Introduction

This package provides simple interface for cross validation and hyper-parameter tuning for statistical/machine learning models. Currently, I’m designing specification of APIs and object therefore they can be changed in future version. If you find bugs or if you have any requests, please let me know by GitHub or email: paste following code into R to get my address: rawToChar(as.raw(c(109, 111, 103, 64, 102, 102, 112, 114, 105, 46, 97, 102, 102, 114, 99, 46, 103, 111, 46, 106, 112))).

Installation

To install the package, copy & paste following script into R console. Currently, it may produce many warnings related with compilation of documents, but it does not affect any functionality of the package.

install.packages(
    c("R6", "model.adapter", "cv.models"), type = "source",
    repos = c(
        "http://florivory.net/R/repos", options()$repos
    )
)

Basic usage

Evaluation of predictive ability of a model by cross-validation

cv.models function evaluate predictive ability of a model. Most basic usage of the cv.models function is putting call of statistical/machine learning model function directory into cv.models as follow.

library(cv.models)
data(iris)
cv <- cv.models(glm(Petal.Length ~ ., data = iris))
print(cv)

## Result of cross validation
## Cross validation metrics:
##          mse      rmse r.squared  spearman   kendall q.squared    sd.mse
## 1 0.07160118 0.2637418 0.9773273 0.9338794 0.8322722 0.9740298 0.0257532
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.04762617  0.008654745  0.05044482 0.07480678   0.01150527

In the call of statistical/machine learning models, please use data argument for specifying data like glm(Petal.Length ~ Petal.Width, data = iris). Currently, model call with $ operator such as glm(iris$Petal.Length ~ iris$Petal.Width) can not work. If someone needs to use latter case, please contact me.

Users can use cv.models by passing call object for statistical/machine learning models.

# Using substitute() function
call.glm <- substitute(glm(Petal.Length ~ ., data = iris))
cv <- cv.models(call.glm)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse      rmse r.squared spearman  kendall q.squared     sd.mse
## 1 0.0720893 0.2642072 0.9786271  0.95254 0.855111 0.9758841 0.02458692
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.05037491  0.006491544  0.02646257 0.06361177  0.007255751

# Using call() function
call.glm <- call("glm", Petal.Length ~ ., data = iris)
cv <- cv.models(call.glm)
print(cv)

## Result of cross validation
## Cross validation metrics:
##          mse      rmse r.squared  spearman   kendall q.squared     sd.mse
## 1 0.07225901 0.2609248 0.9764348 0.9429454 0.8348614 0.9741313 0.03779596
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.06812785   0.01431566  0.01652288 0.04044752   0.01500444

Objects of some statistical/machine learning models can be used for cross-validation.
Only model objects keeping original call such as glm or gbm can be used for cv.models.

model <- glm(Petal.Length ~ ., data = iris)
cv <- cv.models(model)
print(cv)

## Result of cross validation
## Cross validation metrics:
##          mse      rmse r.squared  spearman   kendall q.squared     sd.mse
## 1 0.07144265 0.2634059 0.9786586 0.9402786 0.8399003 0.9752645 0.02485682
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.04784199  0.008179856  0.02563387 0.04283829   0.01095734

Metrics calculated for model evaluation

cv.models automatically calculates appropriate metrics of model evaluation by detecting type of the model (i.e., regression or classification models). Currently cv.models calculates following metrics.

Regression model

Name of metrics	Column	Definition/Explanation
Mean squared error (MSE)	“mse”	$MSE = mean((prediction - response) ^ 2)$
Root mean squared error (RMSE)	“rmse”	$RMSE = sqrt(mean((prediction - response) ^ 2))$
R squared	“r.squared”	$R ^ 2 = cor(prediction, response) ^ 2$ This is calculated only for referencing purpose. I don’t recommend this metrics because adjustment of intercept and slope is done during calculation. For example, idel models produce prediction on a line y = x when plotting actual and predicted values. However, when plotted points of actual and predicted values are completely on a line of y = -2x + 1 (in other words, completely wrong prediction model), value of R squared become 1.
Spearman’s ρ	“spearman”	$\rho = cor(prediction, response, method = "spearman")$
Kendall’s τ	“kendall”	$\tau = cor(prediction, response, method = "kendall")$
Q squared	“q.squared”	$Q ^ 2 = 1 - \sum((prediction - response) ^ 2) / \sum((response - mean(response)) ^ 2)$, See Consonni et al. (2009). Currently, mean values of each fold were used for mean of data ($mean(response)$) by default. On the other hand, mean value of all data is used when `aggregate.method = "join"` (see below) is specified. I will consider to find better default for improving consistency.

Classification models

Name of metrics	Column	Definition/Explanation
Optimal threshold	“threshold”	Optimal threshold separating presence/absence. By default, determined by Youden’s J.
Specificity	“specificity”	See Wikipedia
Sensitivity	“sensitivity”
Accuracy	“accuracy”
True negative count (TN)	“tn”
True positive count (TP)	“tp”
False negative count (FN)	“fn”
False positive count (FP)	“fp”
Negative predictive value (NPV)	“npv”
Positive predictive value (PPV)	“ppv”
Diagnostic likelihood ratio (DRL)+	“dlr.positive”	$DRL.positive = Sensitivity / (1 - Specificity)$, See Lopez-Raton et al. (2014)
Diagnostic likelihood ratio (DRL)-	“dlr.negative”	$DRL.negative = (1 - Sensitivity) / Specificity$, See Lopez-Raton et al. (2014)
Matthews correlation coefficient (MCC)	“mcc”
Informedness	“informedness”	$Informedness = Sensitivity + Specificity - 1$
Markedness	“markedness”	$Markedness = PPV + NPV - 1$
Log-likelihood	“loglik”	$Log_likelihood = \sum(log(p * y + (1 - p) * (1 - y)))$, See Lawson et al. (2014)
Likelihood based R squared	“rsq.loglik”	See Lawson et al. (2014)
Cohen’s Kappa	“kappa”	See Cohen (1960)

Using models requiring additional arguments for predict method

For some models like gbm requires additional argument(s) for predict method which can affect predictive ability. To use such models with cv.models, specify the argument(s) as additional argument(s) of cv.models.

library(gbm)
cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse      rmse r.squared spearman   kendall q.squared     sd.mse
## 1 0.1097684 0.3217449  0.966524 0.910217 0.8059406 0.9595215 0.05740915
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.08332443   0.02538766    0.102032  0.1277251   0.02270992

Controlling positive class

By default, cv.models determines positive class of the response variable by following rules.

