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Summarizing Functional Linear Model Fits

Source: R/summary.flm.R
summary.flm.Rd

summary method for class flm. Function returning a summary of the results of IWT for the test on a functional analysis of variance: minimum IWT-adjusted p-values of the F-tests on the whole model and on each factor are reported.

Usage

# S3 method for class 'flm'
summary(object, ...)

Arguments

object

An object of class flm, usually, a result of a call to functional_lm_test().

...

Further arguments passed to or from other methods.

Value

No value returned. The function summary.fanova() computes and returns a list of summary statistics of the fitted functional linear model given in object, using the component call from its arguments, plus:

  • ttest: A \((L+1) \times 1\) matrix with columns for the functional regression coefficients, and corresponding (two-sided) IWT-adjusted minimum p-values of t-tests (i.e., the minimum p-value over all \(p\) basis components used to describe functional data).

  • R2: Range of the functional R-squared.

  • ftest: IWT-adjusted minimum p-value of functional F-test.

References

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.

See also

IWTimage() for the plot of p-values heatmaps and plot.fanova() for the plot of analysis of variance results.

Examples

temperature <- rbind(NASAtemp$milan[, 1:100], NASAtemp$paris[, 1:100])
groups <- c(rep(0, 22), rep(1, 22))

# Performing the IWT
IWT_result <- functional_lm_test(
  temperature ~ groups,
  B = 2L,
  correction = "IWT"
)
#> 
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# Summary of the IWT results
summary(IWT_result)
#> $call
#> iwt_lm(formula = formula, dx = dx, n_perm = B, method = method, 
#>     recycle = recycle)
#> 
#> $ttest
#>             Minimum p-value    
#> (Intercept)               0 ***
#> groups                    0 ***
#> 
#> $R2
#>               Range of functional R-squared
#> Min R-squared                  0.0003189364
#> Max R-squared                  0.2476892354
#> 
#> $ftest
#>   Minimum p-value    
#> 1               0 ***
#>