holodeck
allows quick and simple creation of simulated multivariate
data with variables that co-vary or discriminate between levels of a
categorical variable. The resulting simulated multivariate dataframes
are useful for testing the performance of multivariate statistical
techniques under different scenarios, power analysis, or just doing a
sanity check when trying out a new multivariate method.
From CRAN:
install.packages("holodeck)
Development version from r-universe:
install.packages('holodeck', repos = c('https://aariq.r-universe.dev', 'https://cloud.r-project.org'))
holodeck
is built to work with dplyr
functions, including
group_by()
and the pipe (%>%
). purrr
is helpful for iterating
simulated data. For these examples I’ll use ropls
for PCA and PLS-DA.
library(holodeck)
library(dplyr)
library(tibble)
library(purrr)
library(ropls)
Let’s say we want to learn more about how principal component analysis (PCA) works. Specifically, what matters more in terms of creating a principal component—variance or covariance of variables? To this end, you might create a dataframe with a few variables with high covariance and low variance and another set of variables with low covariance and high variance
set.seed(925)
df1 <-
sim_covar(n_obs = 20, n_vars = 5, cov = 0.9, var = 1, name = "high_cov") %>%
sim_covar(n_vars = 5, cov = 0.1, var = 2, name = "high_var")
Explore covariance structure visually. The diagonal is variance.
df1 %>%
cov() %>%
heatmap(Rowv = NA, Colv = NA, symm = TRUE, margins = c(6,6), main = "Covariance")
Now let’s make this dataset a little more complex. We can add a factor variable, some variables that discriminate between the levels of that factor, and add some missing values.
set.seed(501)
df2 <-
df1 %>%
sim_cat(n_groups = 3, name = "factor") %>%
group_by(factor) %>%
sim_discr(n_vars = 5, var = 1, cov = 0, group_means = c(-1.3, 0, 1.3), name = "discr") %>%
sim_discr(n_vars = 5, var = 1, cov = 0, group_means = c(0, 0.5, 1), name = "discr2") %>%
sim_missing(prop = 0.1) %>%
ungroup()
df2
#> # A tibble: 20 × 21
#> factor high_cov_1 high_cov_2 high_cov_3 high_cov_4 high_cov_5 high_var_1
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 a 0.472 -0.362 0.253 0.281 NA -0.0873
#> 2 a -1.50 -1.65 -1.47 -1.93 NA NA
#> 3 a 1.13 NA NA 1.41 0.345 0.871
#> 4 a 0.982 0.740 1.16 1.14 0.866 NA
#> 5 a -0.773 NA NA -1.21 -1.25 -1.53
#> 6 a 0.302 0.130 -0.309 0.0725 0.725 0.890
#> 7 a -0.117 0.00163 0.0596 -0.542 -0.269 NA
#> 8 b 2.16 2.47 1.38 1.62 1.62 -2.43
#> 9 b NA -0.509 -0.529 -0.842 -1.04 1.25
#> 10 b 0.609 0.195 0.720 0.930 0.595 -0.562
#> 11 b 1.81 1.15 1.43 1.09 1.39 -0.934
#> 12 b 0.954 0.234 0.247 0.248 0.751 1.95
#> 13 b -1.03 NA -1.70 -1.27 -1.64 0.670
#> 14 b NA 0.380 0.177 NA 0.550 2.68
#> 15 c -0.214 -0.390 -0.476 -0.878 -0.328 0.665
#> 16 c 0.827 0.556 0.620 0.491 0.814 -0.0121
#> 17 c -0.399 -0.862 -0.385 -0.935 -0.802 NA
#> 18 c -1.09 -1.32 -0.720 -1.88 -1.76 -2.05
#> 19 c -0.181 -0.155 -0.774 0.0395 -0.770 1.81
#> 20 c 0.882 NA 0.758 1.24 NA 1.11
#> # ℹ 14 more variables: high_var_2 <dbl>, high_var_3 <dbl>, high_var_4 <dbl>,
#> # high_var_5 <dbl>, discr_1 <dbl>, discr_2 <dbl>, discr_3 <dbl>,
#> # discr_4 <dbl>, discr_5 <dbl>, discr2_1 <dbl>, discr2_2 <dbl>,
#> # discr2_3 <dbl>, discr2_4 <dbl>, discr2_5 <dbl>
pca <- opls(select(df2, -factor), fig.pdfC = "none", info.txtC = "none")
plot(pca, parAsColFcVn = df2$factor, typeVc = "x-score")
getLoadingMN(pca) %>%
as_tibble(rownames = "variable") %>%
arrange(desc(abs(p1)))
#> # A tibble: 20 × 4
#> variable p1 p2 p3
#> <chr> <dbl> <dbl> <dbl>
#> 1 high_cov_2 0.415 0.0534 0.0137
#> 2 high_cov_1 0.407 0.0383 0.0208
#> 3 high_cov_5 0.401 0.0163 0.104
#> 4 high_cov_3 0.400 0.0301 -0.0837
#> 5 high_cov_4 0.387 0.0218 0.00556
#> 6 discr_5 -0.224 0.262 -0.136
#> 7 high_var_2 -0.195 0.0848 0.240
#> 8 discr2_1 0.167 0.396 -0.167
#> 9 discr_2 -0.163 0.322 -0.202
#> 10 high_var_5 0.115 -0.132 0.261
#> 11 discr2_5 0.0967 0.267 0.114
#> 12 high_var_1 -0.0930 -0.0102 0.457
#> 13 discr2_4 0.0834 0.308 0.0924
#> 14 discr_3 -0.0627 0.376 -0.0152
#> 15 discr2_2 -0.0412 0.138 0.539
#> 16 discr_1 -0.0407 0.319 0.0471
#> 17 discr2_3 -0.0394 0.176 -0.358
#> 18 discr_4 0.0363 0.400 0.144
#> 19 high_var_3 -0.0101 -0.0629 0.0483
#> 20 high_var_4 -0.00471 0.131 0.308
It looks like PCA mostly picks up on the variables with high covariance,
not the variables that discriminate among levels of factor
. This
makes sense, as PCA is an unsupervised analysis.
plsda <- opls(select(df2, -factor), df2$factor, predI = 2, permI = 10, fig.pdfC = "none", info.txtC = "none")
plot(plsda, typeVc = "x-score")
getVipVn(plsda) %>%
tibble::enframe(name = "variable", value = "VIP") %>%
arrange(desc(VIP))
#> # A tibble: 20 × 2
#> variable VIP
#> <chr> <dbl>
#> 1 discr_4 1.54
#> 2 discr_1 1.48
#> 3 discr_2 1.47
#> 4 discr_5 1.44
#> 5 discr_3 1.42
#> 6 discr2_1 1.31
#> 7 discr2_4 1.09
#> 8 high_cov_2 1.08
#> 9 discr2_3 0.996
#> 10 high_cov_1 0.944
#> 11 discr2_2 0.884
#> 12 high_cov_5 0.790
#> 13 discr2_5 0.650
#> 14 high_var_5 0.639
#> 15 high_var_2 0.582
#> 16 high_cov_4 0.530
#> 17 high_cov_3 0.423
#> 18 high_var_4 0.358
#> 19 high_var_1 0.200
#> 20 high_var_3 0.0860
PLS-DA, a supervised analysis, finds discrimination among groups and finds that the discriminating variables we generated are most responsible for those differences.
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