ranger_model$finalModel## Ranger result
##
## Call:
## ranger::ranger(dependent.variable.name = ".outcome", data = x, mtry = param$mtry, min.node.size = param$min.node.size, splitrule = as.character(param$splitrule), write.forest = TRUE, probability = classProbs, ...)
##
## Type: Classification
## Number of trees: 500
## Sample size: 95
## Number of independent variables: 60
## Mtry: 31
## Target node size: 1
## Variable importance mode: impurity
## Splitrule: extratrees
## OOB prediction error: 5.26 %- Упражнение 12.
Реализуйте случайный лес для данных про кредиты, выведите описание лучешй модели и постройте визуализацию.
def_ranger <- train(default ~ ., data = def_train,
method = 'ranger',
importance = 'impurity')## note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .def_ranger$finalModel## Ranger result
##
## Call:
## ranger::ranger(dependent.variable.name = ".outcome", data = x, mtry = param$mtry, min.node.size = param$min.node.size, splitrule = as.character(param$splitrule), write.forest = TRUE, probability = classProbs, ...)
##
## Type: Classification
## Number of trees: 500
## Sample size: 7001
## Number of independent variables: 3
## Mtry: 2
## Target node size: 1
## Variable importance mode: impurity
## Splitrule: extratrees
## OOB prediction error: 3.26 %plot(def_ranger)
К сожалению, построить информативно про все сотни деревьев невозможно.
Можно попытаться выделить важность переменных:
ranger_import <- varImp(ranger_model)
ranger_import## ranger variable importance
##
## only 20 most important variables shown (out of 60)
##
## Overall
## StudentAbsenceDaysUnder-7 100.000
## VisITedResources 82.002
## AnnouncementsView 43.708
## ParentschoolSatisfactionGood 22.991
## raisedhands 22.897
## Discussion 13.827
## ParentAnsweringSurveyYes 10.046
## PlaceofBirthKuwaIT 5.870
## genderM 5.485
## NationalITyJordan 5.388
## PlaceofBirthJordan 4.954
## GradeIDG-04 4.799
## GradeIDG-07 3.580
## TopicMath 3.170
## SectionIDB 3.135
## TopicIT 3.029
## TopicEnglish 2.916
## NationalITyKW 2.899
## SemesterS 2.869
## StageIDlowerlevel 2.772plot(ranger_import)
- Упражнение 13.
Выделите важность переменных в модели def_ranger.
def_import <- varImp(def_ranger)
def_import## ranger variable importance
##
## Overall
## balance 100.00
## income 50.69
## studentYes 0.00plot(def_import)
И, конечно, построить прогнозы:
educ_ranger <- mutate(educ_test,
yhat = predict(ranger_model, educ_test, na.action = na.pass))
confusionMatrix(educ_ranger$yhat, educ_ranger$y)## Confusion Matrix and Statistics
##
## Reference
## Prediction H L
## H 70 0
## L 0 25
##
## Accuracy : 1
## 95% CI : (0.9619, 1)
## No Information Rate : 0.7368
## P-Value [Acc > NIR] : 2.515e-13
##
## Kappa : 1
## Mcnemar's Test P-Value : NA
##
## Sensitivity : 1.0000
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 1.0000
## Prevalence : 0.7368
## Detection Rate : 0.7368
## Detection Prevalence : 0.7368
## Balanced Accuracy : 1.0000
##
## 'Positive' Class : H
## По умолчанию, пакет caret сам решает, сколько значений параметров перебирать и какие конкретно.
Список перебираемых параметров:
modelLookup(model = 'ranger')## model parameter label forReg forClass
## 1 ranger mtry #Randomly Selected Predictors TRUE TRUE
## 2 ranger splitrule Splitting Rule TRUE TRUE
## 3 ranger min.node.size Minimal Node Size TRUE TRUE
## probModel
## 1 TRUE
## 2 TRUE
## 3 TRUEНо мы можем заказать перебор любых.
Можно заказать количество перебираемых значений для каждого параметра:
ranger_model <- train(y ~ . - Class, data = educ_test,
method = "ranger",
na.action = na.omit,
importance = 'impurity',
tuneLength = 4)Или явно значения
grid <- expand.grid(mtry = c(5, 10), min.node.size = c(1, 5), splitrule = 'gini')
ranger_model <- train(y ~ . - Class, data = educ_test,
tuneGrid = grid, method = "ranger", na.action = na.omit)
ranger_model## Random Forest
##
## 95 samples
## 17 predictors
## 2 classes: 'H', 'L'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 95, 95, 95, 95, 95, 95, ...
## Resampling results across tuning parameters:
##
## mtry min.node.size Accuracy Kappa
## 5 1 0.9519126 0.8736549
## 5 5 0.9449514 0.8519193
## 10 1 0.9514463 0.8732505
## 10 5 0.9525191 0.8754121
##
## Tuning parameter 'splitrule' was held constant at a value of gini
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were mtry = 10, splitrule = gini
## and min.node.size = 5.Ура :)