Permutation test for generalised linear models

grouped_perm_glm is a nonparametric test for generalised linear models. It assesses the significance of coefficients by permutation, computing the distribution of the test statistic by randomly rearranging the outcome variable.

Usage

grouped_perm_glm(
  tbl,
  formla,
  var_to_perm,
  family = gaussian,
  permNum = 1000,
  seed = 42
)

Arguments

tbl

A data frame or tibble containing all model variables.

formla

A formula describing the regression model to fit; passed directly to stats::glm().

var_to_perm

Character. Name of the column to permute (typically the outcome variable).

family

A description of the error distribution and link function; passed to stats::glm(). Defaults to stats::gaussian().

permNum

Integer. Number of permutations to generate. Default 1000.

seed

Integer. Random seed for reproducibility; passed to base::set.seed(). Default 42.

Value

A tibble with one row per model term and columns:

term

Name of the regression term.

estimate

Estimated coefficient.

statistic

Observed t-statistic.

p.value

Asymptotic two-sided p-value from the fitted model.

p.perm

Permutation p-value: proportion of permuted |statistics| >= |observed statistic|. A value of 0 means no permuted statistic was as extreme; report as p < 1/permNum.

Examples

counts    <- sample(1:100, 9, replace = TRUE)
outcomes  <- c(18, 17, 15, 20, 10, 20, 25, 13, 12)
treatment <- gl(3, 3)
TBL <- data.frame(counts, outcomes, treatment)
grouped_perm_glm(TBL, outcomes ~ counts + treatment, "outcomes")
#> # A tibble: 4 × 5
#>   term        estimate statistic   p.value p.perm
#>   <chr>          <dbl>     <dbl>     <dbl>  <dbl>
#> 1 (Intercept)   22.4       11.5  0.0000887  0.012
#> 2 counts        -0.195     -4.58 0.00595    0.011
#> 3 treatment2     2.27       1.04 0.346      0.34 
#> 4 treatment3     6.23       2.47 0.0567     0.058