If the response variable is numeric, use 1 as the positive class.
If the response variable is logical, use TRUE as the positive class.
If the response variable is factor, use the first level (i.e., levels(response)[1]) as the positive class.
If the response variable is character, use the first unique element (i.e., unique(response)[1]) as the positive class.

When using factor or character as the response variable of the model, you can use positive.class argument to control which class is used for positive class. Classes which are not treated as positive class are treated as negative class. In the following example, cv.models treat versicolor in the iris data as the positive class, and setosa and virginica are treated as the negative class.

cv <- cv.models(
    gbm(Species ~ ., data = iris, n.trees = 50, distribution = "multinomial"),
    n.cores = 1, n.trees = 50, positive.class = "versicolor"
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##   method threshold sensitivity specificity       ppv npv dlr.positive
## 1 Youden 0.6129907           1   0.9725758 0.9383333   1          Inf
##   dlr.negative  fp fn       auc tp  tn accuracy informedness markedness
## 1            0 0.3  0 0.9901717  5 9.7     0.98    0.9725758  0.9383333
##         mcc    loglik rsq.loglik     kappa sd.threshold sd.sensitivity
## 1 0.9547984 -2.467852  0.6411764 0.9514063    0.4612871              0
##   sd.specificity    sd.ppv sd.npv sd.dlr.positive sd.dlr.negative
## 1      0.0443321 0.1012423      0             NaN               0
##       sd.fp sd.fn     sd.auc    sd.tp    sd.tn sd.accuracy sd.informedness
## 1 0.4830459     0 0.01836965 1.563472 1.418136  0.03220306       0.0443321
##   sd.markedness     sd.mcc sd.loglik sd.rsq.loglik   sd.kappa
## 1     0.1012423 0.07331211  2.515344     0.2936008 0.07889443

Controlling calculation of metrics

By default, cv.models calculates performance metrics for each fold and then averages them. But this method can’t work for Leave-One-Out cross validation (LOOCV) or data with class imbalance in the response variable. I’m not sure what is the best method handling this situation, but currently by specifying aggregate.method = "join", cv.models calculate metrics after joining results from all folds.

cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    aggregate.method = "join", n.trees = 50
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse      rmse r.squared  spearman  kendall q.squared sd.mse
## 1 0.1113121 0.3336346 0.9647023 0.9418911 0.796786 0.9640407     NA
##   sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1      NA           NA          NA         NA           NA

In this situation, SD of each metrics become NA.

Use Class Stratification

When class imbalance exists in the response variable, random dividing of dataset into folds can create fold(s) without observation with specific class and can disrupt cross validation. Class stratification (a method to divide dataset into folds with keeping frequency of classes) can help this situation.

To use class stratification, specify stratify = TRUE in cv.models.

library(randomForest)

# Create dataset with small frequency of setosa.
test.data <- subset(iris, Species != "setosa")
test.data <- rbind(test.data, head(subset(iris, Species == "setosa"), 10))

# Cross validation.
cv <- cv.models(
    randomForest(Species ~ ., data = iris, n.cores = 1),
    aggregate.method = "join", n.trees = 50, stratify = TRUE
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##   method threshold sensitivity specificity ppv npv dlr.positive
## 1 Youden      0.94           1           1   1   1          Inf
##   dlr.negative fp fn auc tp  tn accuracy informedness markedness mcc
## 1            0  0  0   1 50 100        1            1          1   1
##       loglik rsq.loglik kappa sd.threshold sd.sensitivity sd.specificity
## 1 -0.2362728  0.9871859     1           NA             NA             NA
##   sd.ppv sd.npv sd.dlr.positive sd.dlr.negative sd.fp sd.fn sd.auc sd.tp
## 1     NA     NA              NA              NA    NA    NA     NA    NA
##   sd.tn sd.accuracy sd.informedness sd.markedness sd.mcc sd.loglik
## 1    NA          NA              NA            NA     NA        NA
##   sd.rsq.loglik sd.kappa
## 1            NA       NA

Currently, class stratification is implemented only for classification models.

Controlling method for optimal threshold determination

Previous version of cv.models used Youden’s J with coords function in pROC package to find optimal threshold dividing positive and negative classes. After ver. 0.1.0, cv.models uses optimal.cutpoints function in OptimalCutpoints package and this allows us to use other metrics for determining optimal threshold. By default, cv.models still use Youden’s J for determination of the threshold, but users can specify a list having options passed to optimal.cutpoints for the cutpoint.options argument to control method used for threshold determination. In the following example, sensitivity, instead of Youden’s J, is maximized by specifying list(methods = "MaxSe") for cutpoint.options.

