Overview of the sccomp package

Stefano Mangiola

2024-01-21

Lifecycle:maturing R build status

Sccomp is a generalised method for differential composition and variability analyses.

Characteristics

Installation

Bioconductor

if (!requireNamespace("BiocManager")) install.packages("BiocManager")
BiocManager::install("sccomp")

Github

devtools::install_github("stemangiola/sccomp")

Analysis

sccomp can model changes in composition and variability. By default, the formula for variability is either ~1, which assumes that the cell-group variability is independent of any covariate or ~ factor_of_interest, which assumes that the model is dependent on the factor of interest only. The variability model must be a subset of the model for composition.

Binary factor

From Seurat, SingleCellExperiment, metadata objects

single_cell_object |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    .sample =  sample, 
    .cell_group = cell_group, 
    bimodal_mean_variability_association = TRUE,
    cores = 1 
  )

From counts

counts_obj |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    .sample = sample,
    .cell_group = cell_group,
    .count = count, 
    bimodal_mean_variability_association = TRUE,
    cores = 1 
  )
## 
## SAMPLING FOR MODEL 'glm_multi_beta_binomial' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 0.000693 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 6.93 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1: 
## Chain 1: 
## Chain 1: Iteration:    1 / 4300 [  0%]  (Warmup)
## Chain 1: Iteration:  301 / 4300 [  7%]  (Sampling)
## Chain 1: Iteration: 1300 / 4300 [ 30%]  (Sampling)
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## Chain 1: Iteration: 3300 / 4300 [ 76%]  (Sampling)
## Chain 1: Iteration: 4300 / 4300 [100%]  (Sampling)
## Chain 1: 
## Chain 1:  Elapsed Time: 4.419 seconds (Warm-up)
## Chain 1:                33.207 seconds (Sampling)
## Chain 1:                37.626 seconds (Total)
## Chain 1:
## # A tibble: 72 × 14
##    cell_group parameter   factor c_lower c_effect c_upper c_n_eff c_R_k_hat
##    <chr>      <chr>       <chr>    <dbl>    <dbl>   <dbl>   <dbl>     <dbl>
##  1 B1         (Intercept) <NA>    0.880     1.12   1.35     4970.      1.00
##  2 B1         typecancer  type   -1.06     -0.647 -0.253    4152.      1.00
##  3 B2         (Intercept) <NA>    0.373     0.697  0.981    5682.      1.00
##  4 B2         typecancer  type   -1.19     -0.717 -0.247    4503.      1.00
##  5 B3         (Intercept) <NA>   -0.677    -0.394 -0.128    4389.      1.00
##  6 B3         typecancer  type   -0.753    -0.308  0.0938   4722.      1.00
##  7 BM         (Intercept) <NA>   -1.33     -1.03  -0.757    4090.      1.00
##  8 BM         typecancer  type   -0.735    -0.306  0.109    3374.      1.00
##  9 CD4 1      (Intercept) <NA>    0.0721    0.296  0.507    4243.      1.00
## 10 CD4 1      typecancer  type   -0.0987    0.187  0.479    3491.      1.00
## # ℹ 62 more rows
## # ℹ 6 more variables: v_lower <dbl>, v_effect <dbl>, v_upper <dbl>,
## #   v_n_eff <dbl>, v_R_k_hat <dbl>, count_data <list>

Of the output table, the estimate columns start with the prefix c_ indicate composition, or with v_ indicate variability (when formula_variability is set).

Contrasts

seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ 0 + type, 
    .sample = sample,
    .cell_group = cell_group, 
    bimodal_mean_variability_association = TRUE,
    cores = 1 
  ) |> 
  sccomp_test( contrasts =  c("typecancer - typehealthy", "typehealthy - typecancer"))
## 
## SAMPLING FOR MODEL 'glm_multi_beta_binomial' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 0.000516 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 5.16 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1: 
## Chain 1: 
## Chain 1: Iteration:    1 / 4300 [  0%]  (Warmup)
## Chain 1: Iteration:  301 / 4300 [  7%]  (Sampling)
## Chain 1: Iteration: 1300 / 4300 [ 30%]  (Sampling)
## Chain 1: Iteration: 2300 / 4300 [ 53%]  (Sampling)
## Chain 1: Iteration: 3300 / 4300 [ 76%]  (Sampling)
## Chain 1: Iteration: 4300 / 4300 [100%]  (Sampling)
## Chain 1: 
## Chain 1:  Elapsed Time: 3.336 seconds (Warm-up)
## Chain 1:                27.295 seconds (Sampling)
## Chain 1:                30.631 seconds (Total)
## Chain 1:
## # A tibble: 60 × 18
##    cell_group  parameter factor c_lower c_effect c_upper   c_pH0   c_FDR c_n_eff
##    <chr>       <chr>     <chr>    <dbl>    <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1 B immature  typecanc… <NA>    -1.91    -1.39   -0.884 0       0            NA
##  2 B immature  typeheal… <NA>     0.884    1.39    1.91  0       0            NA
##  3 B mem       typecanc… <NA>    -2.35    -1.71   -1.06  0       0            NA
##  4 B mem       typeheal… <NA>     1.06     1.71    2.35  0       0            NA
##  5 CD4 cm S10… typecanc… <NA>    -1.49    -1.03   -0.594 2.50e-4 6.25e-5      NA
##  6 CD4 cm S10… typeheal… <NA>     0.594    1.03    1.49  2.50e-4 6.25e-5      NA
##  7 CD4 cm hig… typecanc… <NA>     0.792    1.76    2.87  2.50e-4 1.00e-4      NA
##  8 CD4 cm hig… typeheal… <NA>    -2.87    -1.76   -0.792 2.50e-4 1.00e-4      NA
##  9 CD4 cm rib… typecanc… <NA>     0.298    0.986   1.70  1.42e-2 4.32e-3      NA
## 10 CD4 cm rib… typeheal… <NA>    -1.70    -0.986  -0.298 1.42e-2 4.32e-3      NA
## # ℹ 50 more rows
## # ℹ 9 more variables: c_R_k_hat <dbl>, v_lower <dbl>, v_effect <dbl>,
## #   v_upper <dbl>, v_pH0 <dbl>, v_FDR <dbl>, v_n_eff <dbl>, v_R_k_hat <dbl>,
## #   count_data <list>

Categorical factor (e.g. Bayesian ANOVA)

This is achieved through model comparison with loo. In the following example, the model with association with factors better fits the data compared to the baseline model with no factor association. For comparisons check_outliers must be set to FALSE as the leave-one-out must work with the same amount of data, while outlier elimination does not guarantee it.

