Last updated: 2024-05-01

Checks: 7 0

Knit directory: misc/analysis/

This reproducible R Markdown analysis was created with workflowr (version 1.7.1). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

R Markdown file: up-to-date

Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Environment: empty

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

Seed: set.seed(1)

The command set.seed(1) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Session information: recorded

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Cache: none

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

File paths: relative

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Repository version: 67a1ff6

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version 67a1ff6. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated: 


Ignored files:
    Ignored:    .DS_Store
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    analysis/.RData
    Ignored:    analysis/.Rhistory
    Ignored:    analysis/ALStruct_cache/
    Ignored:    data/.Rhistory
    Ignored:    data/methylation-data-for-matthew.rds
    Ignored:    data/pbmc/
    Ignored:    data/pbmc_purified.RData

Untracked files:
    Untracked:  .dropbox
    Untracked:  Icon
    Untracked:  analysis/GHstan.Rmd
    Untracked:  analysis/GTEX-cogaps.Rmd
    Untracked:  analysis/PACS.Rmd
    Untracked:  analysis/Rplot.png
    Untracked:  analysis/SPCAvRP.rmd
    Untracked:  analysis/abf_comparisons.Rmd
    Untracked:  analysis/admm_02.Rmd
    Untracked:  analysis/admm_03.Rmd
    Untracked:  analysis/cache/
    Untracked:  analysis/cholesky.Rmd
    Untracked:  analysis/compare-transformed-models.Rmd
    Untracked:  analysis/cormotif.Rmd
    Untracked:  analysis/cp_ash.Rmd
    Untracked:  analysis/eQTL.perm.rand.pdf
    Untracked:  analysis/eb_prepilot.Rmd
    Untracked:  analysis/eb_var.Rmd
    Untracked:  analysis/ebpmf1.Rmd
    Untracked:  analysis/ebpmf_sla_text.Rmd
    Untracked:  analysis/ebspca_sims.Rmd
    Untracked:  analysis/explore_psvd.Rmd
    Untracked:  analysis/fa_check_identify.Rmd
    Untracked:  analysis/fa_iterative.Rmd
    Untracked:  analysis/flash_test_tree.Rmd
    Untracked:  analysis/flash_tree.Rmd
    Untracked:  analysis/flashier_newgroups.Rmd
    Untracked:  analysis/flashier_nmf_triples.Rmd
    Untracked:  analysis/flashier_pbmc.Rmd
    Untracked:  analysis/flashier_snn_shifted_prior.Rmd
    Untracked:  analysis/greedy_ebpmf_exploration_00.Rmd
    Untracked:  analysis/ieQTL.perm.rand.pdf
    Untracked:  analysis/lasso_em_03.Rmd
    Untracked:  analysis/m6amash.Rmd
    Untracked:  analysis/mash_bhat_z.Rmd
    Untracked:  analysis/mash_ieqtl_permutations.Rmd
    Untracked:  analysis/methylation_example.Rmd
    Untracked:  analysis/mixsqp.Rmd
    Untracked:  analysis/mr.ash_lasso_init.Rmd
    Untracked:  analysis/mr.mash.test.Rmd
    Untracked:  analysis/mr_ash_modular.Rmd
    Untracked:  analysis/mr_ash_parameterization.Rmd
    Untracked:  analysis/mr_ash_ridge.Rmd
    Untracked:  analysis/mv_gaussian_message_passing.Rmd
    Untracked:  analysis/nejm.Rmd
    Untracked:  analysis/nmf_bg.Rmd
    Untracked:  analysis/normal_conditional_on_r2.Rmd
    Untracked:  analysis/normalize.Rmd
    Untracked:  analysis/pbmc.Rmd
    Untracked:  analysis/pca_binary_weighted.Rmd
    Untracked:  analysis/pca_l1.Rmd
    Untracked:  analysis/poisson_nmf_approx.Rmd
    Untracked:  analysis/poisson_shrink.Rmd
    Untracked:  analysis/poisson_transform.Rmd
    Untracked:  analysis/qrnotes.txt
    Untracked:  analysis/ridge_iterative_02.Rmd
    Untracked:  analysis/ridge_iterative_splitting.Rmd
    Untracked:  analysis/samps/
    Untracked:  analysis/sc_bimodal.Rmd
    Untracked:  analysis/shrinkage_comparisons_changepoints.Rmd
    Untracked:  analysis/susie_cov.Rmd
    Untracked:  analysis/susie_en.Rmd
    Untracked:  analysis/susie_z_investigate.Rmd
    Untracked:  analysis/svd-timing.Rmd
    Untracked:  analysis/temp.RDS
    Untracked:  analysis/temp.Rmd
    Untracked:  analysis/test-figure/
