# lmperm: Permutation test for regression parameters In permuco: Permutation Tests for Regression, (Repeated Measures) ANOVA/ANCOVA and Comparison of Signals

## Description

Compute permutation marginal test for linear model. This function produces t statistics with univariate and bivariate p-values. It gives the choice between multiple methods to handle nuisance variables.

## Usage

 1 lmperm(formula, data = NULL, np = 5000, method = NULL, ...) 

## Arguments

 formula A formula object. data A data frame or matrix. np The number of permutations. Default value is 5000. method A character string indicating the method use to handle nuisance variables. Default is "freedman_lane". Se details for the other methods. ... Futher arguments, see details.

## Details

The following methods are available for the fixed effects model defined as y = Dη + Xβ + ε. If we want to test β = 0 and take into account the effects of the nuisance variables D, we transform the data :

 method argument y D X "draper_stoneman" y D PX "freedman_lane" (H_D+PR_D)y D X "manly" Py D X "terBraak" (H_{X,D}+PR_{X,D})y D X "kennedy" PR_D y R_D X "huh_jhun" PV'R_Dy V'R_D X "dekker" y D PR_D X

Other arguments could be pass in ... :

P : a matrix containing the permutations of class matrix or Pmat for the reproductibility of the results. The first column must be the identity. P overwrites np argument.

rnd_rotation : a random matrix of size n \times n to compute the rotation used for the "huh_jhun" method.

## Value

A lmperm object. see aovperm.

## References

Kherad-Pajouh, S., & Renaud, O. (2010). An exact permutation method for testing any effect in balanced and unbalanced fixed effect ANOVA. Computational Statistics & Data Analysis, 54(7), 1881-1893.

Kherad-Pajouh, S., & Renaud, O. (2015). A general permutation approach for analyzing repeated measures ANOVA and mixed-model designs. Statistical Papers, 56(4), 947-967.

Winkler, A. M., Ridgway, G. R., Webster, M. A., Smith, S. M., & Nichols, T. E. (2014). Permutation inference for the general linear model. Neuroimage, 92, 381-397.

aovperm plot.lmperm
  1 2 3 4 5 6 7 8 9 10 11 12 13 ## data data("emergencycost") ## Testing at 14 days emergencycost$LOS14 <- emergencycost$LOS - 14 ## Univariate t test contrasts(emergencycost$insurance) <- contr.sum contrasts(emergencycost$sex) <- contr.sum ## Warning : np argument must be greater (recommendation: np>=5000) modlm_cost_14 <- lmperm(cost ~ LOS14*sex*insurance, data = emergencycost, np = 2000) modlm_cost_14