AIC

Description

Calculate AIC (Akaike Information Criterion).

Usage

aic(loglik, k)

Arguments

Value

A number, a value of AIC.

Examples

aic(10, 5)

Backward step

Description

Remove the worst variable from a model according to the given criterion.

Usage

backward(data, crit = mbic, ...)

Arguments

Details

Type browseVignettes("bigstep") for more details.

Value

An object of class big.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
d %>%
  fast_forward(crit = aic) %>%
  backward() %>%
  backward()

BIC

Description

Calculate BIC (Bayesian Information Criterion).

Usage

bic(loglik, k, n)

Arguments

Value

A number, a value of BIC.

Examples

bic(10, 5, 100)

Model selection

Description

Model selection using the stepwise procedure and the chosen criterion.

Details

The main goal of the package bigstep is to allow you to select a regression model using the stepwise procedure when data is very big, potentially larger than available RAM in your computer. What is more, the package gives you a lot of control over how this procedure should look like. At this moment, you can use one of these functions: stepwise, forward, backward, fast_forward, multi_backward and combinations of them. They can be treated as blocks from which the whole procedure of finding the best model is built.

When your data is larger than RAM you have in your computer, it is impossible to read it in a normal way. Fortunately, in a process of building a regression model it is not necessary to have access to all predictors at the same time. Instead, you can read only a part of the matrix X, check all variables from that part and then read another one. To do that with this package, you only need to read the matrix X using read.big.matrix from bigmemory package. The prepare_data function has a parameter maxp which represents the maximum size (that is the number of elements) of one part. If X is bigger, it will be split. It will be done even if your matrix is big but you have enough RAM to read it in a normal way. It may seem unnecessary, but it is worth to do because R is not very efficient in dealing with big matrices.

Another problem with a large number of predictors is choosing an appropriate criterion. Classical ones like AIC or BIC are bad choice because they will almost certainly select a model with two many variables [1]. You can use modifications of them like mBIC [2], mBIC2 [3], mAIC or mAIC2. In brief, these criteria have much heavier penalty for the number of parameters, so they prefer smaller models than their classic versions.

If you want to read more, type browseVignettes("bigstep")

Author(s)

Piotr Szulc

References

[1] M. Bogdan, J.K. Ghosh, M. Zak-Szatkowska. Selecting explanatory variables with the modified version of Bayesian Information Criterion. Quality and Reliability Engineering International, 24:989-999, 2008.

[2] M. Bogdan, J.K. Ghosh, R.W. Doerge. Modifying the Schwarz Bayesian Information Criterion to locate multiple interacting quantitative trait loci. Genetics, 167:989-999, 2004.

[3] F. Frommlet, A. Chakrabarti, M. Murawska, M. Bogdan. Asymptotic Bayes optimality under sparsity for general distributions under the alternative, Technical report, arXiv:1005.4753v2, 2011.

Examples

## Not run: 
library(bigstep)

### small data
set.seed(1)
n <- 200
p <- 20
X <- matrix(rnorm(n * p), ncol = p)
colnames(X) <- paste0("X", 1:p)
y <- 1 + 0.4 * rowSums(X[, c(5, 10, 15, 20)]) + rnorm(n)

data <- prepare_data(y, X)
results <- stepwise(data, crit = aic)
results$model
summary(results)

### bigger data
set.seed(1)
n <- 1e3
p <- 1e4
X <- matrix(rnorm(p * n), ncol = p)
colnames(X) <- paste0("X", 1:p)
Xadd <- matrix(rnorm(5 * n), n, 5)  # additional variables
colnames(Xadd) <- paste0("Xadd", 1:5)
y <- 0.2 * rowSums(X[, 1000 * (1:10)]) + Xadd[, 1] - 0.1 * Xadd[, 3] + rnorm(n)

data <- prepare_data(y, X, Xadd = Xadd)
data %>%
  reduce_matrix(minpv = 0.15) %>%
  stepwise(mbic) ->
  results
summary(results)

### big data
Xbig <- read.big.matrix("X.txt", sep = " ", header = TRUE,
                        backingfile = "X.bin", descriptorfile = "X.desc")
# Xbig <- attach.big.matrix("X.desc") # much faster
y <- read.table("y.txt")
# data <- prepare_data(y, Xbig) # slow because of checking NA
data <- prepare_data(y, Xbig, na = FALSE) # set if you know that you do not have NA
m <- data %>%
  reduce_matrix(minpv = 0.001) %>%
  fast_forward(crit = bic, maxf = 50) %>%
  multi_backward(crit = mbic) %>%
  stepwise(crit = mbic)
summary(m)

# more examples: type browseVignettes("bigstep")

## End(Not run)

Fast-forward step

Description

Add variables to a model as long as they reduce the given criterion. Variables are searched according to candidates and every one which reduces the criterion is added (not necessarily the best one).