    Untracked:  analysis/test.Rmd
    Untracked:  analysis/test.Rpres
    Untracked:  analysis/test.md
    Untracked:  analysis/test_qr.R
    Untracked:  analysis/test_sparse.Rmd
    Untracked:  analysis/tree_dist_top_eigenvector.Rmd
    Untracked:  analysis/z.txt
    Untracked:  code/multivariate_testfuncs.R
    Untracked:  code/rqb.hacked.R
    Untracked:  data/4matthew/
    Untracked:  data/4matthew2/
    Untracked:  data/E-MTAB-2805.processed.1/
    Untracked:  data/ENSG00000156738.Sim_Y2.RDS
    Untracked:  data/GDS5363_full.soft.gz
    Untracked:  data/GSE41265_allGenesTPM.txt
    Untracked:  data/Muscle_Skeletal.ACTN3.pm1Mb.RDS
    Untracked:  data/P.rds
    Untracked:  data/Thyroid.FMO2.pm1Mb.RDS
    Untracked:  data/bmass.HaemgenRBC2016.MAF01.Vs2.MergedDataSources.200kRanSubset.ChrBPMAFMarkerZScores.vs1.txt.gz
    Untracked:  data/bmass.HaemgenRBC2016.Vs2.NewSNPs.ZScores.hclust.vs1.txt
    Untracked:  data/bmass.HaemgenRBC2016.Vs2.PreviousSNPs.ZScores.hclust.vs1.txt
    Untracked:  data/eb_prepilot/
    Untracked:  data/finemap_data/fmo2.sim/b.txt
    Untracked:  data/finemap_data/fmo2.sim/dap_out.txt
    Untracked:  data/finemap_data/fmo2.sim/dap_out2.txt
    Untracked:  data/finemap_data/fmo2.sim/dap_out2_snp.txt
    Untracked:  data/finemap_data/fmo2.sim/dap_out_snp.txt
    Untracked:  data/finemap_data/fmo2.sim/data
    Untracked:  data/finemap_data/fmo2.sim/fmo2.sim.config
    Untracked:  data/finemap_data/fmo2.sim/fmo2.sim.k
    Untracked:  data/finemap_data/fmo2.sim/fmo2.sim.k4.config
    Untracked:  data/finemap_data/fmo2.sim/fmo2.sim.k4.snp
    Untracked:  data/finemap_data/fmo2.sim/fmo2.sim.ld
    Untracked:  data/finemap_data/fmo2.sim/fmo2.sim.snp
    Untracked:  data/finemap_data/fmo2.sim/fmo2.sim.z
    Untracked:  data/finemap_data/fmo2.sim/pos.txt
    Untracked:  data/logm.csv
    Untracked:  data/m.cd.RDS
    Untracked:  data/m.cdu.old.RDS
    Untracked:  data/m.new.cd.RDS
    Untracked:  data/m.old.cd.RDS
    Untracked:  data/mainbib.bib.old
    Untracked:  data/mat.csv
    Untracked:  data/mat.txt
    Untracked:  data/mat_new.csv
    Untracked:  data/matrix_lik.rds
    Untracked:  data/paintor_data/
    Untracked:  data/running_data_chris.csv
    Untracked:  data/running_data_matthew.csv
    Untracked:  data/temp.txt
    Untracked:  data/y.txt
    Untracked:  data/y_f.txt
    Untracked:  data/zscore_jointLCLs_m6AQTLs_susie_eQTLpruned.rds
    Untracked:  data/zscore_jointLCLs_random.rds
    Untracked:  explore_udi.R
    Untracked:  output/fit.k10.rds
    Untracked:  output/fit.nn.pbmc.purified.rds
    Untracked:  output/fit.nn.rds
    Untracked:  output/fit.nn.s.001.rds
    Untracked:  output/fit.nn.s.01.rds
    Untracked:  output/fit.nn.s.1.rds
    Untracked:  output/fit.nn.s.10.rds
    Untracked:  output/fit.snn.s.001.rds
    Untracked:  output/fit.snn.s.01.nninit.rds
    Untracked:  output/fit.snn.s.01.rds
    Untracked:  output/fit.varbvs.RDS
    Untracked:  output/fit2.nn.pbmc.purified.rds
    Untracked:  output/glmnet.fit.RDS
    Untracked:  output/snn07.txt
    Untracked:  output/snn34.txt
    Untracked:  output/test.bv.txt
    Untracked:  output/test.gamma.txt
    Untracked:  output/test.hyp.txt
    Untracked:  output/test.log.txt
    Untracked:  output/test.param.txt
    Untracked:  output/test2.bv.txt
    Untracked:  output/test2.gamma.txt
    Untracked:  output/test2.hyp.txt
    Untracked:  output/test2.log.txt
    Untracked:  output/test2.param.txt
    Untracked:  output/test3.bv.txt
    Untracked:  output/test3.gamma.txt
    Untracked:  output/test3.hyp.txt
    Untracked:  output/test3.log.txt
    Untracked:  output/test3.param.txt
    Untracked:  output/test4.bv.txt
    Untracked:  output/test4.gamma.txt
    Untracked:  output/test4.hyp.txt
    Untracked:  output/test4.log.txt
    Untracked:  output/test4.param.txt
    Untracked:  output/test5.bv.txt
    Untracked:  output/test5.gamma.txt
    Untracked:  output/test5.hyp.txt
    Untracked:  output/test5.log.txt
    Untracked:  output/test5.param.txt

