vsn2 {vsn} | R Documentation

## Fit the vsn model

### Description

`vsn2` fits the vsn model to the data in `x` and returns a `vsn` object with the fit parameters and the transformed data matrix. The data are, typically, feature intensity readings from a microarray, but this function may also be useful for other kinds of intensity data that obey an additive-multiplicative error model. To obtain an object of the same class as `x`, containing the normalised data and the same metdata as `x`, use

        fit = vsn2(x, ...)
        nx = predict(fit, newdata=x)

or the wrapper `justvsn`. Please see the vignette Introduction to vsn.

### Usage

    vsnMatrix(x,
              reference,
              strata,
              lts.quantile = 0.9,
              subsample    = 0L,
              verbose      = interactive(),
              returnData   = TRUE,
              calib        = "affine",
              pstart,
              minDataPointsPerStratum = 42L,
              optimpar     = list(),
              defaultpar   = list(factr=5e7, pgtol=2e-4, maxit=60000L,
                                  trace=0L, cvg.niter=7L, cvg.eps=0))

    ## S4 method for signature 'ExpressionSet'
    vsn2(x, reference, strata, ...)

    ## S4 method for signature 'AffyBatch'
    vsn2(x, reference, strata, subsample, ...)

    ## S4 method for signature 'NChannelSet'
    vsn2(x, reference, strata, backgroundsubtract=FALSE,
           foreground=c("R","G"), background=c("Rb", "Gb"), ...)

    ## S4 method for signature 'RGList'
    vsn2(x, reference, strata, ...)

### Arguments

`x` | An object containing the data to which the model is fitted.
`reference` | Optional, a `vsn` object from a previous fit. If this argument is specified, the data in `x` are normalized "towards" an existing set of reference arrays whose parameters are stored in the object `reference`. If this argument is not specified, then the data in `x` are normalized "among themselves". See Details for a more precise explanation.
`strata` | Optional, a `factor` or `integer` whose length is `nrow(x)`. It can be used for stratified normalization (i.e. separate offsets a and factors b for each level of `strata`). If missing, all rows of `x` are assumed to come from one stratum. If `strata` is an integer, its values must cover the range 1,…,n, where n is the number of strata.
`lts.quantile` | Numeric of length 1. The quantile that is used for the resistant least trimmed sum of squares regression. Allowed values are between 0.5 and 1. A value of 1 corresponds to ordinary least sum of squares regression.
`subsample` | Integer of length 1. If its value is greater than 0, the model parameters are estimated from a subsample of the data of size `subsample` only, yet the fitted transformation is then applied to all data. For large datasets, this can substantially reduce the CPU time and memory consumption at a negligible loss of precision. Note that the `AffyBatch` method of `vsn2` sets a value of `30000` for this parameter if it is missing from the function call - which is different from the behaviour of the other methods.
`backgroundsubtract` | Logical of length 1: should local background estimates be subtracted before fitting vsn?
`foreground, background` | Aligned character vectors of the same length, naming the channels of `x` that should be used as foreground and background values.
`verbose` | Logical. If TRUE, some messages are printed.
`returnData` | Logical. If TRUE, the transformed data are returned in a slot of the resulting `vsn` object. Setting this option to `FALSE` allows saving memory if the data are not needed.
`calib` | Character of length 1. Allowed values are `affine` and `none`. The default, `affine`, corresponds to the behaviour in package versions <= 3.9, and to what is described in references [1] and [2]. The option `none` is an experimental new feature, in which no affine calibration is performed and only two global variance stabilisation transformation parameters `a` and `b` are fitted. This functionality might be useful in conjunction with other calibration methods, such as quantile normalisation - see the vignette Introduction to vsn.
`pstart` | Optional, a three-dimensional numeric array that specifies start values for the iterative parameter estimation algorithm. If not specified, the function tries to guess useful start values. The first dimension corresponds to the levels of `strata`, the second dimension to the columns of `x` and the third dimension must be 2, corresponding to offsets and factors.
`minDataPointsPerStratum` | The minimum number of data points per stratum. Normally there is no need for the user to change this; refer to the vignette for further documentation.
`optimpar` | Optional, a list with parameters for the likelihood optimisation algorithm. Default parameters are taken from `defaultpar`. See details.
`defaultpar` | The default parameters for the likelihood optimisation algorithm. Values in `optimpar` take precedence over those in `defaultpar`. The purpose of this argument is to expose the default values in this manual page - it is not intended to be changed, please use `optimpar` for that.
`...` | Arguments that get passed on to `vsnMatrix`.

