The real use case
In neuroimaging and multivariate biomedical research, it is common to
run the same model across many features simultaneously — brain regions,
EEG channels, metabolites, or questionnaire subscales. ptestR is
designed for exactly this pattern via the nest() +
map() + unnest() idiom from the tidyverse.
Simulated dataset
We simulate a dataset with 15 subjects, each measured at 3 time
points, across 2 groups and 4 features. This gives 45 observations per
feature — enough for lmer to fit random intercepts per
subject comfortably.
set.seed(42)
n_subj <- 15
n_time <- 3
features <- c("feature_A", "feature_B", "feature_C", "feature_D")
# Subject-level covariates
subjects <- data.frame(
subject = seq_len(n_subj),
group = rep(c("control", "case"), length.out = n_subj),
age = round(rnorm(n_subj, mean = 35, sd = 8), 1)
)
# Expand to subject × time × feature, then add values
df <- expand.grid(
subject = seq_len(n_subj),
time = seq_len(n_time),
feature = features,
stringsAsFactors = FALSE
) |>
left_join(subjects, by = "subject") |>
mutate(
# Random intercept per subject (shared across features)
rand_int = rep(rnorm(n_subj, sd = 1), times = n_time * length(features)),
value = case_when(
feature == "feature_A" ~ 0.6 * (group == "case") + 0.2 * time + rand_int + rnorm(n()),
feature == "feature_B" ~ 0.1 * (group == "case") + 0.1 * time + rand_int + rnorm(n()),
feature == "feature_C" ~ -0.5 * (group == "case") + 0.3 * time + rand_int + rnorm(n()),
feature == "feature_D" ~ 0.0 * (group == "case") + 0.0 * time + rand_int + rnorm(n())
)
) |>
select(subject, time, group, age, feature, value)
glimpse(df)
#> Rows: 180
#> Columns: 6
#> $ subject <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4,…
#> $ time <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2,…
#> $ group <chr> "control", "case", "control", "case", "control", "case", "cont…
#> $ age <dbl> 46.0, 30.5, 37.9, 40.1, 38.2, 34.2, 47.1, 34.2, 51.1, 34.5, 45…
#> $ feature <chr> "feature_A", "feature_A", "feature_A", "feature_A", "feature_A…
#> $ value <dbl> 1.29140052, 1.22058442, -1.42135190, -2.24939330, 2.02506847, …Each nested sub-dataset (one per feature) will have
n_subj × n_time = 45 rows with 15 distinct subjects — well
within lmer’s requirements.
Running across features with grouped_perm_glmm()
The pattern is: group_by() the feature →
nest() → map() the permutation function →
unnest() the results.
results <- df |>
group_by(feature) |>
nest() |>
mutate(
perm = map(data, \(d) grouped_perm_glmm(
tbl = d,
formla = value ~ group + age + time + (1 | subject),
var_to_perm = "value",
permNum = 499,
seed = 42
))
) |>
unnest(perm) |>
select(-data)
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results
#> # A tibble: 16 × 6
#> # Groups: feature [4]
#> feature term effect estimate statistic p.perm
#> <chr> <chr> <chr> <dbl> <dbl> <dbl>
#> 1 feature_A (Intercept) fixed -0.899 -0.484 0.595
#> 2 feature_A age fixed 0.0190 0.403 0.685
#> 3 feature_A groupcontrol fixed -0.897 -1.20 0.220
#> 4 feature_A time fixed 0.484 2.82 0.00401
#> 5 feature_B (Intercept) fixed -1.71 -0.784 0.435
#> 6 feature_B age fixed 0.0341 0.617 0.517
#> 7 feature_B groupcontrol fixed -0.324 -0.369 0.705
#> 8 feature_B time fixed 0.221 1.05 0.321
#> 9 feature_C (Intercept) fixed -2.62 -1.04 0.259
#> 10 feature_C age fixed 0.0231 0.359 0.683
#> 11 feature_C groupcontrol fixed 0.466 0.455 0.649
#> 12 feature_C time fixed 0.769 4.32 0
#> 13 feature_D (Intercept) fixed -1.96 -1.18 0.265
#> 14 feature_D age fixed 0.0481 1.14 0.242
#> 15 feature_D groupcontrol fixed -0.505 -0.754 0.469
#> 16 feature_D time fixed -0.0504 -0.342 0.758Filtering to a term of interest
Filter to the group effect across all features:
group_results <- results |>
filter(term == "groupcontrol") |>
arrange(p.perm)
group_results |>
select(feature, estimate, statistic, p.perm)
#> # A tibble: 4 × 4
#> # Groups: feature [4]
#> feature estimate statistic p.perm
#> <chr> <dbl> <dbl> <dbl>
#> 1 feature_A -0.897 -1.20 0.220
#> 2 feature_D -0.505 -0.754 0.469
#> 3 feature_C 0.466 0.455 0.649
#> 4 feature_B -0.324 -0.369 0.705Feature A and C should show the strongest effects (we simulated them that way), while feature D should be near noise.
