Description Usage Arguments Value References See Also Examples

The function implements the Interval Wise Testing procedure for testing mean differences between several functional populations in a one-way or multi-way functional analysis of variance framework. Functional data are tested locally and unadjusted and adjusted p-value functions are provided. The unadjusted p-value function controls the point-wise error rate. The adjusted p-value function controls the interval-wise error rate.

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` |
Used only if a |

`recycle` |
Flag used to decide whether the recycled version of the IWT should be used (see Pini and Vantini, 2017 for details). Default is |

`IWTaov`

returns an object of `class`

"`IWTaov`

". The function `summary`

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

" is a list containing at least the following components:

`call` |
The matched call. |

`design_matrix` |
The design matrix of the functional-on-scalar linear model. |

`unadjusted_pval_F` |
Evaluation on a grid of the unadjusted p-value function of the functional F-test. |

`pval_matrix_F` |
Matrix of dimensions |

`adjusted_pval_F` |
Evaluation on a grid of the adjusted p-value function of the functional F-test. |

`unadjusted_pval_factors` |
Evaluation on a grid of the unadjusted p-value function of the functional F-tests on each factor of the analysis of variance (rows). |

`pval.matrix.factors` |
Array of dimensions |

`adjusted.pval.factors` |
adjusted p-values of the functional F-tests on each factor of the analysis of variance (rows) and each basis coefficient (columns). |

`data.eval` |
Evaluation on a fine uniform grid of the functional data obtained through the basis expansion. |

`coeff.regr.eval` |
Evaluation on a fine uniform grid of the functional regression coefficients. |

`fitted.eval` |
Evaluation on a fine uniform grid of the fitted values of the functional regression. |

`residuals.eval` |
Evaluation on a fine uniform grid of the residuals of the functional regression. |

`R2.eval` |
Evaluation on a fine uniform grid of the functional R-squared of the regression. |

`heatmap.matrix.F` |
Heatmap matrix of p-values of functional F-test (used only for plots). |

`heatmap.matrix.factors` |
Heatmap matrix of p-values of functional F-tests on each factor of the analysis of variance (used only for plots). |

Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. *Journal of Nonparametric Statistics*, 29(2), 407-424

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.IWTaov`

for summaries and `plot.IWTaov`

for plotting the results.
See `ITPaov`

for a functional analysis of variance test based on B-spline basis expansion.
See also `IWTlm`

to fit and test a functional-on-scalar linear model 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)
temperature <- rbind(NASAtemp$milan,NASAtemp$paris)
groups <- c(rep(0,22),rep(1,22))
# Performing the IWT
IWT.result <- IWTaov(temperature ~ groups,B=1000)
# Summary of the ITP results
summary(IWT.result)
# Plot of the IWT results
layout(1)
plot(IWT.result)
# All graphics on the same device
layout(matrix(1:4,nrow=2,byrow=FALSE))
plot(IWT.result,main='NASA data', plot.adjpval = TRUE,xlab='Day',xrange=c(1,365))
``` |

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