From 28d43ba45a574883402d9fdc0c2fdcf75954f399 Mon Sep 17 00:00:00 2001
From: Steve Phelps <phelps.sg@gmail.com>
Date: Fri, 29 Dec 2023 11:37:18 +0000
Subject: [PATCH] use persistent cache for memoization using mcapply and add
 theoretical predictions to GLMM interaction plot

---
 environment-frozen.yml       | 157 ++++++++++++++++++-----------------
 environment.yml              |   1 +
 jupyter-book/R-MixedModel.py |  80 ++++++++++++++++--
 3 files changed, 153 insertions(+), 85 deletions(-)

diff --git a/environment-frozen.yml b/environment-frozen.yml
index eff36ca..099f566 100644
--- a/environment-frozen.yml
+++ b/environment-frozen.yml
@@ -10,30 +10,30 @@ dependencies:
   - aiosignal=1.3.1=pyhd8ed1ab_0
   - alabaster=0.7.13=pyhd8ed1ab_0
   - annotated-types=0.6.0=pyhd8ed1ab_0
-  - anyio=3.7.1=pyhd8ed1ab_0
+  - anyio=4.2.0=pyhd8ed1ab_0
   - appdirs=1.4.4=pyh9f0ad1d_0
   - argon2-cffi=23.1.0=pyhd8ed1ab_0
   - argon2-cffi-bindings=21.2.0=py311h459d7ec_4
   - arrow=1.3.0=pyhd8ed1ab_0
   - asn1crypto=1.5.1=pyhd8ed1ab_0
-  - astroid=3.0.1=py311h38be061_0
+  - astroid=3.0.2=py311h38be061_0
   - asttokens=2.4.1=pyhd8ed1ab_0
   - async-lru=2.0.4=pyhd8ed1ab_0
   - attrs=23.1.0=pyh71513ae_1
-  - aws-c-auth=0.7.0=h435f46f_0
-  - aws-c-cal=0.6.0=h93469e0_0
-  - aws-c-common=0.8.23=hd590300_0
-  - aws-c-compression=0.2.17=h862ab75_1
-  - aws-c-event-stream=0.3.1=h1e03375_0
-  - aws-c-http=0.7.10=h9ab9c9b_2
-  - aws-c-io=0.13.27=h3870b5a_0
-  - aws-c-mqtt=0.8.13=hd4f18eb_5
-  - aws-c-s3=0.3.12=he2a37c1_2
-  - aws-c-sdkutils=0.1.11=h862ab75_1
-  - aws-checksums=0.1.16=h862ab75_1
-  - aws-crt-cpp=0.20.2=h2a5cb19_18
-  - aws-sdk-cpp=1.10.57=h7b9373a_16
-  - babel=2.13.1=pyhd8ed1ab_0
+  - aws-c-auth=0.7.8=h538f98c_2
+  - aws-c-cal=0.6.9=h5d48c4d_2
+  - aws-c-common=0.9.10=hd590300_0
+  - aws-c-compression=0.2.17=h7f92143_7
+  - aws-c-event-stream=0.3.2=h0bcb0bb_8
+  - aws-c-http=0.7.14=hd268abd_3
+  - aws-c-io=0.13.36=he0cd244_2
+  - aws-c-mqtt=0.10.0=h35285c7_0
+  - aws-c-s3=0.4.5=h0448019_0
+  - aws-c-sdkutils=0.1.13=h7f92143_0
+  - aws-checksums=0.1.17=h7f92143_6
+  - aws-crt-cpp=0.25.0=h1bbe558_2
+  - aws-sdk-cpp=1.11.210=h0853bfa_5
+  - babel=2.14.0=pyhd8ed1ab_0
   - backoff=2.2.1=pyhd8ed1ab_0
   - beautifulsoup4=4.12.2=pyha770c72_0
   - binutils_impl_linux-64=2.40=hf600244_0
@@ -41,12 +41,12 @@ dependencies:
   - blackd=23.12.1=hd8ed1ab_0
   - bleach=6.1.0=pyhd8ed1ab_0
   - blobfile=2.1.0=pyhd8ed1ab_0