Unstaged changes:
    Modified:   .gitignore
    Modified:   analysis/flashier_log1p.Rmd
    Modified:   analysis/flashier_sla_text.Rmd
    Modified:   analysis/mr_ash_pen.Rmd
    Modified:   analysis/susie_flash.Rmd

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.

These are the previous versions of the repository in which changes were made to the R Markdown (analysis/logistic_z_scores.Rmd) and HTML (docs/logistic_z_scores.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File Version Author Date Message
Rmd 67a1ff6 Matthew Stephens 2024-05-01 workflowr::wflow_publish("logistic_z_scores.Rmd") 
library(ggplot2)
library(dplyr)

Attaching package: 'dplyr'
The following objects are masked from 'package:stats':

    filter, lag
The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union
set.seed(1)

Introduction

I want to document an unexpected phenomena I saw when computing z score for logistic regression: when the effect size increases the z scores eventually start decreasing.

Simulation code

First I set up some simulation code for simple logistic regression. We have \(x_i \sim N(0,1)\) and \(y_i \sim Bernoulli(\frac{e^{x_i b}}{1+e^{x_i b}})\). I set up this code to do some comparisons between linear and logistic regression, so it returns more things than we need here.

#' simulate data and return dataframe of results from linear and logistic regression
#' @param n sample size
#' @param b effect size
#' @param nsim number of simulations
simdata = function(n,b,binarize_x=FALSE){
  x = rnorm(n)
  if(binarize_x){
    x = (x > 0) - ( x < 0 )
  }
  y = rbinom(n, 1, exp(x*b)/(1+exp(x*b)))
  coeff.log = summary(glm(y ~ x, family=binomial))$coef
  coeff.lin = summary(glm(y ~ x, family=gaussian))$coef
  z.log = coeff.log[2,3] # z score
  bhat.log = coeff.log[2,1] # estimated effect size
  s.log = coeff.log[2,2] # standard error
  z.lin = coeff.lin[2,3] # z score
  s.lin = coeff.lin[2,2]
  bhat.lin = coeff.lin[2,1]
  
  # these are the normal log-likelihood ratios
  nllr.lin = dnorm(bhat.lin,mean = bhat.lin, sd = s.lin, log=TRUE)-dnorm(bhat.lin, mean = 0, sd = s.lin,log=TRUE)
  nllr.log = dnorm(bhat.log,mean = bhat.log, sd = s.log, log=TRUE)-dnorm(bhat.log, mean = 0, sd = s.log,log=TRUE)
  