Usage

fast_forward(data, crit = bic, ..., maxf = 70)

Arguments

Details

Type browseVignettes("bigstep") for more details.

Value

An object of class big.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
fast_forward(d)

Forward step

Description

Add the best variable to a model according to the given criterion.

Usage

forward(data, crit = mbic, ...)

Arguments

Details

Type browseVignettes("bigstep") for more details.

Value

An object of class big.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
forward(d, crit = bic)
d %>%
  forward() %>%
  forward() %>%
  forward()

Get the model

Description

Extract the model (an object of class lm) from an object of class big.

Usage

get_model(object, ...)

Arguments

Value

An object of class lm.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
m <- stepwise(d)
get_model(m)

mAIC

Description

Calculate mAIC (modified Akaike Information Criterion).

Usage

maic(loglik, k, p, const = 0.5)

Arguments

Value

A number, a value of mAIC.

Examples

maic(10, 5, 100, 50)

mAIC2

Description

Calculate mAIC2 (the second version of modified Akaike Information Criterion).

Usage

maic2(loglik, k, n, p, const = 0.5)

Arguments

Value

A number, a value of mAIC2.

Examples

maic2(10, 5, 100, 50)

mBIC

Description

Calculate mBIC (modified Bayesian Information Criterion).

Usage

mbic(loglik, k, n, p, const = 4)

Arguments

Value

A number, a value of mBIC.

Examples

mbic(10, 5, 100, 50)

mBIC2

Description

Calculate mBIC2 (the second version of modified Bayesian Information Criterion).

Usage

mbic2(loglik, k, n, p, const = 4)

Arguments

Value

A number, a value of mBIC2.

Examples

mbic2(10, 5, 100, 50)

Multi-backward step

Description

Remove the worst variables from a model as long as they reduce the given criterion (backward elimination).

Usage

multi_backward(data, crit = mbic, ...)

Arguments

Details

Type browseVignettes("bigstep") for more details.

Value

An object of class big.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
d %>%
  fast_forward(crit = aic) %>%
  multi_backward(crit = bic)

Data preparation

Description

Create an object of class big which is needed to perform the selection procedure.

Usage

prepare_data(
  y,
  X,
  type = "linear",
  candidates = NULL,
  Xadd = NULL,
  na = NULL,
  maxp = 1e+06,
  verbose = TRUE
)

Arguments

Details

The function automatically removes observations which have missing values in y. Type browseVignettes("bigstep") for more details.

Value

An object of class big.

Examples

X <- matrix(rnorm(20), ncol = 4)
y <- X[, 2] + rnorm(5)
data <- prepare_data(y, X)

Reducing number of variables

Description

Perform the Pearson correlation tests between a vector y and every variable from a matrix X (separately) and remove uncorrelated variables. The function is much faster when you do not have any missing values (set na = FALSE in prepare_data in that case).

Usage

reduce_matrix(data, minpv = 0.15)

Arguments

Details

Type browseVignettes("bigstep") for more details.

Value

An object of class big.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
reduce_matrix(d)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

bigmemory

attach.big.matrix, read.big.matrix

magrittr

%>%

Stepwise

Description

Build a model according to the stepwise procedure (bidirectional) and the given criterion.

Usage

stepwise(data, crit = mbic, ...)

Arguments

Details

Type browseVignettes("bigstep") for more details.

Value

An object of class big.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
stepwise(d)
d %>%
  fast_forward(crit = aic) %>%
  stepwise(crit = bic)

Summarizing model fit

Description

summary method for class big.

Usage

## S3 method for class 'big'
summary(object, ...)

Arguments

Value

An object of class summary.lm.

Examples

set.seed(1)
n <- 30
p <- 10
X <- matrix(rnorm(n * p), ncol = p)
y <- X[, 2] + 2*X[, 3] - X[, 6] + rnorm(n)
d <- prepare_data(y, X)
m <- stepwise(d)
summary(m)