-  - brotli=1.0.9=h166bdaf_9
-  - brotli-bin=1.0.9=h166bdaf_9
-  - brotli-python=1.0.9=py311ha362b79_9
+  - brotli=1.1.0=hd590300_1
+  - brotli-bin=1.1.0=hd590300_1
+  - brotli-python=1.1.0=py311hb755f60_1
   - bwidget=1.9.14=ha770c72_1
   - bzip2=1.0.8=hd590300_5
-  - c-ares=1.23.0=hd590300_0
+  - c-ares=1.24.0=hd590300_0
   - ca-certificates=2023.11.17=hbcca054_0
   - cached-property=1.5.2=hd8ed1ab_1
   - cached_property=1.5.2=pyha770c72_1
@@ -59,7 +59,7 @@ dependencies:
   - colorama=0.4.6=pyhd8ed1ab_0
   - comm=0.1.4=pyhd8ed1ab_0
   - contourpy=1.2.0=py311h9547e67_0
-  - cryptography=38.0.4=py311h42a1071_0
+  - cryptography=41.0.7=py311hcb13ee4_1
   - curl=8.5.0=hca28451_0
   - cycler=0.12.1=pyhd8ed1ab_0
   - dataclasses=0.8=pyhc8e2a94_3
@@ -67,7 +67,7 @@ dependencies:
   - decorator=5.1.1=pyhd8ed1ab_0
   - defusedxml=0.7.1=pyhd8ed1ab_0
   - dill=0.3.7=pyhd8ed1ab_0
-  - distlib=0.3.7=pyhd8ed1ab_0
+  - distlib=0.3.8=pyhd8ed1ab_0
   - distro=1.8.0=pyhd8ed1ab_0
   - docutils=0.17.1=py311h38be061_4
   - entrypoints=0.4=pyhd8ed1ab_0
@@ -84,11 +84,11 @@ dependencies:
   - fontconfig=2.14.2=h14ed4e7_0
   - fonts-conda-ecosystem=1=0
   - fonts-conda-forge=1=0
-  - fonttools=4.46.0=py311h459d7ec_0
+  - fonttools=4.47.0=py311h459d7ec_0
   - fqdn=1.5.1=pyhd8ed1ab_0
   - freetype=2.12.1=h267a509_2
   - fribidi=1.0.10=h36c2ea0_0
-  - frozenlist=1.4.0=py311h459d7ec_1
+  - frozenlist=1.4.1=py311h459d7ec_0
   - gcc_impl_linux-64=13.2.0=h338b0a0_3
   - gettext=0.21.1=h27087fc_0
   - gflags=2.2.2=he1b5a44_1004
@@ -96,14 +96,14 @@ dependencies:
   - glog=0.6.0=h6f12383_0
   - gmp=6.3.0=h59595ed_0
   - graphite2=1.3.13=h58526e2_1001
-  - greenlet=3.0.1=py311hb755f60_0
+  - greenlet=3.0.2=py311hb755f60_0
   - gxx_impl_linux-64=13.2.0=h338b0a0_3
   - h11=0.14.0=pyhd8ed1ab_0
   - h2=4.1.0=pyhd8ed1ab_0
   - harfbuzz=8.3.0=h3d44ed6_0
   - hpack=4.0.0=pyh9f0ad1d_0
   - httpcore=1.0.2=pyhd8ed1ab_0
-  - httpx=0.25.2=pyhd8ed1ab_0
+  - httpx=0.26.0=pyhd8ed1ab_0
   - hyperframe=6.0.1=pyhd8ed1ab_0
   - icu=73.2=h59595ed_0
   - identify=2.5.33=pyhd8ed1ab_0
@@ -117,7 +117,7 @@ dependencies:
   - ipython=8.19.0=pyh707e725_0
   - ipywidgets=8.1.1=pyhd8ed1ab_0
   - isoduration=20.11.0=pyhd8ed1ab_0
-  - isort=5.12.0=pyhd8ed1ab_1
+  - isort=5.13.2=pyhd8ed1ab_0
   - jedi=0.19.1=pyhd8ed1ab_0
   - jinja2=3.1.2=pyhd8ed1ab_1
   - joblib=1.3.2=pyhd8ed1ab_0
@@ -132,10 +132,10 @@ dependencies:
   - jupyter-lsp=2.2.1=pyhd8ed1ab_0
   - jupyter_client=8.6.0=pyhd8ed1ab_0
