Description Usage Arguments Value References See Also Examples

The function is used to fit and test functional linear models. It can be used to carry out regression, and analysis of variance. It implements the interval-wise testing procedure (IWT) for testing the significance of the effects of scalar covariates on a functional population.

1 2 |

`formula` |
An object of class " |

`B` |
The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. The defualt is |

`method` |
Permutation method used to calculate the p-value of permutation tests. Choose " |

`dx` |
step size for the point-wise evaluations of functional data. dx is only used ia an object of class 'fd' is provided as response in the formula. |

`recycle` |
flag specifying whether the recycled version of IWT has to be used. |

`IWTlm`

returns an object of `class`

"`IWTlm`

". The function `summary`

is used to obtain and print a summary of the results.
An object of class "`ITPlm`

" is a list containing at least the following components:

`call` |
call of the function. |

`design_matrix` |
design matrix of the linear model. |

`unadjusted_pval_F` |
unadjusted p-value function of the F test. |

`pval_matrix_F` |
Matrix of dimensions c(p,p) of the p-values of the interval-wise F-tests. The element (i,j) of matrix pval_matrix_F contains the p-value of the test on interval (j,j+1,...,j+(p-i)). |

`adjusted_pval_F` |
adjusted p-value function of the F test. |

`unadjusted_pval_part` |
unadjusted p-value functions of the functional t-tests on each covariate, separately (rows) on each domain point (columns). |

`pval_matrix_part` |
Array of dimensions c(L+1,p,p) of the p-values of the interval-wise t-tests on covariates. The element (l,i,j) of array pval_matrix_part contains the p-value of the test of covariate l on interval (j,j+1,...,j+(p-i)). |

`adjusted_pval_part` |
adjusted p-values of the functional t-tests on each covariate (rows) on each domain point (columns). |

`data.eval` |
evaluation of functional data. |

`coeff.regr.eval` |
evaluation of the regression coefficients. |

`fitted.eval` |
evaluation of the fitted values. |

`residuals.eval` |
evaluation of the residuals. |

`R2.eval` |
evaluation of the functional R-suared. |

A. Pini and S. Vantini (2017). The Interval Testing Procedure: Inference for Functional Data Controlling the Family Wise Error Rate on Intervals. Biometrics 73(3): 835–845.

Pini, A., Vantini, S., Colosimo, B. M., & Grasso, M. (2018). Domain‐selective functional analysis of variance for supervised statistical profile monitoring of signal data. *Journal of the Royal Statistical Society: Series C (Applied Statistics)* 67(1), 55-81.

Abramowicz, K., Hager, C. K., Pini, A., Schelin, L., Sjostedt de Luna, S., & Vantini, S. (2018).
Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament. *Scandinavian Journal of Statistics* 45(4), 1036-1061.

D. Freedman and D. Lane (1983). A Nonstochastic Interpretation of Reported Significance Levels. *Journal of Business & Economic Statistics* 1(4), 292-298.

B. F. J. Manly (2006). Randomization, *Bootstrap and Monte Carlo Methods in Biology*. Vol. 70. CRC Press.

See `summary.IWTlm`

for summaries and `plot.IWTlm`

for plotting the results.
See `ITPlmbspline`

for a functional linear model test based on an a-priori selected B-spline basis expansion.
See also `IWTaov`

to fit and test a functional analysis of variance applying the IWT, and `IWT1`

, `IWT2`

for one-population and two-population tests.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# Importing the NASA temperatures data set
data(NASAtemp)
# Defining the covariates
temperature <- rbind(NASAtemp$milan,NASAtemp$paris)
groups <- c(rep(0,22),rep(1,22))
# Performing the IWT
IWT.result <- IWTlm(temperature ~ groups,B=1000)
# Summary of the IWT results
summary(IWT.result)
# Plot of the IWT results
layout(1)
plot(IWT.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))
# All graphics on the same device
layout(matrix(1:6,nrow=3,byrow=FALSE))
plot(IWT.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))
``` |

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