If elpd_diff is away from zero of > 5 se_diff difference of 5, we are confident that a model is better than the other reference. In this case, -79.9 / 11.5 = -6.9, therefore we can conclude that model one, the one with factor association, is better than model two.

library(loo)

# Fit first model
model_with_factor_association = 
  seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    .sample =  sample, 
    .cell_group = cell_group, 
    check_outliers = FALSE, 
    bimodal_mean_variability_association = TRUE,
    cores = 1, 
    enable_loo = TRUE
  )

# Fit second model
model_without_association = 
  seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ 1, 
    .sample =  sample, 
    .cell_group = cell_group, 
    check_outliers = FALSE, 
    bimodal_mean_variability_association = TRUE,
    cores = 1 , 
    enable_loo = TRUE
  )

# Compare models
loo_compare(
  model_with_factor_association |> attr("fit") |> loo(),
  model_without_association |> attr("fit") |> loo()
)

Differential variability, binary factor

We can model the cell-group variability also dependent on the type, and so test differences in variability

res = 
  seurat_obj |>
  sccomp_estimate( 
    formula_composition = ~ type, 
    formula_variability = ~ type,
    .sample = sample,
    .cell_group = cell_group,
    bimodal_mean_variability_association = TRUE,
    cores = 1 
  )
## 
## SAMPLING FOR MODEL 'glm_multi_beta_binomial' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 0.000496 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 4.96 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1: 
## Chain 1: 
## Chain 1: Iteration:    1 / 4300 [  0%]  (Warmup)
## Chain 1: Iteration:  301 / 4300 [  7%]  (Sampling)
## Chain 1: Iteration: 1300 / 4300 [ 30%]  (Sampling)
## Chain 1: Iteration: 2300 / 4300 [ 53%]  (Sampling)
## Chain 1: Iteration: 3300 / 4300 [ 76%]  (Sampling)
## Chain 1: Iteration: 4300 / 4300 [100%]  (Sampling)
## Chain 1: 
## Chain 1:  Elapsed Time: 6.123 seconds (Warm-up)
## Chain 1:                53.761 seconds (Sampling)
## Chain 1:                59.884 seconds (Total)
## Chain 1:
res
## # A tibble: 60 × 14
##    cell_group       parameter factor c_lower c_effect  c_upper c_n_eff c_R_k_hat
##    <chr>            <chr>     <chr>    <dbl>    <dbl>    <dbl>   <dbl>     <dbl>
##  1 B immature       (Interce… <NA>    0.367     0.769  1.18      5805.      1.00
##  2 B immature       typeheal… type    0.842     1.43   1.99      5061.      1.00
##  3 B mem            (Interce… <NA>   -1.49     -0.866 -0.161     4036.      1.00
##  4 B mem            typeheal… type    1.04      1.86   2.64      3728.      1.00
##  5 CD4 cm S100A4    (Interce… <NA>    1.31      1.66   1.98      5708.      1.00
##  6 CD4 cm S100A4    typeheal… type    0.474     0.939  1.39      5281.      1.00
##  7 CD4 cm high cyt… (Interce… <NA>   -1.03     -0.542  0.00954   5234.      1.00
##  8 CD4 cm high cyt… typeheal… type   -3.06     -1.22   1.16      3103.      1.00
##  9 CD4 cm ribosome  (Interce… <NA>   -0.0538    0.306  0.694     4884.      1.00
## 10 CD4 cm ribosome  typeheal… type   -1.81     -0.964  0.0781    4678.      1.00
## # ℹ 50 more rows
## # ℹ 6 more variables: v_lower <dbl>, v_effect <dbl>, v_upper <dbl>,
## #   v_n_eff <dbl>, v_R_k_hat <dbl>, count_data <list>

Suggested settings

For single-cell RNA sequencing

We recommend setting bimodal_mean_variability_association = TRUE. The bimodality of the mean-variability association can be confirmed from the plots$credible_intervals_2D (see below).

For CyTOF and microbiome data

We recommend setting bimodal_mean_variability_association = FALSE (Default).