  # these are the logistic/binomial log-likelihood ratios
  llr.lin = sum(dbinom(y, size=1, prob=1/(1+exp(-x*bhat.lin)), log=TRUE) - dbinom(y, size=1, prob=0.5, log=TRUE))
  
  llr.log = sum(dbinom(y, size=1, prob=1/(1+exp(-x*bhat.log)), log=TRUE) - dbinom(y, size=1, prob=0.5, log=TRUE))
  
  return(data.frame(n=n, b=b, z.log=z.log, s.log=s.log, bhat.log=bhat.log, z.lin=z.lin, s.lin=s.lin, bhat.lin=bhat.lin, nllr.lin = nllr.lin, nllr.log = nllr.log, llr.lin = llr.lin, llr.log = llr.log))
}

dsimdata = function(design){
  design %>% rowwise() %>% mutate(simdata(n,b))
}

Simulate Data

I simulate data with two different sample sizes and effect sizes that are \(b \sim N(0,sd=2)\). The z scores increase with b, but then start to decrease.

sim1 = dsimdata(data.frame(n=1000,b=rnorm(50,0,2)))
sim2 = dsimdata(data.frame(n=10000,b=rnorm(50,0,2)))
sim3 = dsimdata(data.frame(n=100000,b=rnorm(50,0,2)))
ggplot(rbind(sim1,sim2,sim3), 
       mapping = aes(b, z.log)) +
  geom_point(mapping = aes(color = b, shape=as.factor(n))) + 
   ylab("z score (logistic regression)")

Try binary x

I repated this with binary x to see if it changes things. It seems to be the same story.

sim1b = dsimdata(data.frame(n=1000,b=rnorm(50,0,2), binarize_x = TRUE))
sim2b = dsimdata(data.frame(n=10000,b=rnorm(50,0,2), binarize_x = TRUE))
sim3b = dsimdata(data.frame(n=100000,b=rnorm(50,0,2), binarize_x = TRUE))
ggplot(rbind(sim1b,sim2b,sim3b), 
       mapping = aes(b, z.log)) +
  geom_point(mapping = aes(color = b, shape=as.factor(n))) +
  ylab("z score (logistic regression)")

Single simulation

Just to emphasize: this phenomena seems not to be related to problems of separation or even small counts, since it occurs even with large n at moderate b.

Here is a single simulation to illustrate that we have large counts in all four groups when n=100k and b=2.5.

n = 100000
b = 2.5
x = rnorm(n)
x = (x>0) - (x<0) # binarize x
y = rbinom(n, 1, exp(x*b)/(1+exp(x*b)))
table(x,y)
    y
x        0     1
  -1 46105  3740
  1   3803 46352

sessionInfo()
R version 4.2.1 (2022-06-23)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur ... 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] dplyr_1.1.4   ggplot2_3.4.4

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.12       highr_0.10        pillar_1.9.0      compiler_4.2.1   
 [5] bslib_0.6.1       later_1.3.2       jquerylib_0.1.4   git2r_0.33.0     
 [9] workflowr_1.7.1   tools_4.2.1       digest_0.6.33     gtable_0.3.4     
[13] jsonlite_1.8.8    evaluate_0.23     lifecycle_1.0.4   tibble_3.2.1     
[17] pkgconfig_2.0.3   rlang_1.1.2       cli_3.6.2         rstudioapi_0.15.0
[21] yaml_2.3.8        xfun_0.41         fastmap_1.1.1     withr_3.0.0      
[25] stringr_1.5.1     knitr_1.45        generics_0.1.3    fs_1.6.3         
[29] vctrs_0.6.5       sass_0.4.8        tidyselect_1.2.0  rprojroot_2.0.4  
[33] grid_4.2.1        glue_1.6.2        R6_2.5.1          fansi_1.0.6      
[37] rmarkdown_2.25    farver_2.1.1      magrittr_2.0.3    whisker_0.4.1    
[41] scales_1.3.0      promises_1.2.1    htmltools_0.5.7   colorspace_2.1-0 
[45] httpuv_1.6.13     labeling_0.4.3    utf8_1.2.4        stringi_1.8.3    
[49] munsell_0.5.0     cachem_1.0.8