R: Model selection

selectModel {bigstep} | R Documentation

## Model selection

### Description

Model selection using the stepwise procedure and the chosen criterion.

### Usage

    selectModel(X, y, fitFun = fitLinear, crit = mbic, Xm = NULL,
      stay = NULL, minpv = 0.15, multif = TRUE, crit.multif = bic,
      maxf = min(ncol(X), 70), minb = 0, fastST = FALSE, maxp = 1e+06,
      verbose = TRUE, file.out = NULL, ...)

### Arguments

`X` | a numeric matrix or an object of class big.matrix (see 'Details'). The rows of `X` contain the samples, the columns of `X` contain the observed variables. If your have variables in rows, see 'Details'.
`y` | a numeric vector of responses. The length of `y` must equal the number of rows of `X`.
`fitFun` | a function which fits the regression model and calculate the logarithm of the likelihood function (loglike). You can use your own function or one of these: `fitLinear`, `fitLogistic`, `fitPoisson`.
`crit` | a function defining the model selection criterion. You can use your own function or one of these: `bic`, `mbic`, `mbic2`, `aic`, `maic`, `maic2`.
`Xm` | a numeric matrix. Additional variables which will be included in the first step of the model selection procedure.
`stay` | a numeric vector. Columns from `Xm` which should be included in the model in all selection steps.
`minpv` | a numeric. Variables from X with p-values for the likelihood ratio tests (see 'Details') higher than `minpv` will be excluded from the model selection procedure. If you do not want to do this, set `minpv=1` (not recommended if you have big data).
`multif` | a logical. If `TRUE`, the multi-forward step will be performed (see 'Details').
`crit.multif` | a function defining the model selection criterion in the multi-forward step. See `crit` (but only criteria with small penalties are recommended).
`maxf` | a numeric, a maximal number of variables in the final model in the multi-forward step.
`minb` | a numeric, a minimal number of variables in the final model in the backward selection (see 'Details').
`fastST` | a logical. If `TRUE`, the Pearson correlation coefficients between `y` and all columns of `X` are calculated instead of the likelihood ratio tests (see 'Details'). It is faster but works only if you do not have any missing values.
`maxp` | a numeric. If `X` is big, it will be splitted into parts with `maxp` elements. It will not change results, but it is necessary if your computer does not have enough RAM. Set to a lower value if you still have problems.
`verbose` | a logical. Set `FALSE` if you do not want to see any information during the selection procedure.
`file.out` | a character string, If not `NULL` (and `minpv<1`), the variables with p-value < `minpv` will be saved to `file.out` (txt file).
`...` | optional arguments to `crit` or `crit.multif`.

### Details

To find the best model (linear or generalized), the following algorithm (a modification of the stepwise selection) is used [3]. In the first step the likelihood ratio tests between two regression models are performed: 1) with only the intercept, 2) with the intercept and every single variable from the matrix `X`. P-values are calculated and variables with p > `minpv` are excluded from the model selection procedure. In the second step (multi-forward) we start with the null model and add variables which decrease `crit.multif` (in order from the smallest p-value). The step is finished after we add `maxf` variables or none of remaining variables improve `crit.multif`. Then the classical backward selection is performed (with `crit`). When there is no variables to remove, the last step, the classical stepwise procedure, is performed (with `crit`).

Results from this four-step procedure should be very similar to the classical stepwise procedure (when we start with the null model and do not omit variables with high p-values) but the first one is much quicker. The most time-consuming part is the forward step in the stepwise selection (in the multi-forward step we do not add the best variable but any which decrease `crit.multif`) and it is performed less often when we start with a reasonable model (sometimes you can find the best model without using the stepwise selection). But you can omit the first three steps if you set `multif=FALSE` and `minpv=1`. Resignation from the multi-forward step can be reasonable when you expect that the final model should be very small (a few variables).

If your data are too big to store in RAM, you should read them with the `read.big.matrix` function from the `bigmemory` packages. The `selectModel` function will recognize that `X` is not an ordinary matrix and split your data to smaller parts. It will not change results but is necessary to work with big data.

The default criterion in the model selection procedure is a modification of the Bayesian Information Criterion, mBIC [1]. It was constructed to control the so-called Family-wise Error Rate (FWER) at the level near 0.05 when you have a lot of explanatory variables and only a few of them should stay in the final model. If you are interested in controlling the so-called False Discovery Rate (FDR) is such type of data, you can change `crit` to `mBIC2` [2], which controls FDR at the level near 0.05. There are more criteria to choose from or you can easily define your own (see 'Examples')

If you do not have the desing matrix in one file, you have to combine them. It can be problematic if your data are big, so you can use the `combineBigMatrices` function from this package. You can use it also when you have to transpose `X` (because you have variables in rows) or you want to change names of columns.

### Value

The names of variables in the final model.

### Author(s)

Piotr Szulc

### References

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

[2] F. Frommlet, A. Chakrabarti, M. Murawska, M. Bogdan (2011), "Asymptotic Bayes optimality under sparsity for generally distributed effect sizes under the alternative". Technical report at arXiv:1005.4753.

[3] F. Frommlet, F. Ruhaltinger, P. Twarog, M. Bogdan (2012), "A model selection approach to genome wide association studies", Computational Statistics and Data Analysis 56: 1038-1051.

### Examples

    set.seed(1)
    n <- 100
    M <- 10
    X <- matrix(rnorm(M*n), ncol=M)
    colnames(X) <- 1:M
    y <- X[, 2] - X[, 3] + X[, 6] - X[, 10] + rnorm(n)
    selectModel(X, y, p=M)

    # more examples: type ?bigstep

[Package bigstep version 0.7.4 Index]