Visualisation

Summary plots

plots = res |> sccomp_test() |> plot_summary() 
## Warning: `plot_summary()` was deprecated in sccomp 1.7.1.
## ℹ sccomp says: plot_summary() is soft-deprecated. Please use sccomp_test().
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
##              cell_group   parameter factor     c_lower     c_effect
## 1            B immature (Intercept)   <NA>  0.36714960  0.769063346
## 2            B immature typehealthy   type  0.84180431  1.434520538
## 3                 B mem (Intercept)   <NA> -1.48921622 -0.866042080
## 4                 B mem typehealthy   type  1.04093816  1.861888385
## 5         CD4 cm S100A4 (Intercept)   <NA>  1.30946655  1.662220821
## 6         CD4 cm S100A4 typehealthy   type  0.47432050  0.938966484
## 7  CD4 cm high cytokine (Intercept)   <NA> -1.03279974 -0.541792777
## 8  CD4 cm high cytokine typehealthy   type -3.06131684 -1.218953275
## 9       CD4 cm ribosome (Intercept)   <NA> -0.05380041  0.305894694
## 10      CD4 cm ribosome typehealthy   type -1.80627582 -0.964037534
## 11 CD4 em high cytokine (Intercept)   <NA> -1.16827385 -0.707911378
## 12 CD4 em high cytokine typehealthy   type -2.32982524 -1.267436140
## 13            CD4 naive (Intercept)   <NA>  0.74838491  1.211643519
## 14            CD4 naive typehealthy   type  0.45151064  1.142218863
## 15         CD4 ribosome (Intercept)   <NA> -0.29726785  0.046538669
## 16         CD4 ribosome typehealthy   type  1.44939833  2.056778591
## 17             CD8 em 1 (Intercept)   <NA>  0.28301490  0.683160799
## 18             CD8 em 1 typehealthy   type -0.03043376  0.781722909
## 19             CD8 em 2 (Intercept)   <NA> -0.91347221  0.138266684
## 20             CD8 em 2 typehealthy   type -3.54389720 -1.134040355
## 21             CD8 em 3 (Intercept)   <NA> -1.39088676 -0.662575055
## 22             CD8 em 3 typehealthy   type -1.74806697 -0.814719668
## 23            CD8 naive (Intercept)   <NA>  0.58731122  1.020907451
## 24            CD8 naive typehealthy   type -0.70878641  0.005401482
## 25     CD8 transitional (Intercept)   <NA>  0.90096497  1.209803385
## 26     CD8 transitional typehealthy   type  0.17957566  0.683288824
## 27                 MAIT (Intercept)   <NA> -1.05144268 -0.597450401
## 28                 MAIT typehealthy   type  0.46635056  1.209515514
## 29               Mac M1 (Intercept)   <NA>  0.62583442  0.949116764
## 30               Mac M1 typehealthy   type  0.03165886  0.593128278
## 31        Mac M1 FCER1A (Intercept)   <NA> -1.33254732 -0.983485510
## 32        Mac M1 FCER1A typehealthy   type -1.79881252 -1.068023548
## 33                 Mono (Intercept)   <NA> -1.80820415 -1.337378989
## 34                 Mono typehealthy   type -0.84397959 -0.118718215
## 35          Mono NKG7 1 (Intercept)   <NA> -1.47715155 -0.873120573
## 36          Mono NKG7 1 typehealthy   type -4.00459122 -2.864291927
## 37          Mono NKG7 2 (Intercept)   <NA> -0.42176260 -0.014464654
## 38          Mono NKG7 2 typehealthy   type -2.43766291 -1.292219635
## 39  Mono classic inflam (Intercept)   <NA>  1.49888142  1.783381517
## 40  Mono classic inflam typehealthy   type -1.24301291 -0.450991681
## 41     Mono non-classic (Intercept)   <NA>  0.61714585  0.963521050
## 42     Mono non-classic typehealthy   type -0.65137438  0.005515399
## 43    Myeloid migratory (Intercept)   <NA> -0.36121811  0.022998608
## 44    Myeloid migratory typehealthy   type -1.34255050 -0.563779831
## 45                   NK (Intercept)   <NA>  1.12159264  1.434522221
## 46                   NK typehealthy   type -0.04635236  0.539163697
## 47           NK cycling (Intercept)   <NA> -1.67444697 -1.209958145
## 48           NK cycling typehealthy   type -0.79650498 -0.186326087
## 49     NK high cytokine (Intercept)   <NA> -2.22419952 -1.640829858
## 50     NK high cytokine typehealthy   type -1.18688802  0.008488138
## 51                 Stem (Intercept)   <NA> -1.08664179 -0.569628573
## 52                 Stem typehealthy   type -3.22879492 -2.239123013
## 53                T gd1 (Intercept)   <NA> -1.06777916 -0.689845024
## 54                T gd1 typehealthy   type  0.04203475  0.920521874
## 55                T gd2 (Intercept)   <NA> -1.24443601 -0.668973219
## 56                T gd2 typehealthy   type -0.42754553  0.511537788
## 57                 cDC2 (Intercept)   <NA> -0.75392563 -0.296024832
## 58                 cDC2 typehealthy   type -0.34412558  0.310340803
## 59                  pDC (Intercept)   <NA> -1.15399879 -0.672606034
## 60                  pDC typehealthy   type -0.08755515  0.668205977
##         c_upper   c_pH0        c_FDR  c_n_eff c_R_k_hat     v_lower    v_effect
## 1   1.183132826 0.00475 4.423077e-04 5804.832 1.0000831 -4.49425352 -3.82358583
## 2   1.994177904 0.00000 0.000000e+00 5061.157 0.9998241 -1.66080948 -0.52051568
## 3  -0.161027248 0.02975 5.058824e-03 4035.640 0.9999466 -5.30849510 -4.56068059
## 4   2.641768018 0.00050 1.666667e-04 3728.405 0.9998594 -2.07579401 -0.95967928
## 5   1.984312313 0.00000 0.000000e+00 5707.761 1.0000218 -3.81280686 -3.20068858
## 6   1.387948444 0.00050 2.500000e-04 5280.886 0.9999268 -2.04575627 -0.92366410
## 7   0.009540860 0.11375 2.150000e-02 5233.777 0.9999258 -5.44334446 -4.70472262
## 8   1.159410683 0.20850 5.860714e-02 3103.410 0.9997532 -0.44392772  1.53301428
## 9   0.694424086 0.27725 3.568000e-02 4883.767 0.9997599 -5.39572536 -4.60644556
## 10  0.078117977 0.06800 2.067308e-02 4677.789 0.9997866 -0.60058289  0.65709209
## 11 -0.204860178 0.02425 3.515625e-03 4780.251 1.0001014 -5.93855098 -5.13019205
## 12  0.201051958 0.06275 1.672917e-02 2895.990 0.9998174 -1.10290540  0.35584273
## 13  1.655136157 0.00000 0.000000e+00 5285.436 0.9999870 -3.67413841 -3.06665923
## 14  1.793717568 0.00475 1.625000e-03 5405.964 0.9997956 -0.85541465  0.20563263
## 15  0.429904455 0.80150 9.215179e-02 5246.524 0.9998781 -5.68149382 -4.89247233
## 16  2.619605775 0.00000 0.000000e+00 6002.252 0.9998448 -0.60909191  0.56178635
## 17  1.095717492 0.00925 1.071429e-03 4554.364 0.9997555 -4.77020511 -4.06351740
## 18  1.587738529 0.07650 2.801667e-02 5604.482 0.9999109  0.02303552  1.07856220
## 19  1.204499556 0.54700 6.587963e-02 3939.377 0.9997515 -3.68320039 -1.98962494
## 20  1.298021163 0.24225 6.695455e-02 4757.427 0.9997847 -1.61667240  0.52709121
## 21  0.171016844 0.12025 2.561458e-02 4073.178 1.0002938 -4.73115288 -3.94816269
## 22  0.059869878 0.08325 3.444118e-02 4185.374 1.0008161 -4.08976614 -2.69211811
## 23  1.424392767 0.00000 0.000000e+00 5106.271 0.9997750 -4.15480611 -3.52264186
## 24  0.764224605 0.70400 1.646552e-01 5720.550 0.9999066 -0.96716520  0.02866965
## 25  1.509690170 0.00000 0.000000e+00 5063.679 0.9999499 -4.84064851 -4.08000028
## 26  1.170887508 0.03225 8.200000e-03 4955.100 1.0000125 -1.14741183  0.06981578
## 27 -0.107181538 0.05200 1.050000e-02 4971.923 1.0000566 -5.84097162 -5.07193711
## 28  