   - jupyter_console=6.6.3=pyhd8ed1ab_0
-  - jupyter_core=5.5.0=py311h38be061_0
+  - jupyter_core=5.5.1=py311h38be061_0
   - jupyter_events=0.9.0=pyhd8ed1ab_0
   - jupyter_server=2.12.1=pyhd8ed1ab_0
-  - jupyter_server_terminals=0.4.4=pyhd8ed1ab_1
+  - jupyter_server_terminals=0.5.0=pyhd8ed1ab_0
   - jupyterlab=4.0.9=pyhd8ed1ab_0
   - jupyterlab_pygments=0.3.0=pyhd8ed1ab_0
   - jupyterlab_server=2.25.2=pyhd8ed1ab_0
@@ -151,18 +151,21 @@ dependencies:
   - lcms2=2.16=hb7c19ff_0
   - ld_impl_linux-64=2.40=h41732ed_0
   - lerc=4.0.0=h27087fc_0
-  - libabseil=20230125.3=cxx17_h59595ed_0
-  - libarrow=12.0.0=hc410076_9_cpu
+  - libabseil=20230802.1=cxx17_h59595ed_0
+  - libarrow=14.0.2=hfb4d3a9_0_cpu
+  - libarrow-acero=14.0.2=h59595ed_0_cpu
+  - libarrow-dataset=14.0.2=h59595ed_0_cpu
+  - libarrow-substrait=14.0.2=h61ff412_0_cpu
   - libblas=3.9.0=20_linux64_openblas
-  - libbrotlicommon=1.0.9=h166bdaf_9
-  - libbrotlidec=1.0.9=h166bdaf_9
-  - libbrotlienc=1.0.9=h166bdaf_9
+  - libbrotlicommon=1.1.0=hd590300_1
+  - libbrotlidec=1.1.0=hd590300_1
+  - libbrotlienc=1.1.0=hd590300_1
   - libcblas=3.9.0=20_linux64_openblas
   - libcrc32c=1.1.2=h9c3ff4c_0
   - libcurl=8.5.0=hca28451_0
   - libdeflate=1.19=hd590300_0
   - libedit=3.1.20191231=he28a2e2_2
-  - libev=4.33=h516909a_1
+  - libev=4.33=hd590300_2
   - libevent=2.1.12=hf998b51_1
   - libexpat=2.5.0=hcb278e6_1
   - libffi=3.4.2=h7f98852_5
@@ -170,26 +173,27 @@ dependencies:
   - libgcc-ng=13.2.0=h807b86a_3
   - libgfortran-ng=13.2.0=h69a702a_3
   - libgfortran5=13.2.0=ha4646dd_3
-  - libglib=2.78.2=h783c2da_0
+  - libglib=2.78.3=h783c2da_0
   - libgomp=13.2.0=h807b86a_3
-  - libgoogle-cloud=2.12.0=hac9eb74_1
-  - libgrpc=1.54.3=hb20ce57_0
-  - libiconv=1.17=h166bdaf_0
+  - libgoogle-cloud=2.12.0=h5206363_4
+  - libgrpc=1.59.3=hd6c4280_0
+  - libiconv=1.17=hd590300_2
   - libjpeg-turbo=3.0.0=hd590300_1
   - liblapack=3.9.0=20_linux64_openblas
-  - libnghttp2=1.58.0=h47da74e_0
+  - libnghttp2=1.58.0=h47da74e_1
   - libnsl=2.0.1=hd590300_0
-  - libnuma=2.0.16=h0b41bf4_1
   - libopenblas=0.3.25=pthreads_h413a1c8_0
+  - libparquet=14.0.2=h352af49_0_cpu
   - libpng=1.6.39=h753d276_0
-  - libprotobuf=3.21.12=hfc55251_2
+  - libprotobuf=4.24.4=hf27288f_0
+  - libre2-11=2023.06.02=h7a70373_0
   - libsanitizer=13.2.0=h7e041cc_3
   - libsodium=1.0.18=h36c2ea0_1
   - libsqlite=3.44.2=h2797004_0
   - libssh2=1.11.0=h0841786_0
   - libstdcxx-devel_linux-64=13.2.0=ha9c7c90_103