cv <- cv.models(
    gbm(Species ~ ., data = iris, n.trees = 50, distribution = "multinomial"),
    n.cores = 1, n.trees = 50, positive.class = "setosa",
    cutpoint.options = list(methods = "MaxSe")
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##   method threshold sensitivity specificity ppv npv dlr.positive
## 1  MaxSe 0.9958904           1           1   1   1          Inf
##   dlr.negative fp fn auc tp tn accuracy informedness markedness mcc
## 1            0  0  0   1  5 10        1            1          1   1
##        loglik rsq.loglik kappa sd.threshold sd.sensitivity sd.specificity
## 1 -0.02085396  0.8966806     1  0.001572169              0              0
##   sd.ppv sd.npv sd.dlr.positive sd.dlr.negative sd.fp sd.fn sd.auc
## 1      0      0             NaN               0     0     0      0
##      sd.tp    sd.tn sd.accuracy sd.informedness sd.markedness sd.mcc
## 1 1.763834 1.763834           0               0             0      0
##     sd.loglik sd.rsq.loglik sd.kappa
## 1 0.006152772    0.01801658        0

optimal.cutpoints can determine multiple thresholds simultaneously. For example, by specifying list(methods = c("MaxSe", "MaxSp")) for cutpoint.options, cv.models can calculate two sets of metrics with the thresholds determined by sensitivity and specificity, yet they bring same results… :).

cv <- cv.models(
    gbm(Species ~ ., data = iris, n.trees = 50, distribution = "multinomial"),
    n.cores = 1, n.trees = 50, positive.class = "setosa",
    cutpoint.options = list(methods = c("MaxSe", "MaxSp"))
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##   method threshold sensitivity specificity ppv npv dlr.positive
## 1  MaxSe 0.9959352           1           1   1   1          Inf
## 2  MaxSp 0.9959352           1           1   1   1          Inf
##   dlr.negative fp fn auc tp tn accuracy informedness markedness mcc
## 1            0  0  0   1  5 10        1            1          1   1
## 2            0  0  0   1  5 10        1            1          1   1
##        loglik rsq.loglik kappa sd.threshold sd.sensitivity sd.specificity
## 1 -0.02285701  0.8887343     1  0.001461932              0              0
## 2 -0.02285701  0.8887343     1  0.001461932              0              0
##   sd.ppv sd.npv sd.dlr.positive sd.dlr.negative sd.fp sd.fn sd.auc
## 1      0      0             NaN               0     0     0      0
## 2      0      0             NaN               0     0     0      0
##      sd.tp    sd.tn sd.accuracy sd.informedness sd.markedness sd.mcc
## 1 2.788867 2.788867           0               0             0      0
## 2 2.788867 2.788867           0               0             0      0
##     sd.loglik sd.rsq.loglik sd.kappa
## 1 0.008369546    0.02159467        0
## 2 0.008369546    0.02159467        0

Users can specify methods, op.prev and control of optimal.cutpoints in the list used for cutpoint.options and other options are ignored. For the details of optimal.cutpoints see the manual and reference (Lopez-Raton et al. 2014) of it.

Changing number of folds

To change number of folds, change folds argument.

cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50, folds = 5
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse      rmse r.squared  spearman   kendall q.squared    sd.mse
## 1 0.1051745 0.3216322 0.9663009 0.9387993 0.8253669 0.9642212 0.0293904
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.04646493   0.01193624  0.03115216   0.044694   0.01079232

Fix random number

Because cross validation and some modeling methods use stochastic processes, cv.models returns slightly different results every time. To fix the result, specify some number for seed argument. When seed is set, cv.models returns same result independent of parallel computation.

# Results are different each time.
cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##          mse      rmse r.squared  spearman   kendall q.squared     sd.mse
## 1 0.09922069 0.3105432 0.9691495 0.9298997 0.8242038 0.9664689 0.03640097
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.05561364   0.01098273  0.04932323 0.08184355   0.01029104

cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse      rmse r.squared spearman   kendall q.squared    sd.mse
## 1 0.1082467 0.3173534 0.9674564 0.932942 0.8336295 0.9630571 0.0624551
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.09149091   0.01911328  0.03345093 0.06072541   0.02018797

# If seed is set, same result is returned every time.
cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50, seed = 12345
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse      rmse r.squared  spearman   kendall q.squared     sd.mse
## 1 0.1059846 0.3208402 0.9668684 0.9323122 0.8262999  0.961941 0.04231908
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.05817747   0.01486364  0.04670806 0.06900898   0.01723832

cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50, seed = 12345
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse      rmse r.squared  spearman   kendall q.squared     sd.mse
## 1 0.1059846 0.3208402 0.9668684 0.9323122 0.8262999  0.961941 0.04231908
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.05817747   0.01486364  0.04670806 0.06900898   0.01723832

Use user specified grouping for cross validation

By default, cv.models randomly separates data into several folds and runs cross validation. However, when each observation are not independent each other (e.g., when dataset having some internal structure such as spatial autocorrelation), cross validation with random separation would bring optimistic estimates of model performance measures (Roberts et al. 2017). In this situation, blocked cross validation would bring better results (Roberts et al. 2017) and groupings of datasets produced by other packages such as blockCV package (Valavi et al. 2018) can be used for cross validation. To use user defined grouping rather than default random separation of dataset, specify a vector representing grouping of observations for group argument of cv.models. For the group argument, a vector of character, factor, integer and logical having same length as the number of observation can be used.

Following example shows testing predictive ability of the model for different species using the iris data.

cv <- cv.models(
    randomForest(Petal.Length ~ ., data = iris, n.cores = 1, n.trees = 50),
    n.cores = 1, group = iris$Species
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##       mse     rmse r.squared  spearman   kendall q.squared   sd.mse
## 1 4.19397 1.749769 0.1980847 0.3585859 0.2723849 -106.9464 4.610268
##    sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 1.303234    0.3233384   0.3140936  0.2351445     177.1127

Control parallel processing

By default, cv.models uses all logical/physical cores. To control number of cores (i.e., processes) used for cross validation, specify a number for n.cores argument.