### Value

An object of class `vsn`.

### Note on overall scale and location of the glog transformation

The data are returned on a glog scale to base 2. More precisely, the transformed data are subject to the transformation glog_2(f(b)*x+a) + c, where the function glog_2(u) = log_2(u+√{u*u+1}) = asinh(u)/\log(2) is called the generalised logarithm, the offset a and the scaling parameter b are the fitted model parameters (see references), and f(x)=\exp(x) is a parameter transformation that allows ensuring positivity of the factor in front of x while using an unconstrained optimisation over b [4]. The overall offset c is computed from the b's such that for large x the transformation approximately corresponds to the \log_2 function. This is done separately for each stratum, but with the same value across arrays. More precisely, if the element `b[s,i]` of the array b is the scaling parameter for the `s`-th stratum and the `i`-th array, then `c[s]` is computed as `log2(2*f(mean(b[,i])))`. The offset c is inconsequential for all differential expression calculations, but many users like to see the data in a range that they are familiar with.

### Specific behaviour of the different methods

`vsn2` methods exist for `ExpressionSet`, `NChannelSet`, `AffyBatch` (from the `affy` package), `RGList` (from the `limma` package), `matrix` and `numeric`. If `x` is an `NChannelSet`, then `vsn2` is applied to the matrix that is obtained by horizontally concatenating the color channels. Optionally, available background estimates can be subtracted before. If `x` is an `RGList`, it is converted into an `NChannelSet` using a copy of Martin Morgan's code for `RGList` to `NChannelSet` coercion, then the `NChannelSet` method is called.

### Standalone versus reference normalisation

If the `reference` argument is not specified, then the model parameters μ_k and σ are fit from the data in `x`. This is the mode of operation described in [1] and that was the only option in versions 1.X of this package. If `reference` is specified, the model parameters μ_k and σ are taken from it. This allows for 'incremental' normalization [4].

### Convergence of the iterative likelihood optimisation

`L-BFGS-B` uses three termination criteria:

1. `(f_k - f_{k+1}) / max(|f_k|, |f_{k+1}|, 1) <= factr * epsmch` where `epsmch` is the machine precision.

2. `|gradient| < pgtol`

3. `iterations > maxit`

These are set by the elements `factr`, `pgtol` and `maxit` of `optimpar`. The remaining elements are

`trace`

  An integer between 0 and 6, indicating the verbosity level of `L-BFGS-B`, higher values create more output.

`cvg.niter`

  The number of iterations to be used in the least trimmed sum of squares regression.

`cvg.eps`

  Numeric. A convergence threshold for the least trimmed sum of squares regression.

### Author(s)

Wolfgang Huber

### References

[1] Variance stabilization applied to microarray data calibration and to the quantification of differential expression, Wolfgang Huber, Anja von Heydebreck, Holger Sueltmann, Annemarie Poustka, Martin Vingron; Bioinformatics (2002) 18 Suppl.1 S96-S104.

[2] Parameter estimation for the calibration and variance stabilization of microarray data, Wolfgang Huber, Anja von Heydebreck, Holger Sueltmann, Annemarie Poustka, and Martin Vingron; Statistical Applications in Genetics and Molecular Biology (2003) Vol. 2 No. 1, Article 3. http://www.bepress.com/sagmb/vol2/iss1/art3.

[3] L-BFGS-B: Fortran Subroutines for Large-Scale Bound Constrained Optimization, C. Zhu, R.H. Byrd, P. Lu and J. Nocedal, Technical Report, Northwestern University (1996).

[4] Package vignette: Likelihood Calculations for vsn

### See Also

`justvsn`, `predict`

### Examples

    data("kidney")

    fit = vsn2(kidney)                   ## fit
    nkid = predict(fit, newdata=kidney)  ## apply fit

    plot(exprs(nkid), pch=".")
    abline(a=0, b=1, col="red")

[Package vsn version 3.56.0 Index]