FDR correction
With multiple features, apply FDR correction across all models for each term:
group_results <- group_results |>
mutate(p.fdr = p.adjust(p.perm, method = "fdr"))
group_results |>
select(feature, estimate, statistic, p.perm, p.fdr)
#> # A tibble: 4 × 5
#> # Groups: feature [4]
#> feature estimate statistic p.perm p.fdr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 feature_A -0.897 -1.20 0.220 0.220
#> 2 feature_D -0.505 -0.754 0.469 0.469
#> 3 feature_C 0.466 0.455 0.649 0.649
#> 4 feature_B -0.324 -0.369 0.705 0.705Handling p.perm = 0
When no permuted statistic is as extreme as the observed one,
p.perm = 0. This is not a true zero — it means the effect
is stronger than all permNum permuted null statistics.
Report as p < 1/permNum:
group_results |>
mutate(
p.label = ifelse(p.perm == 0,
paste0("p < ", round(1 / 499, 4)),
paste0("p = ", round(p.perm, 3)))
) |>
select(feature, p.label, p.fdr)
#> # A tibble: 4 × 3
#> # Groups: feature [4]
#> feature p.label p.fdr
#> <chr> <chr> <dbl>
#> 1 feature_A p = 0.22 0.220
#> 2 feature_D p = 0.469 0.469
#> 3 feature_C p = 0.649 0.649
#> 4 feature_B p = 0.705 0.705With permNum = 9999 (recommended for publication), the
bound becomes p < 0.0001.
Plotting the results
A simple dot plot showing effect size and significance:
if (requireNamespace("ggplot2", quietly = TRUE)) {
library(ggplot2)
group_results |>
mutate(sig = p.fdr < 0.05) |>
ggplot(aes(x = estimate, y = feature, colour = sig)) +
geom_vline(xintercept = 0, linetype = "dashed", colour = "#DCC3AA") +
geom_point(size = 4) +
scale_colour_manual(
values = c("TRUE" = "#810B38", "FALSE" = "#DCC3AA"),
labels = c("TRUE" = "FDR < 5%", "FALSE" = "ns"),
name = NULL
) +
labs(
title = "Group effect by feature",
x = "Coefficient estimate",
y = NULL
) +
theme_minimal(base_size = 12)
}
Using grouped_perm_glm() instead
If your data have no repeated measures, swap to
grouped_perm_glm() and drop the random-effects term:
# Summarise to one observation per subject × feature (e.g. mean across time)
df_subj <- df |>
group_by(subject, group, age, feature) |>
summarise(value = mean(value), .groups = "drop")
glm_results <- df_subj |>
group_by(feature) |>
nest() |>
mutate(
perm = map(data, \(d) grouped_perm_glm(
tbl = d,
formla = value ~ group + age,
var_to_perm = "value",
permNum = 499,
seed = 42
))
) |>
unnest(perm) |>
select(-data)
glm_results |>
filter(term == "groupcontrol") |>
select(feature, estimate, statistic, p.perm) |>
arrange(p.perm)
#> # A tibble: 4 × 4
#> # Groups: feature [4]
#> feature estimate statistic p.perm
#> <chr> <dbl> <dbl> <dbl>
#> 1 feature_A -0.897 -1.20 0.228
#> 2 feature_D -0.505 -0.754 0.469
#> 3 feature_C 0.466 0.455 0.659
#> 4 feature_B -0.324 -0.369 0.683Tips for large-scale analyses
Use more permutations for publication. 499 is used here for speed; use 9 999 or more for final results.
Parallelise with furrr. Each
map() call is independent — swap purrr::map()
for furrr::future_map() for free parallelisation:
library(furrr)
plan(multisession, workers = 4)
results <- df |>
group_by(feature) |>
nest() |>
mutate(
perm = future_map(data, \(d) grouped_perm_glmm(
d,
formla = value ~ group + age + time + (1 | subject),
var_to_perm = "value",
permNum = 9999,
seed = 42
), .options = furrr_options(seed = TRUE))
) |>
unnest(perm) |>
select(-data)Further reading
-
vignette("getting-started")— core concepts andgrouped_perm_glm() -
vignette("mixed-effects-models")—grouped_perm_glmm()in depth -
?grouped_perm_glmm,?grouped_perm_glm