# Cross validation with 2 cores.
cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50, n.cores = 2
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##         mse     rmse r.squared  spearman   kendall q.squared     sd.mse
## 1 0.1089966 0.323703 0.9687782 0.9363097 0.8391552  0.962467 0.04566111
##      sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.06841881  0.009601633  0.04613624 0.08131339   0.01444266

Hyper-parameter selection

cv.models can conduct grid search to find which combination of hyper-parameters can bring model(s) with best performance using cross validation. To conduct grid search for hyper-parameters, supply a named list having vector of candidate parameters for grid argument. In the following example, cv.models calculates performance measures with cross validation for all combination of hyper-parameters (in this example, 1 and 5 for interaction.depth and 1 and 10 for n.minobsinnode) of gbm

# See the effect of hyper parameter on predictive ability of the model.
cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    n.trees = 50,
    grid = list(interaction.depth = c(1, 5), n.minobsinnode = c(1, 10))
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##   interaction.depth n.minobsinnode        mse      rmse r.squared
## 1                 1              1 0.07970788 0.2778357 0.9735727
## 2                 5              1 0.07156345 0.2621945 0.9763217
## 3                 1             10 0.10164681 0.3121165 0.9688425
## 4                 5             10 0.09726478 0.3067847 0.9671420
##    spearman   kendall q.squared     sd.mse    sd.rmse sd.r.squared
## 1 0.9378012 0.8526449 0.9704077 0.03137318 0.05286475   0.01697545
## 2 0.9359555 0.8339149 0.9725090 0.03094536 0.05595131   0.01293670
## 3 0.9264031 0.8262655 0.9636375 0.04557239 0.06855731   0.01499536
## 4 0.9033653 0.7841828 0.9643673 0.03723326 0.05914151   0.01497294
##   sd.spearman sd.kendall sd.q.squared
## 1  0.03324120 0.05584728   0.01625107
## 2  0.03288226 0.05709310   0.01505707
## 3  0.07819431 0.09631725   0.01763200
## 4  0.08094862 0.09215561   0.01479924

For models having extra argument(s) for predict method affecting predictive ability (e.g., n.tree argument of gbm), users can specify a list of candidate parameter(s) for grid.predict to conduct grid search for such parameter(s).

# See the effect of hyper parameter on predictive ability of the model.
cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    grid = list(interaction.depth = c(1, 5), n.minobsinnode = c(1, 10)),
    grid.predict = list(n.trees = c(10, 50, 80))
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##    interaction.depth n.minobsinnode n.trees        mse      rmse r.squared
## 1                  1              1      10 0.70940672 0.8347681 0.9276824
## 2                  1              1      50 0.07255751 0.2605845 0.9774829
## 3                  1              1      80 0.06828483 0.2533573 0.9779486
## 4                  5              1      10 0.45822331 0.6706116 0.9780200
## 5                  5              1      50 0.07100390 0.2640894 0.9777949
## 6                  5              1      80 0.07503506 0.2720042 0.9763532
## 7                  1             10      10 0.72188918 0.8345397 0.9284288
## 8                  1             10      50 0.10160226 0.3095017 0.9678100
## 9                  1             10      80 0.09462196 0.2995565 0.9688744
## 10                 5             10      10 0.50339378 0.7040647 0.9672351
## 11                 5             10      50 0.09227950 0.2948742 0.9733669
## 12                 5             10      80 0.09235612 0.2952405 0.9735409
##     spearman   kendall q.squared     sd.mse    sd.rmse sd.r.squared
## 1  0.9290615 0.8471718 0.7569029 0.20330561 0.11817559  0.030193683
## 2  0.9408784 0.8488161 0.9744224 0.03665937 0.07190453  0.013515508
## 3  0.9365843 0.8411318 0.9757082 0.03562060 0.06745296  0.013617705
## 4  0.9450372 0.8651972 0.8404915 0.12484258 0.09720186  0.012273615
## 5  0.9340507 0.8470638 0.9737058 0.01995886 0.03742636  0.009553237
## 6  0.9328022 0.8374948 0.9724562 0.01850928 0.03413663  0.008959014
## 7  0.9131920 0.8177403 0.7377688 0.30248827 0.16810262  0.037922414
## 8  0.9037919 0.8014867 0.9605600 0.05114317 0.08035315  0.021650395
## 9  0.8969894 0.7897869 0.9625695 0.04388729 0.07369497  0.021304530
## 10 0.9348503 0.8223210 0.8321282 0.13776870 0.09241579  0.018733256
## 11 0.9321754 0.8118652 0.9680747 0.04770093 0.07694683  0.016718066
## 12 0.9298682 0.8072078 0.9679590 0.04748347 0.07593245  0.016728812
##    sd.spearman sd.kendall sd.q.squared
## 1   0.02437750 0.03299084   0.05754771
## 2   0.02094661 0.04276941   0.01433604
## 3   0.03540891 0.05493194   0.01441225
## 4   0.03521232 0.06358434   0.02411691
## 5   0.04367401 0.06367079   0.01125424
## 6   0.04360961 0.06678759   0.01009343
## 7   0.05123220 0.07460691   0.07289115
## 8   0.08817375 0.12461058   0.02460951
## 9   0.10013855 0.14334661   0.02362557
## 10  0.02155212 0.04877876   0.03500259
## 11  0.03233777 0.04936805   0.01860968
## 12  0.03315534 0.05306460   0.01898663

Extract model(s) with best predictive ability

After grid search, you can extract model(s) with best predictive ability using find.best.models function for the result of cv.models. In the following example, find.best.models function extracts model(s) with the highest value of Q^2.