1.994107339 0.00400 1.000000e-03 5257.759 1.0000176 -0.73510840  0.37131706
## 29  1.272474270 0.00025 2.500000e-05 4409.177 0.9997518 -4.97692567 -4.23413718
## 30  1.189804639 0.08200 3.139062e-02 5201.672 1.0001217 -0.80065900  0.32442542
## 31 -0.569027745 0.00050 8.333333e-05 4830.164 0.9998641 -6.99648526 -5.99416465
## 32 -0.232526205 0.02125 5.527778e-03 5182.060 0.9997500 -1.49146819 -0.04611469
## 33 -0.770142514 0.00025 4.545455e-05 5001.958 0.9998030 -6.64371797 -5.72459045
## 34  0.678280270 0.58800 1.283241e-01 4668.201 0.9997748 -2.13823677 -0.77018561
## 35 -0.129099907 0.03600 6.777778e-03 5439.393 0.9997927 -5.23724861 -4.49122738
## 36 -0.802901636 0.01175 3.562500e-03 1658.449 0.9997710 -5.12773436 -2.30922799
## 37  0.418256355 0.82575 1.406500e-01 4820.927 1.0000209 -5.42796707 -4.68582016
## 38  0.347809883 0.07500 2.455357e-02 3288.742 0.9998232 -0.15878334  1.19736475
## 39  2.043633191 0.00000 0.000000e+00 4091.411 0.9997501 -4.33538469 -3.59449821
## 40  0.339799146 0.26025 8.273958e-02 6458.211 0.9999115  0.37413719  1.44243821
## 41  1.314842463 0.00000 0.000000e+00 5000.956 1.0002260 -4.69962115 -4.01304728
## 42  0.697524601 0.72025 1.831750e-01 5622.655 0.9999752 -0.87949469  0.26184492
## 43  0.413704376 0.81350 1.170259e-01 4197.125 0.9999760 -5.60232320 -4.82230577
## 44  0.326072004 0.19575 5.111250e-02 4953.893 0.9999792 -0.76973453  0.36538390
## 45  1.724650445 0.00000 0.000000e+00 4542.086 0.9999133 -4.53828869 -3.82212997
## 46  1.119820329 0.12375 4.350000e-02 6669.402 0.9999531 -0.54556570  0.63920081
## 47 -0.723752570 0.00000 0.000000e+00 5799.727 1.0002459 -6.62859084 -5.78883275
## 48  0.407401864 0.51675 1.106442e-01 5297.126 1.0008828 -3.36471236 -1.60589786
## 49 -0.981964853 0.00000 0.000000e+00 5666.606 0.9997554 -6.42438087 -5.55654861
## 50  1.712619969 0.60625 1.453929e-01 3096.247 0.9998278 -0.69309414  0.67627679
## 51  0.001981351 0.09425 1.730682e-02 4315.549 1.0002616 -5.47641541 -4.75648605
## 52 -0.759296871 0.00700 2.392857e-03 2898.335 1.0008208 -2.74683116 -0.85498719
## 53 -0.247686364 0.01700 2.133333e-03 4820.365 0.9997553 -6.45661301 -5.57265623
## 54  1.900919770 0.05600 1.254545e-02 5756.661 1.0000903  0.15042828  1.35109723
## 55 -0.004348855 0.07650 1.364286e-02 5405.766 0.9997821 -5.29849773 -4.55772137
## 56  1.541217415 0.25250 7.502174e-02 5943.765 0.9999870 -1.19153685 -0.10591760
## 57  0.200285213 0.33975 4.737500e-02 4855.585 0.9997861 -5.36179925 -4.62170153
## 58  1.001998000 0.37425 9.440000e-02 4453.938 1.0000085 -1.76171017 -0.63317498
## 59 -0.151674725 0.03600 8.315789e-03 5020.575 0.9997530 -5.81014918 -5.04923079
## 60  1.497681456 0.11725 3.904167e-02 5016.910 1.0001961 -1.11464141 -0.01018327
##        v_upper   v_pH0      v_FDR  v_n_eff v_R_k_hat   count_data
## 1  -3.01594734 0.00000 0.00000000 5409.314 0.9999002 c("10x_6....
## 2   0.64489741 0.29950 0.14586111 6159.312 0.9997500 c("10x_6....
## 3  -3.57864093 0.00000 0.00000000 3519.519 1.0005457 c("10x_6....
## 4   0.23494621 0.10400 0.05611111 4261.362 1.0008244 c("10x_6....
## 5  -2.44650791 0.00000 0.00000000 5312.461 0.9997632 c("10x_6....
## 6   0.28833540 0.11550 0.06205000 4377.167 1.0002416 c("10x_6....
## 7  -3.79514969 0.00000 0.00000000 6881.401 0.9997504 c("10x_6....
## 8   3.51682878 0.09825 0.05012500 3613.886 0.9997533 c("10x_6....
## 9  -3.70263597 0.00000 0.00000000 8045.754 0.9998078 c("10x_6....
## 10  1.96292805 0.24000 0.11041071 5328.321 0.9998238 c("10x_6....
## 11 -4.16504193 0.00000 0.00000000 7844.006 0.9997662 c("10x_6....
## 12  1.94510705 0.41900 0.20035870 4015.516 0.9997925 c("10x_6....
## 13 -2.25344017 0.00000 0.00000000 4686.363 1.0021748 c("10x_6....
## 14  1.28787048 0.49425 0.22224000 4874.766 1.0007906 c("10x_6....
## 15 -3.99899991 0.00000 0.00000000 5816.735 0.9997749 c("10x_6....
## 16  1.82008789 0.27650 0.13682353 5464.671 0.9998611 c("10x_6....
## 17 -3.22230735 0.00000 0.00000000 7598.794 0.9997555 c("10x_6....
## 18  2.19544084 0.05200 0.02680000 4961.944 0.9997587 c("10x_6....
## 19 -0.60663354 0.00375 0.00012500 3276.876 0.9998203 c("10x_6....
## 20  2.66022070 0.37450 0.15789474 4677.905 0.9999591 c("10x_6....
## 21 -2.67633748 0.00000 0.00000000 2524.829 1.0000877 c("10x_6....
## 22 -1.35504439 0.00050 0.00050000 3574.751 0.9999963 c("10x_6....
## 23 -2.73242973 0.00000 0.00000000 6046.399 0.9997716 c("10x_6....
## 24  1.07409430 0.62875 0.28440833 4146.001 0.9997579 c("10x_6....
## 25 -3.25130320 0.00000 0.00000000 6257.730 1.0001361 c("10x_6....
## 26  1.32194977 0.58200 0.25992857 5480.366 0.9997586 c("10x_6....
## 27 -4.17176192 0.00000 0.00000000 6200.257 0.9997548 c("10x_6....
## 28  1.54555210 0.38525 0.16926250 5547.914 0.9997650 c("10x_6....
## 29 -3.41533777 0.00000 0.00000000 4768.682 0.9997587 c("10x_6....
## 30  1.49281552 0.41350 0.19042045 4414.391 0.9997528 c("10x_6....
## 31 -4.93406855 0.00000 0.00000000 5913.986 1.0004125 c("10x_6....
## 32  1.42011291 0.58000 0.24800000 4469.144 1.0017238 c("10x_6....
## 33 -4.67247613 0.00000 0.00000000 4841.088 1.0010174 c("10x_6....
## 34  0.69247644 0.22100 0.07650000 4836.522 1.0013204 c("10x_6....
## 35 -3.47612063 0.00000 0.00000000 4929.612 0.9998365 c("10x_6....
## 36  0.67789815 0.08400 0.03633333 2328.391 0.9999460 c("10x_6....
## 37 -3.81334114 0.00000 0.00000000 6741.012 0.9997905 c("10x_6....
## 38  2.71988969 0.08475 0.04325000 3806.932 0.9997547 c("10x_6....
## 39 -2.74397225 0.00000 0.00000000 6197.531 0.9997701 c("10x_6....
## 40  2.58005633 0.01425 0.00737500 5120.894 0.9998826 c("10x_6....
## 41 -3.20985712 0.00000 0.00000000 6615.290 0.9997545 c("10x_6....
## 42  1.47759316 0.45350 0.21090625 4925.025 1.0000988 c("10x_6....
## 43 -3.94847912 0.00000 0.00000000 6388.722 1.0006200 c("10x_6....
## 44  1.62040948 0.39050 0.17979762 5114.924 0.9998885 c("10x_6....
## 45 -2.97726301 0.00000 0.00000000 6076.717 0.9999879 c("10x_6....
## 46  1.79098166 0.23375 0.10044231 6150.762 1.0000851 c("10x_6....
## 47 -4.82573753 0.00000 0.00000000 5072.326 0.9997768 c("10x_6....
## 48 -0.07313994 0.03675 0.02050000 5370.470 1.0000990 c("10x_6....
## 49 -4.51508835 0.00000 0.00000000 7366.782 1.0004126 c("10x_6....
## 50  2.18789925 0.24700 0.11951667 3798.662 1.0004409 c("10x_6....
## 51 -3.84185317 0.00000 0.00000000 6667.789 0.9997500 c("10x_6....
## 52  1.05148876 0.25675 0.12809375 3206.943 0.9997500 c("10x_6....
## 53 -4.58170979 0.00000 0.00000000 5372.081 0.9997860 c("10x_6....
## 54  2.67644598 0.03050 0.01508333 4389.058 0.9998464 c("10x_6....
## 55 -3.58871639 0.00000 0.00000000 6109.684 0.9999189 c("10x_6....
## 56  1.06580944 0.56000 0.23523077 4692.084 1.0000305 c("10x_6....
## 57 -3.71581854 0.00000 0.00000000 5725.641 0.9997870 c("10x_6....
## 58  0.51819715 0.23050 0.08933333 5026.768 1.0000341 c("10x_6....
## 59 -4.08480824 0.00000 0.00000000 5956.403 0.9998031 c("10x_6....
## 60  1.15204092 0.62550 0.27253448 5516.992 0.9997873 c("10x_6....

