cv.models.rmd

---
title: "Quick Start Guide for cv.models"
author: "Michio Oguro"
date: "`r Sys.Date()`"
output:
    html_document:
        fig_width: 6
        fig_height: 6
        fig_retina: 2
        dpi: 300
        dev.args: list(dpi = 300)
        toc: true
        toc_depth: 2
        md_extensions: -ascii_identifiers
vignette: >
    %\VignetteIndexEntry{Quick start guide for cv.models}
    %\VignetteEngine{knitr::rmarkdown}
    \usepackage[utf8]{inputenc}
---

[日本語](cv.models.j.html)

```{R, preparation, echo = FALSE, message = FALSE, include = FALSE}
library(cv.models)
library(gbm)
set.seed(12345)
```

# 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](https://github.com/Marchen/cv.models) 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.

```{R, install, eval = FALSE}
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.

```{R, basic_usage}
library(cv.models)
data(iris)
cv <- cv.models(glm(Petal.Length ~ ., data = iris))
print(cv)
```

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.

```{R, basic_usage2}
# Using substitute() function
call.glm <- substitute(glm(Petal.Length ~ ., data = iris))
cv <- cv.models(call.glm)
print(cv)

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

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`.

```{R, wrong_usage}
model <- glm(Petal.Length ~ ., data = iris)
cv <- cv.models(model)
print(cv)
```

## 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"|$R ^ 2 = cor(prediction, response) ^ 2$<br>**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"|$Q ^ 2 = 1 - \sum((prediction - response) ^ 2) / \sum((response - mean(response)) ^ 2)$, <br>See Consonni et al. (2009).<br>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](https://en.wikipedia.org/wiki/Sensitivity_and_specificity)
**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"|$DRL.positive = Sensitivity / (1 - Specificity)$, <br>See Lopez-Raton et al. (2014)
**Diagnostic likelihood ratio (DRL)-**    |"dlr.negative"|$DRL.negative = (1 - Sensitivity) / Specificity$, <br>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"      |$Log_likelihood = \sum(log(p * y + (1 - p) * (1 - y)))$, <br>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`.

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

## Controlling positive class

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

1. If the response variable is numeric, use `1` as the positive class.
2. If the response variable is logical, use `TRUE` as the positive class.
3. If the response variable is factor, use the first level (i.e., `levels(response)[1]`) as the positive class.
4. 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.

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

## 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.

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

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`.

```{R, class_stratification}
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)
```

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`.

```{R, cutoff_example1}
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)
```

`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... :).

```{R, cutoff_example2}
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)
```

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.

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

## 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.

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

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

## 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.

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

## 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.

```{R, n_cores}
# 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)
```

## 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`

```{R, hyperparameter1}
# 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)
```

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).

```{R, hyperparmeter2}
# 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)
```

## 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.

```{R, bestmodel}
# 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)
# Get best model.
best <- find.best.models(cv, "q.squared")
print(best)
```

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

```{R, bestmodel2}
# See the class of the result of find.best.models().
class(best)
# The results of find.best.models() is a list of cv.result object.
class(best[[1]])
print(best[[1]])
```

## Extracting data from cv.models object

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

```{R, extract_data}
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)

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

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

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

```{R, extract_data2}
# Extract prediction from the first model of best models.
best <- find.best.models(cv, "q.squared")
fit <- extract.fit(best, 1)
head(fit)

# 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)
```

## 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.

```{R, plot}
# 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.

```{R, gbm_wrong_ntree}
# 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)
```

### weights

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

```{R, gbm_weights_1, eval = FALSE}
# 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$`.

```{R, gbm_weights_2}
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`.

```{R, call_with_other_data_error, eval = FALSE}
# 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`.

```{R, call_with_other_data_ok}
# 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.**

```{R}
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.