# See the effect of hyper parameter on predictive ability of the model.
cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    grid = list(interaction.depth = c(1, 5), n.minobsinnode = c(1, 10)),
    grid.predict = list(n.trees = c(10, 50, 80))
)
print(cv)

## Result of cross validation
## Cross validation metrics:
##    interaction.depth n.minobsinnode n.trees        mse      rmse r.squared
## 1                  1              1      10 0.71846209 0.8313373 0.9375318
## 2                  1              1      50 0.07800233 0.2761946 0.9770139
## 3                  1              1      80 0.07182894 0.2663227 0.9770512
## 4                  5              1      10 0.45879621 0.6741641 0.9773939
## 5                  5              1      50 0.06968244 0.2581932 0.9762469
## 6                  5              1      80 0.07297073 0.2639482 0.9741611
## 7                  1             10      10 0.72679446 0.8386957 0.9223218
## 8                  1             10      50 0.11476425 0.3300293 0.9652568
## 9                  1             10      80 0.10587586 0.3181813 0.9666815
## 10                 5             10      10 0.49000899 0.6929212 0.9693967
## 11                 5             10      50 0.09287782 0.3008929 0.9733423
## 12                 5             10      80 0.08891006 0.2940389 0.9748969
##     spearman   kendall q.squared     sd.mse    sd.rmse sd.r.squared
## 1  0.9211462 0.8297653 0.7621652 0.31841651 0.17429336  0.024474695
## 2  0.9476352 0.8598201 0.9732361 0.02629821 0.04370169  0.007656814
## 3  0.9380785 0.8433653 0.9745011 0.01759604 0.03164326  0.006777259
## 4  0.9497234 0.8622065 0.8289065 0.09806133 0.06911280  0.011764558
## 5  0.9555615 0.8708582 0.9739878 0.03161776 0.05791498  0.012940980
## 6  0.9463290 0.8555012 0.9720997 0.03264445 0.06057217  0.015555032
## 7  0.8988592 0.8029528 0.7545430 0.28155642 0.16118993  0.044251930
## 8  0.9213254 0.8042133 0.9595982 0.04945501 0.08058753  0.016519557
## 9  0.9171429 0.7930354 0.9620922 0.04117472 0.07177516  0.016537674
## 10 0.9266675 0.8139262 0.8382962 0.14209819 0.10471793  0.011958271
## 11 0.9387832 0.8290341 0.9681454 0.03056807 0.05100402  0.009005588
## 12 0.9310652 0.8133410 0.9694114 0.03073416 0.05218757  0.009269696
##    sd.spearman sd.kendall sd.q.squared
## 1   0.03011275 0.03784255  0.046181444
## 2   0.02484243 0.04270127  0.005470736
## 3   0.02855585 0.05496531  0.006521107
## 4   0.01579183 0.03141194  0.073645898
## 5   0.02780311 0.04833118  0.014315469
## 6   0.03109811 0.05857567  0.016755934
## 7   0.05972741 0.06872107  0.048706163
## 8   0.05259488 0.06576310  0.018044766
## 9   0.05243438 0.06157570  0.017725410
## 10  0.03192243 0.05546427  0.025920873
## 11  0.03089184 0.05802708  0.010064317
## 12  0.03197896 0.06039529  0.010330123

# Get best model.
best <- find.best.models(cv, "q.squared")
print(best)

## ------------------------------------------------
## Result of model selection by cross validation
## -> 1 best models was found:
## ------------------------------------------------
## Model index 1
## ------------------------------------------------ 
## Result of cross validation
## Cross validation metrics:
##   interaction.depth n.minobsinnode n.trees        mse      rmse r.squared
## 1                 1              1      80 0.07182894 0.2663227 0.9770512
##    spearman   kendall q.squared     sd.mse    sd.rmse sd.r.squared
## 1 0.9380785 0.8433653 0.9745011 0.01759604 0.03164326  0.006777259
##   sd.spearman sd.kendall sd.q.squared
## 1  0.02855585 0.05496531  0.006521107

The result of find.best.models function is object of cv.best.models, which is a list of cv.result object.

# See the class of the result of find.best.models().
class(best)

## [1] "cv.best.models"

# The results of find.best.models() is a list of cv.result object.
class(best[[1]])

## [1] "cv.result"

print(best[[1]])

## Result of cross validation
## Cross validation metrics:
##   interaction.depth n.minobsinnode n.trees        mse      rmse r.squared
## 1                 1              1      80 0.07182894 0.2663227 0.9770512
##    spearman   kendall q.squared     sd.mse    sd.rmse sd.r.squared
## 1 0.9380785 0.8433653 0.9745011 0.01759604 0.03164326  0.006777259
##   sd.spearman sd.kendall sd.q.squared
## 1  0.02855585 0.05496531  0.006521107

Extracting data from cv.models object

Using following functions, you can extract information from the result of cv.models.

cv <- cv.models(
    gbm(Petal.Length ~ ., data = iris, distribution = "gaussian", n.cores = 1),
    grid = list(interaction.depth = c(1, 5), n.minobsinnode = c(1, 10)),
    grid.predict = list(n.trees = c(10, 50, 80))
)

# Extract prediction of the 10th model.
# The result is a data.frame having three columns:
# "response" having original values of response variable,
# "prediction" having prediction of the model,
# "index" having index of response variable in the original dataset.
fit <- extract.fit(cv, 10)
head(fit)

##   response prediction index
## 1      1.4   2.275855     1
## 2      1.4   2.238841     2
## 3      1.6   2.238841    30
## 4      1.4   2.275855    34
## 5      1.3   2.238841    43
## 6      4.9   4.379440    53