A plot of group proportion, faceted by groups. The blue boxplots represent the posterior predictive check. If the model is likely to be descriptively adequate to the data, the blue box plot should roughly overlay with the black box plot, which represents the observed data. The outliers are coloured in red. A box plot will be returned for every (discrete) covariate present in formula_composition. The colour coding represents the significant associations for composition and/or variability.

plots$boxplot
## Warning: Unknown or uninitialised column: `boxplot`.
## NULL

A plot of estimates of differential composition (c_) on the x-axis and differential variability (v_) on the y-axis. The error bars represent 95% credible intervals. The dashed lines represent the minimal effect that the hypothesis test is based on. An effect is labelled as significant if bigger than the minimal effect according to the 95% credible interval. Facets represent the covariates in the model.

plots$credible_intervals_1D
## Warning: Unknown or uninitialised column: `credible_intervals_1D`.
## NULL

Visualisation of the MCMC chains from the posterior distribution

It is possible to directly evaluate the posterior distribution. In this example, we plot the Monte Carlo chain for the slope parameter of the first cell type. We can see that it has converged and is negative with probability 1.

res %>% attr("fit") %>% rstan::traceplot("beta[2,1]")

plot of chunk unnamed-chunk-12

Plot 1D significance plot

plots = res |> sccomp_test() |> plot_summary()
##              cell_group   parameter factor     c_lower     c_effect
## 1            B immature (Intercept)   <NA>  0.36714960  0.769063346
## 2            B immature typehealthy   type  0.84180431  1.434520538
## 3                 B mem (Intercept)   <NA> -1.48921622 -0.866042080
## 4                 B mem typehealthy   type  1.04093816  1.861888385
## 5         CD4 cm S100A4 (Intercept)   <NA>  1.30946655  1.662220821
## 6         CD4 cm S100A4 typehealthy   type  0.47432050  0.938966484
## 7  CD4 cm high cytokine (Intercept)   <NA> -1.03279974 -0.541792777
## 8  CD4 cm high cytokine typehealthy   type -3.06131684 -1.218953275
## 9       CD4 cm ribosome (Intercept)   <NA> -0.05380041  0.305894694
## 10      CD4 cm ribosome typehealthy   type -1.80627582 -0.964037534
## 11 CD4 em high cytokine (Intercept)   <NA> -1.16827385 -0.707911378
## 12 CD4 em high cytokine typehealthy   type -2.32982524 -1.267436140
## 13            CD4 naive (Intercept)   <NA>  0.74838491  1.211643519
## 14            CD4 naive typehealthy   type  0.45151064  1.142218863
## 15         CD4 ribosome (Intercept)   <NA> -0.29726785  0.046538669
## 16         CD4 ribosome typehealthy   type  1.44939833  2.056778591
## 17             CD8 em 1 (Intercept)   <NA>  0.28301490  0.683160799
## 18             CD8 em 1 typehealthy   type -0.03043376  0.781722909
## 19             CD8 em 2 (Intercept)   <NA> -0.91347221  0.138266684
## 20             CD8 em 2 typehealthy   type -3.54389720 -1.134040355
## 21             CD8 em 3 (Intercept)   <NA> -1.39088676 -0.662575055
## 22             CD8 em 3 typehealthy   type -1.74806697 -0.814719668
## 23            CD8 naive (Intercept)   <NA>  0.58731122  1.020907451
## 24            CD8 naive typehealthy   type -0.70878641  0.005401482
## 25     CD8 transitional (Intercept)   <NA>  0.90096497  1.209803385
## 26     CD8 transitional typehealthy   type  0.17957566  0.683288824
## 27                 MAIT (Intercept)   <NA> -1.05144268 -0.597450401
## 28                 MAIT typehealthy   type  0.46635056  1.209515514
## 29               Mac M1 (Intercept)   <NA>  0.62583442  0.949116764
## 30               Mac M1 typehealthy   type  0.03165886  0.593128278
## 31        Mac M1 FCER1A (Intercept)   <NA> -1.33254732 -0.983485510
## 32        Mac M1 FCER1A typehealthy   type -1.79881252 -1.068023548
## 33                 Mono (Intercept)   <NA> -1.80820415 -1.337378989
## 34                 Mono typehealthy   type -0.84397959 -0.118718215
## 35          Mono NKG7 1 (Intercept)   <NA> -1.47715155 -0.873120573
## 36          Mono NKG7 1 typehealthy   type -4.00459122 -2.864291927
## 37          Mono NKG7 2 (Intercept)   <NA> -0.42176260 -0.014464654
## 38          Mono NKG7 2 typehealthy   type -2.43766291 -1.292219635
## 39  Mono classic inflam (Intercept)   <NA>  1.49888142  1.783381517
## 40  Mono classic inflam typehealthy   type -1.24301291 -0.450991681
## 41     Mono non-classic (Intercept)   <NA>  0.61714585  0.963521050
## 42     Mono non-classic typehealthy   type -0.65137438  0.005515399
## 43    Myeloid migratory (Intercept)   <NA> -0.36121811  0.022998608
## 44    Myeloid migratory typehealthy   type -1.34255050 -0.563779831
## 45                   NK (Intercept)   <NA>  1.12159264  1.434522221
## 46                   NK typehealthy   type -0.04635236  0.539163697
## 47           NK cycling (Intercept)   <NA> -1.67444697 -1.209958145
## 48           NK cycling typehealthy   type -0.79650498 -0.186326087
## 49     NK high cytokine (Intercept)   <NA> -2.22419952 -1.640829858
## 50     NK high cytokine typehealthy   type -1.18688802  0.008488138
## 51                 Stem (Intercept)   <NA> -1.08664179 -0.569628573
## 52                 Stem typehealthy   type -3.22879492 -2.239123013
## 53                T gd1 (Intercept)   <NA> -1.06777916 -0.689845024
## 54                T gd1 typehealthy   type  0.04203475  0.920521874
## 55                T gd2 (Intercept)   <NA> -1.24443601 -0.668973219
## 56                T gd2 typehealthy   type -0.42754553  0.511537788
## 57                 cDC2 (Intercept)   <NA> -0.75392563 -0.296024832
## 58                 cDC2 typehealthy   type -0.34412558  0.310340803
## 59                  pDC (Intercept)   <NA> -1.15399879 -0.672606034
## 60                  pDC typehealthy   type -0.08755515  0.668205977
##         c_upper   c_pH0        c_FDR  c_n_eff c_R_k_hat     v_lower    v_effect
## 1   1.183132826 0.00475 4.423077e-04 5804.832 1.0000831 -4.49425352 -3.82358583
## 2   1.994177904 0.00000 0.000000e+00 5061.157 0.9998241 -1.66080948 -0.52051568
## 3  -0.161027248 0.02975 5.058824e-03 4035.640 0.9999466 -5.30849510 -4.56068059
## 4   2.641768018 0.00050 1.666667e-04 3728.405 0.9998594 -2.07579401 -0.95967928
## 5   1.984312313 0.00000 0.000000e+00 5707.761 1.0000218 -3.81280686 -3.20068858
## 6   1.387948444 0.00050 2.500000e-04 5280.886 0.9999268 -2.04575627 -0.92366410
## 7   0.009540860 0.11375 2.150000e-02 5233.777 0.9999258 -5.44334446 -4.70472262
## 8   1.159410683 0.20850 5.860714e-02 3103.410 0.9997532 -0.44392772  1.53301428
## 9   0.694424086 0.27725 3.568000e-02 4883.767 0.9997599 -5.39572536 -4.60644556
## 10  0.078117977 0.06800 2.067308e-02 4677.789 0.9997866 -0.60058289  0.65709209
## 11 -0.204860178 0.02425 3.515625e-03 4780.251 1.0001014 -5.93855098 -5.13019205
## 12  0.201051958 0.06275 1.672917e-02 2895.990 0.9998174 -1.10290540  0.35584273
## 13  1.655136157 0.00000 0.000000e+00 5285.436 0.9999870 -3.67413841 -3.06665923
## 14  1.793717568 0.00475 1.625000e-03 5405.964 0.9997956 -0.85541465  0.20563263
## 15  0.429904455 0.80150 9.215179e-02 5246.524 0.9998781 -5.68149382 -4.89247233
## 16  2.619605775 0.00000 0.000000e+00 6002.252 0.9998448 -0.60909191  0.56178635
## 17  1.095717492 0.00925 1.071429e-03 4554.364 0.9997555 -4.77020511 -4.06351740
## 18  1.587738529 0.07650 2.801667e-02 5604.482 0.9999109  0.02303552  1.07856220
## 19  1.204499556 0.54700 6.587963e-02 3939.377 0.9997515 -3.68320039 -1.98962494
## 20  1.298021163 0.24225 6.695455e-02 4757.427 0.9997847 -1.61667240  0.52709121
## 21  0.171016844 0.12025 2.561458e-02 4073.178 1.0002938 -4.73115288 -3.94816269
## 22  0.059869878 0.08325 3.444118e-02 4185.374 1.0008161 -4.08976614 -2.69211811
## 23  1.424392767 0.00000 0.000000e+00 5106.271 0.9997750 -4.15480611 -3.52264186
## 24  0.764224605 0.70400 1.646552e-01 5720.550 0.9999066 -0.96716520  0.02866965
## 25  1.509690170 0.00000 0.000000e+00 5063.679 0.9999499 -4.84064851 -4.08000028
## 26  1.170887508 0.03225 8.200000e-03 4955.100 1.0000125 -1.14741183  0.06981578
## 27 -0.107181538 0.05200 1.050000e-02 4971.923 1.0000566 -5.84097162 -5.07193711
## 28  1.994107339 0.00400 1.000000e-03 5257.759 1.0000176 -0.73510840  0.37131706
## 29  1.272474270 0.00025 2.500000e-05 4409.177 0.9997518 -4.97692567 -4.23413718
## 30  1.189804639 0.08200 3.139062e-02 5201.672 1.0001217 -0.80065900  0.32442542
## 31 -0.569027745 0.00050 8.333333e-05 4830.164 0.9998641 -6.99648526 -5.99416465
## 32 -0.232526205 0.02125 5.527778e-03 5182.060 0.9997500 -1.49146819 -0.04611469
## 33 -0.770142514 0.00025 4.545455e-05 5001.958 0.9998030 -6.64371797 -5.72459045
## 34  0.678280270 0.58800 1.283241e-01 4668.201 0.9997748 -2.13823677 -0.77018561
## 35 -0.129099907 0.03600 6.777778e-03 5439.393 0.9997927 -5.23724861 -4.49122738
## 36 -0.802901636 0.01175 3.562500e-03 1658.449 0.9997710 -5.12773436 -2.30922799
## 37  0.418256355 0.82575 1.406500e-01 4820.927 1.0000209 -5.42796707 -4.68582016
## 38  0.347809883 0.07500 2.455357e-02 3288.742 0.9998232 -0.15878334  1.19736475
## 39  2.043633191 0.00000 0.000000e+00 4091.411 0.9997501 -4.33538469 -3.59449821
## 40  0.339799146 0.26025 8.273958e-02 6458.211 0.9999115  0.37413719  1.44243821
## 41  1.314842463 0.00000 0.000000e+00 5000.956 1.0002260 -4.69962115 -4.01304728
## 42  0.697524601 0.72025 1.831750e-01 5622.655 0.9999752 -0.87949469  0.26184492
## 43  0.413704376 0.81350 1.170259e-01 4197.125 0.9999760 -5.60232320 -4.82230577
## 44  0.326072004 0.19575 5.111250e-02 4953.893 0.9999792 -0.76973453  0.36538390
## 45  1.724650445 0.00000 0.000000e+00 4542.086 0.9999133 -4.53828869 -3.82212997
## 46  1.119820329 0.12375 4.350000e-02 6669.402 0.9999531 -0.54556570  0.63920081
## 47 -0.723752570 0.00000 0.000000e+00 5799.727 1.0002459 -6.62859084 -5.78883275
## 48  0.407401864 0.51675 1.106442e-01 5297.126 1.0008828 -3.36471236 -1.60589786
## 49 -0.981964853 0.00000 0.000000e+00 5666.606 0.9997554 -6.42438087 -5.55654861
## 50  1.712619969 0.60625 1.453929e-01 3096.247 0.9998278 -0.69309414  0.67627679
## 51  0.001981351 0.09425 1.730682e-02 4315.549 1.0002616 -5.47641541 -4.75648605
## 52 -0.759296871 0.00700 2.392857e-03 2898.335 1.0008208 -2.74683116 -0.85498719
## 53 -0.247686364 0.01700 2.133333e-03 4820.365 0.9997553 -6.45661301 -5.57265623
## 54  1.900919770 0.05600 1.254545e-02 5756.661 1.0000903  0.15042828  1.35109723
## 55 -0.004348855 0.07650 1.364286e-02 5405.766 0.9997821 -5.29849773 -4.55772137
## 56  1.541217415 0.25250 7.502174e-02 5943.765 0.9999870 -1.19153685 -0.10591760
## 57  0.200285213 0.33975 4.737500e-02 4855.585 0.9997861 -5.36179925 -4.62170153
## 58  1.001998000 0.37425 9.440000e-02 4453.938 1.0000085 -1.76171017 -0.63317498
## 59 -0.151674725 0.03600 8.315789e-03 5020.575 0.9997530 -5.81014918 -5.04923079
## 60  1.497681456 0.11725 3.904167e-02 5016.910 1.0001961 -1.11464141 -0.01018327
##        v_upper   v_pH0      v_FDR  v_n_eff v_R_k_hat   count_data
## 1  -3.01594734 0.00000 0.00000000 5409.314 0.9999002 c("10x_6....
## 2   0.64489741 0.29950 0.14586111 6159.312 0.9997500 c("10x_6....
## 3  -3.57864093 0.00000 0.00000000 3519.519 1.0005457 c("10x_6....
## 4   0.23494621 0.10400 0.05611111 4261.362 1.0008244 c("10x_6....
## 5  -2.44650791 0.00000 0.00000000 5312.461 0.9997632 c("10x_6....
## 6   0.28833540 0.11550 0.06205000 4377.167 1.0002416 c("10x_6....
## 7  -3.79514969 0.00000 0.00000000 6881.401 0.9997504 c("10x_6....
## 8   3.51682878 0.09825 0.05012500 3613.886 0.9997533 c("10x_6....
## 9  -3.70263597 0.00000 0.00000000 8045.754 0.9998078 c("10x_6....
## 10  1.96292805 0.24000 0.11041071 5328.321 0.9998238 c("10x_6....
## 11 -4.16504193 0.00000 0.00000000 7844.006 0.9997662 c("10x_6....
## 12  1.94510705 0.41900 0.20035870 4015.516 0.9997925 c("10x_6....
## 13 -2.25344017 0.00000 0.00000000 4686.363 1.0021748 c("10x_6....
## 14  1.28787048 0.49425 0.22224000 4874.766 1.0007906 c("10x_6....
## 15 -3.99899991 0.00000 0.00000000 5816.735 0.9997749 c("10x_6....
## 16  1.82008789 0.27650 0.13682353 5464.671 0.9998611 c("10x_6....
## 17 -3.22230735 0.00000 0.00000000 7598.794 0.9997555 c("10x_6....
## 18  2.19544084 0.05200 0.02680000 4961.944 0.9997587 c("10x_6....
## 19 -0.60663354 0.00375 0.00012500 3276.876 0.9998203 c("10x_6....
## 20  2.66022070 0.37450 0.15789474 4677.905 0.9999591 c("10x_6....
## 21 -2.67633748 0.00000 0.00000000 2524.829 1.0000877 c("10x_6....
## 22 -1.35504439 0.00050 0.00050000 3574.751 0.9999963 c("10x_6....
## 23 -2.73242973 0.00000 0.00000000 6046.399 0.9997716 c("10x_6....
## 24  1.07409430 0.62875 0.28440833 4146.001 0.9997579 c("10x_6....
## 25 -3.25130320 0.00000 0.00000000 6257.730 1.0001361 c("10x_6....
## 26  1.32194977 0.58200 0.25992857 5480.366 0.9997586 c("10x_6....
## 27 -4.17176192 0.00000 0.00000000 6200.257 0.9997548 c("10x_6....
## 28  1.54555210 0.38525 0.16926250 5547.914 0.9997650 c("10x_6....
## 29 -3.41533777 0.00000 0.00000000 4768.682 0.9997587 c("10x_6....
## 30  1.49281552 0.41350 0.19042045 4414.391 0.9997528 c("10x_6....
## 31 -4.93406855 0.00000 0.00000000 5913.986 1.0004125 c("10x_6....
## 32  1.42011291 0.58000 0.24800000 4469.144 1.0017238 c("10x_6....
## 33 -4.67247613 0.00000 0.00000000 4841.088 1.0010174 c("10x_6....
## 34  0.69247644 0.22100 0.07650000 4836.522 1.0013204 c("10x_6....
## 35 -3.47612063 0.00000 0.00000000 4929.612 0.9998365 c("10x_6....
## 36  0.67789815 0.08400 0.03633333 2328.391 0.9999460 c("10x_6....
## 37 -3.81334114 0.00000 0.00000000 6741.012 0.9997905 c("10x_6....
## 38  2.71988969 0.08475 0.04325000 3806.932 0.9997547 c("10x_6....
## 39 -2.74397225 0.00000 0.00000000 6197.531 0.9997701 c("10x_6....
## 40  2.58005633 0.01425 0.00737500 5120.894 0.9998826 c("10x_6....
## 41 -3.20985712 0.00000 0.00000000 6615.290 0.9997545 c("10x_6....
## 42  1.47759316 0.45350 0.21090625 4925.025 1.0000988 c("10x_6....
## 43 -3.94847912 0.00000 0.00000000 6388.722 1.0006200 c("10x_6....
## 44  1.62040948 0.39050 0.17979762 5114.924 0.9998885 c("10x_6....
## 45 -2.97726301 0.00000 0.00000000 6076.717 0.9999879 c("10x_6....
## 46  1.79098166 0.23375 0.10044231 6150.762 1.0000851 c("10x_6....
## 47 -4.82573753 0.00000 0.00000000 5072.326 0.9997768 c("10x_6....
## 48 -0.07313994 0.03675 0.02050000 5370.470 1.0000990 c("10x_6....
## 49 -4.51508835 0.00000 0.00000000 7366.782 1.0004126 c("10x_6....
## 50  2.18789925 0.24700 0.11951667 3798.662 1.0004409 c("10x_6....
## 51 -3.84185317 0.00000 0.00000000 6667.789 0.9997500 c("10x_6....
## 52  1.05148876 0.25675 0.12809375 3206.943 0.9997500 c("10x_6....
## 53 -4.58170979 0.00000 0.00000000 5372.081 0.9997860 c("10x_6....
## 54  2.67644598 0.03050 0.01508333 4389.058 0.9998464 c("10x_6....
## 55 -3.58871639 0.00000 0.00000000 6109.684 0.9999189 c("10x_6....
## 56  1.06580944 0.56000 0.23523077 4692.084 1.0000305 c("10x_6....
## 57 -3.71581854 0.00000 0.00000000 5725.641 0.9997870 c("10x_6....
## 58  0.51819715 0.23050 0.08933333 5026.768 1.0000341 c("10x_6....
## 59 -4.08480824 0.00000 0.00000000 5956.403 0.9998031 c("10x_6....
## 60  1.15204092 0.62550 0.27253448 5516.992 0.9997873 c("10x_6....
plots$credible_intervals_1D
## Warning: Unknown or uninitialised column: `credible_intervals_1D`.
## NULL

