Tuning the number of PCs in the PCR with compositional data using the alpha-transformation | R Documentation |

This is a cross-validation procedure to decide on the number of principal components when using regression with compositional data (as predictor variables) using the *α*-transformation.

alfapcr.tune(y, x, model = "gaussian", nfolds = 10, maxk = 50, a = seq(-1, 1, by = 0.1), folds = NULL, ncores = 1, graph = TRUE, col.nu = 15, seed = NULL)

`y` |
A vector with either continuous, binary or count data. |

`x` |
A matrix with the predictor variables, the compositional data. Zero values are allowed. |

`model` |
The type of regression model to fit. The possible values are "gaussian", "binomial" and "poisson". |

`nfolds` |
The number of folds for the K-fold cross validation, set to 10 by default. |

`maxk` |
The maximum number of principal components to check. |

`a` |
A vector with a grid of values of the power transformation, it has to be between -1 and 1. If zero values are present it has to be greater than 0. If |

`folds` |
If you have the list with the folds supply it here. You can also leave it NULL and it will create folds. |

`ncores` |
How many cores to use. If you have heavy computations or do not want to wait for long time more than 1 core (if available) is suggested. It is advisable to use it if you have many observations and or many variables, otherwise it will slow down th process. |

`graph` |
If graph is TRUE (default value) a filled contour plot will appear. |

`col.nu` |
A number parameter for the filled contour plot, taken into account only if graph is TRUE. |

`seed` |
You can specify your own seed number here or leave it NULL. |

The *α*-transformation is applied to the compositional data first and the function "pcr.tune" or "glmpcr.tune" is called.

If graph is TRUE a filled contour will appear. A list including:

`mspe` |
The MSPE where rows correspond to the |

`best.par` |
The best pair of |

`performance` |
The minimum mean squared error of prediction. |

`runtime` |
The time required by the cross-validation procedure. |

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

Tsagris M. (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2): 47-57. https://arxiv.org/pdf/1508.01913v1.pdf

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf

Jolliffe I.T. (2002). Principal Component Analysis.

```
alfa, profile, alfa.pcr, pcr.tune, glmpcr.tune, glm
```

library(MASS) y <- as.vector(fgl[, 1]) x <- as.matrix(fgl[, 2:9]) x <- x/ rowSums(x) mod <- alfapcr.tune(y, x, nfolds = 10, maxk = 50, a = seq(-1, 1, by = 0.1) )

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