# Extract the detailed information of 10th model.
# The result is an object of cv.result.
extract.result(cv, 10)

## Result of cross validation
## Cross validation metrics:
##   interaction.depth n.minobsinnode n.trees     mse      rmse r.squared
## 1                 5             10      10 0.49064 0.6961741 0.9674917
##    spearman  kendall q.squared    sd.mse    sd.rmse sd.r.squared
## 1 0.9302293 0.812527 0.8384762 0.1151032 0.08152483   0.02182448
##   sd.spearman sd.kendall sd.q.squared
## 1  0.03004164 0.05664544    0.0198745

# Extract table of performance metrics.
extract.metrics(cv)

##    interaction.depth n.minobsinnode n.trees        mse      rmse r.squared
## 1                  1              1      10 0.71175871 0.8255634 0.9388859
## 2                  1              1      50 0.08085989 0.2763715 0.9781593
## 3                  1              1      80 0.07465255 0.2672395 0.9791906
## 4                  5              1      10 0.45859380 0.6704822 0.9782709
## 5                  5              1      50 0.06940618 0.2616235 0.9799677
## 6                  5              1      80 0.07398858 0.2704843 0.9780468
## 7                  1             10      10 0.72252293 0.8363674 0.9120885
## 8                  1             10      50 0.10507791 0.3149128 0.9560609
## 9                  1             10      80 0.09986131 0.3077974 0.9580154
## 10                 5             10      10 0.49064000 0.6961741 0.9674917
## 11                 5             10      50 0.09147345 0.2890595 0.9717959
## 12                 5             10      80 0.08797113 0.2826143 0.9728868
##     spearman   kendall q.squared     sd.mse    sd.rmse sd.r.squared
## 1  0.9233408 0.8352378 0.7674455 0.29728458 0.18319308  0.026928756
## 2  0.9354004 0.8446767 0.9721795 0.03830157 0.07054320  0.011071687
## 3  0.9304714 0.8324126 0.9733951 0.03074939 0.05995924  0.009795229
## 4  0.9519100 0.8678236 0.8482883 0.14205656 0.10026301  0.007476456
## 5  0.9460936 0.8450875 0.9765642 0.01653659 0.03264850  0.006240878
## 6  0.9375281 0.8294852 0.9748364 0.01547064 0.03030980  0.007332415
## 7  0.8913047 0.7919933 0.6930442 0.26375839 0.15990477  0.090690587
## 8  0.9142751 0.8096110 0.9504617 0.05289921 0.08102028  0.049334548
## 9  0.9102315 0.7945727 0.9533575 0.04702192 0.07543999  0.045385934
## 10 0.9302293 0.8125270 0.8384762 0.11510317 0.08152483  0.021824479
## 11 0.9418915 0.8312178 0.9699236 0.05906155 0.09379684  0.018712111
## 12 0.9411693 0.8331314 0.9708471 0.05899344 0.09487014  0.018760298
##    sd.spearman sd.kendall sd.q.squared
## 1   0.04039322 0.06626447  0.050097523
## 2   0.03324363 0.06671469  0.012841793
## 3   0.03289490 0.06723819  0.013842410
## 4   0.02662593 0.04486590  0.026471476
## 5   0.02630269 0.05088710  0.005175986
## 6   0.02800890 0.05193071  0.005726293
## 7   0.05659831 0.07296444  0.265949943
## 8   0.06375212 0.08731345  0.056262327
## 9   0.06900359 0.09243878  0.049589749
## 10  0.03004164 0.05664544  0.019874504
## 11  0.02179858 0.04640157  0.018805598
## 12  0.02251280 0.04516270  0.018996378

The extract.fit function can be used for cv.best.models and cv.result objects.

# Extract prediction from the first model of best models.
best <- find.best.models(cv, "q.squared")
fit <- extract.fit(best, 1)
head(fit)

##   response prediction index
## 1      1.3   1.498935     3
## 2      1.5   1.512613    40
## 3      1.5   1.455967    49
## 4      4.5   4.262396    67
## 5      4.1   3.686600    68
## 6      4.8   4.586651    71

# Extract the 10th model as a cv.result object.
result <- extract.result(cv, 10)
# Extract prediction of the 10th model.
fit <- extract.fit(result)
head(fit)

##   response prediction index
## 1      1.4   2.275855     1
## 2      1.4   2.238841     2
## 3      1.6   2.238841    30
## 4      1.4   2.275855    34
## 5      1.3   2.238841    43
## 6      4.9   4.379440    53

Plotting

You can use plot function to show relationship between predicted and actual values. Each point represents pair of prediction and actual values, and the line represents $Y = X$. Currently, plotting can’t work with classification model.

# Plot predicted and actual values obtained from lm model.
cv <- cv.models(
    lm(Petal.Length ~ ., data = iris)
)
plot(cv)

# See the effect of hyper parameter on predictive ability of the model.
cv <- cv.models(
    gbm(
        Petal.Length ~ ., data = iris, weights = iris$Sepal.Width,
        distribution = "gaussian", n.cores = 1
    ),
    grid = list(interaction.depth = c(1, 5), n.minobsinnode = c(1, 10)),
    grid.predict = list(n.trees = c(10, 50, 80))
)
# Show the relationship between prediction and actual values in the 10th result.
plot(cv, 10)

Technical details

to be continued…

Model specific information

gbm

n.trees

When using gbm, please specify a larger or equal value of n.trees in gbm than the values used for grid.predict. When a smaller value of n.trees is used in the call of gbm compared with values used for grid.predict, larger values of n.trees than the value specified in the call have no effect on the result.