Plot 2D significance plot. Data points are cell groups. Error bars are the 95% credible interval. The dashed lines represent the default threshold fold change for which the probabilities (c_pH0, v_pH0) are calculated. pH0 of 0 represent the rejection of the null hypothesis that no effect is observed.

This plot is provided only if differential variability has been tested. The differential variability estimates are reliable only if the linear association between mean and variability for (intercept) (left-hand side facet) is satisfied. A scatterplot (besides the Intercept) is provided for each category of interest. The for each category of interest, the composition and variability effects should be generally uncorrelated.

plots$credible_intervals_2D
## Warning: Unknown or uninitialised column: `credible_intervals_2D`.
## NULL
sessionInfo()
## R Under development (unstable) (2024-01-16 r85808)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.3 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.19-bioc/R/lib/libRblas.so 
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## time zone: America/New_York
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] rstan_2.32.5       StanHeaders_2.32.5 tidyr_1.3.0        forcats_1.0.0     
## [5] ggplot2_3.4.4      sccomp_1.7.5       dplyr_1.1.4       
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.2.0            farver_2.1.1               
##  [3] loo_2.6.0                   bitops_1.0-7               
##  [5] SingleCellExperiment_1.25.0 RCurl_1.98-1.14            
##  [7] digest_0.6.34               dotCall64_1.1-1            
##  [9] lifecycle_1.0.4             SeuratObject_5.0.1         
## [11] magrittr_2.0.3              compiler_4.4.0             
## [13] rlang_1.1.3                 tools_4.4.0                
## [15] utf8_1.2.4                  knitr_1.45                 
## [17] labeling_0.4.3              S4Arrays_1.3.2             
## [19] sp_2.1-2                    pkgbuild_1.4.3             
## [21] curl_5.2.0                  DelayedArray_0.29.0        
## [23] abind_1.4-5                 withr_3.0.0                
## [25] purrr_1.0.2                 BiocGenerics_0.49.1        
## [27] grid_4.4.0                  stats4_4.4.0               
## [29] fansi_1.0.6                 colorspace_2.1-0           
## [31] future_1.33.1               inline_0.3.19              
## [33] progressr_0.14.0            globals_0.16.2             
## [35] scales_1.3.0                SummarizedExperiment_1.33.2
## [37] cli_3.6.2                   crayon_1.5.2               
## [39] generics_0.1.3              RcppParallel_5.1.7         
## [41] future.apply_1.11.1         tzdb_0.4.0                 
## [43] stringr_1.5.1               zlibbioc_1.49.0            
## [45] parallel_4.4.0              XVector_0.43.1             
## [47] matrixStats_1.2.0           vctrs_0.6.5                
## [49] V8_4.4.1                    boot_1.3-28.1              
## [51] Matrix_1.6-5                jsonlite_1.8.8             
## [53] IRanges_2.37.1              hms_1.1.3                  
## [55] patchwork_1.2.0             S4Vectors_0.41.3           
## [57] ggrepel_0.9.5               listenv_0.9.0              
## [59] glue_1.7.0                  parallelly_1.36.0          
## [61] spam_2.10-0                 codetools_0.2-19           
## [63] stringi_1.8.3               gtable_0.3.4               
## [65] GenomeInfoDb_1.39.5         QuickJSR_1.1.0             
## [67] GenomicRanges_1.55.1        munsell_0.5.0              
## [69] tibble_3.2.1                pillar_1.9.0               
## [71] GenomeInfoDbData_1.2.11     R6_2.5.1                   
## [73] evaluate_0.23               lattice_0.22-5             
## [75] Biobase_2.63.0              highr_0.10                 
## [77] readr_2.1.5                 rstantools_2.3.1.1         
## [79] Rcpp_1.0.12                 gridExtra_2.3              
## [81] SparseArray_1.3.3           xfun_0.41                  
## [83] MatrixGenerics_1.15.0       pkgconfig_2.0.3