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.
holodeck is currently not on CRAN, but you can install it from github with the following R code:
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.
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.
#for interactive heatmap, try iheatmapr package:
# iheatmap(row_labels = TRUE, col_labels = TRUE, name = "cov or var")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 x 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 0.247 -1.54
#> 2 a -1.50 -1.65 NA -1.93 -1.27 1.00
#> 3 a 1.13 0.655 0.980 1.41 0.345 -1.90
#> 4 a 0.982 0.740 1.16 1.14 0.866 1.71
#> 5 a -0.773 -1.31 -1.22 -1.21 -1.25 -0.576
#> 6 a 0.302 NA -0.309 0.0725 0.725 2.25
#> 7 a NA 0.00163 0.0596 -0.542 -0.269 2.87
#> 8 b 2.16 2.47 1.38 NA NA 0.146
#> 9 b NA NA -0.529 -0.842 -1.04 NA
#> 10 b 0.609 0.195 0.720 0.930 0.595 0.0765
#> 11 b 1.81 1.15 1.43 1.09 1.39 -0.927
#> 12 b 0.954 0.234 0.247 0.248 0.751 2.77
#> 13 b -1.03 -1.24 -1.70 -1.27 -1.64 1.34
#> 14 b -0.180 NA 0.177 0.433 NA 1.20
#> 15 c -0.214 -0.390 -0.476 -0.878 -0.328 3.18
#> 16 c 0.827 0.556 0.620 0.491 0.814 1.91
#> 17 c -0.399 -0.862 -0.385 -0.935 NA -0.787
#> 18 c -1.09 NA -0.720 -1.88 -1.76 -1.76
#> 19 c -0.181 -0.155 -0.774 0.0395 NA 0.741
#> 20 c 0.882 0.366 0.758 1.24 0.838 0.182
#> # … with 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), printL = FALSE, plotL = FALSE)
plot(pca, parAsColFcVn = df2$factor, typeVc = "x-score")
#> Warning: Character 'parAsColFcVn' set to a factor
getLoadingMN(pca) %>%
as_tibble(rownames = "variable") %>%
arrange(desc(abs(p1)))
#> # A tibble: 20 x 4
#> variable p1 p2 p3
#> <chr> <dbl> <dbl> <dbl>
#> 1 high_cov_3 0.444 -0.0223 -0.0178
#> 2 high_cov_4 0.412 0.0233 0.0301
#> 3 high_cov_1 0.403 0.0335 -0.0248
#> 4 high_cov_5 0.389 0.00518 -0.00792
#> 5 high_cov_2 0.372 0.00949 -0.000838
#> 6 discr2_1 0.225 -0.0295 0.487
#> 7 high_var_2 -0.201 -0.140 -0.0215
#> 8 discr_1 -0.180 -0.309 0.0888
#> 9 discr2_4 0.124 -0.230 -0.235
#> 10 discr_5 0.121 -0.418 -0.00171
#> 11 high_var_3 0.121 0.0872 -0.208
#> 12 discr_4 -0.0761 -0.402 0.0376
#> 13 high_var_5 -0.0535 -0.00698 -0.393
#> 14 high_var_4 0.0457 -0.110 -0.544
#> 15 discr2_3 0.0330 -0.198 -0.00447
#> 16 discr_2 0.0207 -0.373 0.111
#> 17 high_var_1 -0.0199 0.0715 -0.0182
#> 18 discr2_2 -0.00666 0.182 -0.419
#> 19 discr2_5 0.00402 -0.324 -0.0749
#> 20 discr_3 0.00217 -0.389 -0.0967It looks like PCA mostly picks up on the variables with high covariance, not the variables that discriminate among levels of factor. This makes sense, as PCA is an unsupervised analysis.
plsda <- opls(select(df2, -factor), df2$factor, printL = FALSE, plotL = FALSE, predI = 2)
plot(plsda, typeVc = "x-score")
getVipVn(plsda) %>%
tibble::enframe(name = "variable", value = "VIP") %>%
arrange(desc(VIP))
#> # A tibble: 20 x 2
#> variable VIP
#> <chr> <dbl>
#> 1 discr_5 1.76
#> 2 discr_2 1.64
#> 3 discr_4 1.58
#> 4 discr_3 1.50
#> 5 discr_1 1.30
#> 6 discr2_5 1.16
#> 7 discr2_4 1.05
#> 8 high_cov_2 0.995
#> 9 high_var_5 0.989
#> 10 high_cov_1 0.872
#> 11 discr2_3 0.819
#> 12 discr2_2 0.727
#> 13 high_var_2 0.680
#> 14 high_var_3 0.494
#> 15 discr2_1 0.469
#> 16 high_cov_3 0.450
#> 17 high_cov_4 0.406
#> 18 high_var_4 0.203
#> 19 high_var_1 0.202
#> 20 high_cov_5 0.105PLS-DA, a supervised analysis, finds discrimination among groups and finds that the discriminating variables we generated are most responsible for those differences.