   - libstdcxx-ng=13.2.0=h7e041cc_3
-  - libthrift=0.18.1=h8fd135c_2
+  - libthrift=0.19.0=hb90f79a_1
   - libtiff=4.6.0=ha9c0a0a_2
   - libutf8proc=2.8.0=h166bdaf_0
   - libuuid=2.38.1=h0b41bf4_0
@@ -201,7 +205,7 @@ dependencies:
   - libzlib=1.2.13=hd590300_5
   - linkify-it-py=2.0.0=pyhd8ed1ab_0
   - littleutils=0.2.2=py_0
-  - lxml=4.9.3=py311h1a07684_2
+  - lxml=4.9.3=py311h1a07684_3
   - lz4=4.3.2=py311h38e4bf4_1
   - lz4-c=1.9.4=hcb278e6_0
   - make=4.3=hd18ef5c_1
@@ -235,24 +239,23 @@ dependencies:
   - notebook=7.0.6=pyhd8ed1ab_0
   - notebook-shim=0.2.3=pyhd8ed1ab_0
   - nspr=4.35=h27087fc_0
-  - nss=3.95=h1d7d5a4_0
+  - nss=3.96=h1d7d5a4_0
   - numpy=1.26.2=py311h64a7726_0
   - openai=1.6.1=pyhd8ed1ab_0
   - openjpeg=2.5.0=h488ebb8_3
   - openssl=3.2.0=hd590300_1
-  - orc=1.8.4=h2f23424_0
-  - oscrypto=1.2.1=pyhd3deb0d_0
+  - orc=1.9.2=h4b38347_0
   - outdated=0.2.2=pyhd8ed1ab_0
   - overrides=7.4.0=pyhd8ed1ab_0
   - packaging=23.2=pyhd8ed1ab_0
   - pandas=2.1.4=py311h320fe9a_0
   - pandas-flavor=0.6.0=pyhd8ed1ab_1
-  - pandas-stubs=2.1.4.231218=pyhd8ed1ab_0
+  - pandas-stubs=2.1.4.231227=pyhd8ed1ab_0
   - pandoc=3.1.3=h32600fe_0
   - pandocfilters=1.5.0=pyhd8ed1ab_0
   - pango=1.50.14=ha41ecd1_2
   - parso=0.8.3=pyhd8ed1ab_0
-  - pathspec=0.11.2=pyhd8ed1ab_0
+  - pathspec=0.12.1=pyhd8ed1ab_0
   - patsy=0.5.4=pyhd8ed1ab_0
   - pcre2=10.42=hcad00b1_0
   - pexpect=4.8.0=pyh1a96a4e_2
@@ -268,13 +271,12 @@ dependencies:
   - portalocker=2.8.2=py311h38be061_1
   - pre-commit=3.6.0=pyha770c72_0
   - prometheus_client=0.19.0=pyhd8ed1ab_0
-  - prompt-toolkit=3.0.41=pyha770c72_0
-  - prompt_toolkit=3.0.41=hd8ed1ab_0
-  - psutil=5.9.5=py311h459d7ec_1
+  - prompt-toolkit=3.0.42=pyha770c72_0
+  - prompt_toolkit=3.0.42=hd8ed1ab_0
+  - psutil=5.9.7=py311h459d7ec_0
   - pthread-stubs=0.4=h36c2ea0_1001
   - ptyprocess=0.7.0=pyhd3deb0d_0
   - pure_eval=0.2.2=pyhd8ed1ab_0
-  - pyarrow=12.0.0=py311h39c9aba_9_cpu
   - pybtex=0.24.0=pyhd8ed1ab_2
   - pybtex-docutils=1.0.3=py311h38be061_1
   - pycparser=2.21=pyhd8ed1ab_0
@@ -286,7 +288,7 @@ dependencies:
   - pygments=2.17.2=pyhd8ed1ab_0
   - pyjwt=2.8.0=pyhd8ed1ab_0
   - pylint=3.0.3=pyhd8ed1ab_0
-  - pyopenssl=22.1.0=pyhd8ed1ab_0
+  - pyopenssl=23.3.0=pyhd8ed1ab_0
   - pyparsing=3.1.1=pyhd8ed1ab_0
   - pyppeteer=1.0.2=pyhd8ed1ab_0
   - pysocks=1.7.1=pyha2e5f31_6
@@ -308,7 +310,7 @@ dependencies:
   - qtpy=2.4.1=pyhd8ed1ab_0
