View source: R/mgp.functions.R

mgpr | R Documentation |

Multivariate Gaussian process regression where each of the N outputs is unidimensional. The multivariate output is allowed to have multiple independent realisations.

mgpr(Data, m = NULL, meanModel = 0, mu = NULL)

`Data` |
List of two elements: 'input' and 'response'. The element 'input' is a list of N vectors, where each vector represents the input covariate values for a particular output. The element 'response' is the corresponding list of N matrices (if there are multiple realisations) or vectors (for a single realisation) representing the response variables. |

`m` |
If Subset of Data is to be used in the estimation, m denotes the subset size. It cannot be larger than the total sample size. Default to NULL (Subsetting is not used). |

`meanModel` |
Type of mean function applied to all outputs. It can be - 0
Zero mean function for each output. - 1
Constant mean function to be estimated for each output. - 't'
Linear model for the mean function of each output. - 'avg'
The average across replications is used as the mean function of each output. This can only be used if there are more than two realisations observed at the same input values.
Default to 0. If argument 'mu' is specified, then 'meanModel' will be set to 'userDefined'. |

`mu` |
Vector of concatenated mean function values defined by the user. Default to NULL. |

A list containing:

- fitted.mean
Fitted values for the training data

- fitted.sd
Standard deviation of the fitted values for training data

- N
Number of response variables

- X
Original input variables

- Y
Original response

- idx
Index vector identifying to which output the elements of concatenated vectors correspond to.

- Cov
Covariance matrix

- mean
Concatenated mean function

- meanModel
Mean model used for each output

- meanLinearModel
'lm' object for each output if the linear regression model is used for the mean functions. NULL otherwise.

Shi, J. Q., and Choi, T. (2011), “Gaussian Process Regression Analysis for Functional Data”, CRC Press.

## See examples in vignette: # vignette("mgpr", package = "GPFDA")

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