# gbm is called with n.trees = 10,
# but n.trees of 5, 10, 50 and 80 is used in grid.predict.
cv <- cv.models(
    gbm(
        Petal.Length ~ ., data = iris, weights = iris$Sepal.Width,
        distribution = "gaussian", n.trees = 10
    ),
    grid.predict = list(n.trees = c(5, 10, 50, 80))
)
# In this situation, values of n.trees more than the value specified in gbm (10)
# in grid.predict has no effect on predictive ability of the model and
# same results are returned.
print(cv)

## Result of cross validation
## Cross validation metrics:
##   n.trees       mse      rmse r.squared  spearman   kendall q.squared
## 1       5 1.3678147 1.1637576 0.8791430 0.8393686 0.7300279 0.5354089
## 2      10 0.7024126 0.8305721 0.9251183 0.9243442 0.8299453 0.7623343
## 3      50 0.7024126 0.8305721 0.9251183 0.9243442 0.8299453 0.7623343
## 4      80 0.7024126 0.8305721 0.9251183 0.9243442 0.8299453 0.7623343
##      sd.mse   sd.rmse sd.r.squared sd.spearman sd.kendall sd.q.squared
## 1 0.2937742 0.1223969   0.09564163  0.04474389 0.04746734   0.06538468
## 2 0.2003206 0.1181459   0.05797862  0.03408190 0.05040874   0.05462135
## 3 0.2003206 0.1181459   0.05797862  0.03408190 0.05040874   0.05462135
## 4 0.2003206 0.1181459   0.05797862  0.03408190 0.05040874   0.05462135

weights

When formula is defined outside of function call, and weights is specified following way, cv.models can’t work with gbm.

# This can work.
cv <- cv.models(
    gbm(
        Petal.Length ~ ., data = iris, weights = iris$Sepal.Width,
        distribution = "gaussian", n.trees = 10
    ),
    n.trees = 10, n.cores = 1
)

# For unknown reason, this can't work.
f <- Petal.Length ~ .
cv <- cv.models(
    gbm(
        f, data = iris, weights = iris$Sepal.Width,
        distribution = "gaussian", n.trees = 10
    ),
    n.trees = 10, n.cores = 1
)

For a workaround, you can use weights by specifying without iris$.

f <- Petal.Length ~ .
cv <- cv.models(
    gbm(
        f, data = iris, weights = Sepal.Width,
        distribution = "gaussian", n.trees = 10
    ),
    n.trees = 10, n.cores = 1
)

Funcitons using additional data (e.g., weights of gbm and glm)

Some functions use additional data such as weights argument of glm and gbm. In this situation, function call produced by call can’t be used for cv.models.

# call object produced by call function with weights can't be used for cv.models.
call.gbm <- call(
    "gbm", Petal.Length ~ ., data = iris, weights = iris$Sepal.Width,
    distribution = "gaussian", n.trees = 10, n.cores = 1
)
# Error!
cv <- cv.models(call.gbm, n.trees = 10)

# Same for GLM.
call.glm <- call(
    "glm", Petal.Length ~ ., data = iris, weights = iris$Sepal.Width
)
cv <- cv.models(call.glm)

For a workaround please use substitute function instead of call function. Also, please use variable name without iris$ for weights.

# Making call with substitute.
call.gbm <- substitute(
    gbm(
        Petal.Length ~ ., data = iris, weights = Sepal.Width,
        distribution = "gaussian", n.trees = 10, n.cores = 1
    )
)
# OK!
cv <- cv.models(call.gbm, n.trees = 10)

# Same for GLM.
call.glm <- substitute(
    glm(Petal.Length ~ ., data = iris, weights = Sepal.Width)
)
cv <- cv.models(call.glm)

Modelw with `offset` terms

predict methods of some models don’t adjust offset terms. Therefore, cv.models adjusts effect of offset terms if:

The model is a regression model.
The model has only one offset term.
The offset was pecified in the format of formula = y ~ x + offset(param) or offset = param, rather than formula = y ~ x + offset(data$param) or offset = data$param.
The prediction are calculated in response scale.
The model is not glmmML and ranger

When adjusting offset for models with link function, cv.models assumes that offset values in the data is response scale and transformed in the model call as follows. When pre-transformed data is specified for offset term, the adjustment doesn’t work correctly. Note that because cv.models can’t know transformation of data, it can’t produce warning or error messages.

cv <- cv.models(
    glm(Petal.Length ~ Sepal.Width + offset(log(Petal.Width)), data = iris)
)

`ranger::ranger`

It’s not clear whether predict method of ranger::ranger adjusts offset terms or not. Therefore, currently cv.models doesn’t adjust offset terms for ranger models.

`glmmML::glmmML`

glmmML function in glmmML package doesn’t provide predict method therefore cv.models implemented predict method for it. However, because the way of offset adjustment for glmmML is not clear, curent version of cv.models doesn’t adjust offset terms for glmmML.

Models with random effect

Currently, cv.models use population-level prediction (i.e., prediction ignoring random effect) for performance evaluation.

Known issues

To many kinds of complicated objects

The functions in this package create cv.models, cv.best.models and cv.result objects. This may be refactored in the future version.
Almost no tests!

Test codes for the package is still in development. Some function may not be working correctly.
Always AUC become more than 0.5

~~When the model is worse than random prediction, i.e., if it produce reversed prediction, pROC::coords switches positive and negative class when calculating AUC.~~

I’m not sure for the way of AUC calculation in OptimalCutpoints package.
Definition of MSE

Some literature defined MSE as: MSE = sum((response - predict) ^ 2) / (sample size - number of parameter) This is different for the definition used for the one used in this package.
Best model selection with Diagnostic Likelihood Ratio

Currently, cv.models considers models with higher Diagnostic Likelihood Ratio for better model, but I’m not confident this is OK. If you have some reference for the answer, please let me know.

