# Weighted affine calibration of a multiple re-scanned channel

### Description

Weighted affine calibration of a multiple re-scanned channel.

### Usage

1 2 3 4 |

### Arguments

`X` |
An NxK |

`weights` |
If |

`typeOfWeights` |
A |

`method` |
A |

`constraint` |
Constraint making the bias parameters identifiable.
See |

`satSignal` |
Signals equal to or above this threshold is considered saturated signals. |

`...` |
Other arguments passed to |

`average` |
A |

`deviance` |
A |

`project` |
If |

`.fitOnly` |
If |

### Details

Fitting is done by iterated re-weighted principal component analysis (IWPCA).

### Value

If `average`

is specified or `project`

is `TRUE`

,
an Nx1 `matrix`

is returned, otherwise an NxK `matrix`

is returned.
If `deviance`

is specified, a deviance Nx1 `matrix`

is returned
as attribute `deviance`

.
In addition, the fitted model is returned as attribute `modelFit`

.

### Negative, non-positive, and saturated values

Affine multiscan calibration applies also to negative values, which are therefor also calibrated, if they exist.

Saturated signals in any scan are set to `NA`

. Thus, they will not be
used to estimate the calibration function, nor will they affect an
optional projection.

### Missing values

Only observations (rows) in `X`

that contain all finite values are
used in the estimation of the alibration functions. Thus,
observations can be excluded by setting them to `NA`

.

### Weighted normalization

Each data point/observation, that is, each row in `X`

, which is a
vector of length K, can be assigned a weight in [0,1] specifying how much
it should *affect the fitting of the calibration function*.
Weights are given by argument `weights`

,
which should be a `numeric`

`vector`

of length N. Regardless of weights,
all data points are *calibrated* based on the fitted calibration
function.

### Robustness

By default, the model fit of multiscan calibration is done in *L_1*
(`method="L1"`

). This way, outliers affect the parameter estimates
less than ordinary least-square methods.

When calculating the average calibrated signal from multiple scans, by default the median is used, which further robustify against outliers.

For further robustness, downweight outliers such as saturated signals, if possible.

Tukey's biweight function is supported, but not used by default because
then a "bandwidth" parameter has to selected. This can indeed be done
automatically by estimating the standard deviation, for instance using
MAD. However, since scanner signals have heteroscedastic noise
(standard deviation is approximately proportional to the non-logged
signal), Tukey's bandwidth parameter has to be a function of the
signal too, cf. `loess`

. We have experimented with this
too, but found that it does not significantly improve the robustness
compared to *L_1*.
Moreover, using Tukey's biweight as is, that is, assuming homoscedastic
noise, seems to introduce a (scale dependent) bias in the estimates
of the offset terms.

### Using a known/previously estimated offset

If the scanner offsets can be assumed to be known, for instance,
from prior multiscan analyses on the scanner, then it is possible
to fit the scanner model with no (zero) offset by specifying
argument `center=FALSE`

.
Note that you cannot specify the offset. Instead, subtract it
from all signals before calibrating, e.g.
`Xc <- calibrateMultiscan(X-e, center=FALSE)`

where `e`

is the scanner offset (a scalar).
You can assert that the model is fitted without offset by
`stopifnot(all(attr(Xc, "modelFit")$adiag == 0))`

.

### Author(s)

Henrik Bengtsson

### References

[1] H. Bengtsson, J. Vallon-Christersson and G. Jönsson, *Calibration and assessment of channel-specific biases in microarray data with extended dynamical range*, BMC Bioinformatics, 5:177, 2004.

### See Also

`1. Calibration and Normalization`

.
`normalizeAffine`

().

### Examples

1 | ```
## Not run: # For an example, see help(normalizeAffine).
``` |