bigstep {bigstep}

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)