References

Cohen, J. 1960. A Coefficient of Agreement for Nominal Scales. Educational and Psychological Measurement 20:37-46.
Consonni, V., D. Ballabio, and R. Todeschini. 2009. Comments on the Definition of the Q2 Parameter for QSAR Validation. Journal of Chemical Information and Modeling 49:1669-1678.
Lawson CR, Hodgson JA, Wilson RJ, et al. 2014. Prevalence, thresholds and the performance of presence-absence models. Methods in Ecology and Evolution 5:54-64.
Lopez-Raton, M., M. X. Rodriguez-Alvarez, C. Cadarso-Suarez, and F. Gude-Sampedro. 2014. OptimalCutpoints: An R Package for Selecting Optimal Cutpoints in Diagnostic Tests. Journal of Statistical Software 61:36.
Roberts, D. R., V. Bahn, S. Ciuti, M. S. Boyce, J. Elith, G. Guillera-Arroita, S. Hauenstein, J. J. Lahoz-Monfort, B. Schröder, W. Thuiller, D. I. Warton, B. A. Wintle, F. Hartig, and C. F. Dormann. 2017. Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography 40:913-929.
Valavi, R., J. Elith, J. J. Lahoz-Monfort, and G. Guillera-Arroita. 2018. blockCV: an R package for generating spatially or environmentally separated folds for k-fold cross-validation of species distribution models. Methods in Ecology and Evolution 00:1-8.

Version history

2019-07-09: 0.1.4
- Add Spearman’s rho and Kendall’s tau as performance measures for regression models.
- Start continuous integration with Travis-CI.
- Minor bug fixes.
2018-11-10: 0.1.3
- Add group argument which supply user defined grouping for cv.models.
2018-09-14: 0.1.2
- Compatible with model.adapter package ver.0.1.0.
- Implement Class Stratification.
2018-01-31: 0.1.1
- Bug fix: cv.models does not run cross validation when called with call() function or model object.
2018-01-28: 0.1.0
- find.best.models uses seed of random number specified in cv.models to fix the result.
- Dependency on pROC package is replaced with OptimalCutpoints package and optimal threshold can be calculated other criteria than Youden’s J. By this modification, cv.models doesn’t calculate metrics such as 1-npv and does calculate Diagnostic Likelihood Ratio.
- Implemented Cohen’s Kappa for classification model.
- Bug fix: parallel processing produce different result even when seed of random number is specified.
- Bug fix: wrong message from print.cv.best.models().
2017-09-10: 0.0.4
- Experimental: add log-likelihood and likelihood based R^2 for metrics for classification models.
- Bug fix: wrong assignment of CPU cores.
2017-07-07: 0.0.3
- Bug fix: occasional failure for calculation.
2017-07-07: 0.0.2
- Bug fix: correspondence between explanatory and response variable was wrong.
2017-07-05: 0.0.1
- Start versioning.

Quick Start Guide for cv.models

Michio Oguro

2019-07-09

Introduction

Installation

Basic usage

Evaluation of predictive ability of a model by cross-validation

Metrics calculated for model evaluation

Regression model

Classification models

Using models requiring additional arguments for predict method

Controlling positive class

Controlling calculation of metrics

Use Class Stratification

Controlling method for optimal threshold determination

Changing number of folds

Fix random number

Use user specified grouping for cross validation

Control parallel processing

Hyper-parameter selection

Extract model(s) with best predictive ability

Extracting data from cv.models object

Plotting

Technical details

Model specific information

gbm

n.trees

weights

Funcitons using additional data (e.g., weights of gbm and glm)

Modelw with `offset` terms

`ranger::ranger`

`glmmML::glmmML`

Models with random effect

Known issues

References

Version history

Name of metrics	Column	Definition/Explanation
Mean squared error (MSE)	“mse”	\(MSE = mean((prediction - response) ^ 2)\)
Root mean squared error (RMSE)	“rmse”	\(RMSE = sqrt(mean((prediction - response) ^ 2))\)
R squared	“r.squared”	\(R ^ 2 = cor(prediction, response) ^ 2\) This is calculated only for referencing purpose. I don’t recommend this metrics because adjustment of intercept and slope is done during calculation. For example, idel models produce prediction on a line y = x when plotting actual and predicted values. However, when plotted points of actual and predicted values are completely on a line of y = -2x + 1 (in other words, completely wrong prediction model), value of R squared become 1.
Spearman’s ρ	“spearman”	\(\rho = cor(prediction, response, method = "spearman")\)
Kendall’s τ	“kendall”	\(\tau = cor(prediction, response, method = "kendall")\)
Q squared	“q.squared”	\(Q ^ 2 = 1 - \sum((prediction - response) ^ 2) / \sum((response - mean(response)) ^ 2)\), See Consonni et al. (2009). Currently, mean values of each fold were used for mean of data (\(mean(response)\)) by default. On the other hand, mean value of all data is used when `aggregate.method = "join"` (see below) is specified. I will consider to find better default for improving consistency.

Quick Start Guide for cv.models

Michio Oguro

2019-07-09

Introduction

Installation

Basic usage

Evaluation of predictive ability of a model by cross-validation

Metrics calculated for model evaluation

Regression model

Classification models

Using models requiring additional arguments for predict method

Controlling positive class

Controlling calculation of metrics

Use Class Stratification

Controlling method for optimal threshold determination

Changing number of folds

Fix random number

Use user specified grouping for cross validation

Control parallel processing

Hyper-parameter selection

Extract model(s) with best predictive ability

Extracting data from cv.models object

Plotting

Technical details

Model specific information

gbm

n.trees

weights

Funcitons using additional data (e.g., weights of gbm and glm)

Modelw with offset terms

ranger::ranger

glmmML::glmmML

Models with random effect

Known issues

References

Version history

Modelw with `offset` terms

`ranger::ranger`

`glmmML::glmmML`