   - r-abind=1.4_5=r43hc72bb7e_1005
   - r-ape=5.7_1=r43h08d816e_1
-  - r-arrow=12.0.0=r43h59595ed_1
+  - r-arrow=14.0.1=r43h59595ed_0
   - r-askpass=1.2.0=r43h57805ef_0
   - r-assertthat=0.2.1=r43hc72bb7e_4
   - r-backports=1.4.1=r43h57805ef_2
@@ -329,7 +331,7 @@ dependencies:
   - r-cellranger=1.1.0=r43hc72bb7e_1006
   - r-checkmate=2.3.0=r43h57805ef_0
   - r-class=7.3_22=r43h57805ef_1
-  - r-cli=3.6.1=r43ha503ecb_1
+  - r-cli=3.6.2=r43ha503ecb_0
   - r-clipr=0.8.0=r43hc72bb7e_2
   - r-clock=0.7.0=r43ha503ecb_1
   - r-coda=0.19_4=r43hc72bb7e_2
@@ -340,13 +342,13 @@ dependencies:
   - r-conquer=1.3.3=r43h08d816e_2
   - r-corpcor=1.6.10=r43hc72bb7e_2
   - r-corrplot=0.92=r43hc72bb7e_2
-  - r-cowplot=1.1.1=r43hc72bb7e_2
+  - r-cowplot=1.1.2=r43hc72bb7e_0
   - r-cpp11=0.4.7=r43hc72bb7e_0
   - r-crayon=1.5.2=r43hc72bb7e_2
   - r-crosstalk=1.2.1=r43hc72bb7e_0
   - r-cubature=2.0.4.6=r43hcf54a89_1
   - r-curl=5.1.0=r43hf9611b0_0
-  - r-data.table=1.14.8=r43h029312a_2
+  - r-data.table=1.14.10=r43h029312a_0
   - r-datawizard=0.9.0=r43hc72bb7e_0
   - r-dbi=1.1.3=r43hc72bb7e_2
   - r-dbplyr=2.4.0=r43hc72bb7e_0
@@ -363,7 +365,7 @@ dependencies:
   - r-emmeans=1.9.0=r43hc72bb7e_0
   - r-estimability=1.4.1=r43hc72bb7e_2
   - r-evaluate=0.23=r43hc72bb7e_0
-  - r-fansi=1.0.5=r43h57805ef_0
+  - r-fansi=1.0.6=r43h57805ef_0
   - r-farver=2.1.1=r43ha503ecb_2
   - r-fastmap=1.1.1=r43ha503ecb_1
   - r-fontawesome=0.5.2=r43hc72bb7e_0
@@ -429,10 +431,10 @@ dependencies:
   - r-mass=7.3_60=r43h57805ef_1
   - r-matrix=1.6_0=r43h316c678_0
   - r-matrixmodels=0.5_3=r43hc72bb7e_0
-  - r-matrixstats=1.1.0=r43h57805ef_0
+  - r-matrixstats=1.2.0=r43h57805ef_0
   - r-mcmcglmm=2.35=r43ha503ecb_0
   - r-memoise=2.0.1=r43hc72bb7e_2
-  - r-mgcv=1.9_0=r43h316c678_0
+  - r-mgcv=1.9_1=r43h316c678_0
   - r-mime=0.12=r43h57805ef_2
   - r-minqa=1.2.6=r43hcf54a89_0
   - r-mitools=2.4=r43hc72bb7e_4
@@ -460,7 +462,7 @@ dependencies:
   - r-polynom=1.4_1=r43hc72bb7e_2
   - r-prettyunits=1.2.0=r43hc72bb7e_0
   - r-proc=1.18.5=r43ha503ecb_0
-  - r-processx=3.8.2=r43h57805ef_0
+  - r-processx=3.8.3=r43h57805ef_0
   - r-prodlim=2023.08.28=r43ha503ecb_0
   - r-progress=1.2.3=r43hc72bb7e_0
   - r-progressr=0.14.0=r43hc72bb7e_0
@@ -470,11 +472,12 @@ dependencies:
   - r-purrr=1.0.2=r43h57805ef_0
   - r-qgam=1.3.4=r43h57805ef_2
   - r-quantreg=5.97=r43hd9ac46e_0
+  - r-r.cache=0.16.0=r43hc72bb7e_2
   - r-r.methodss3=1.8.2=r43hc72bb7e_2
   - r-r.oo=1.25.0=r43hc72bb7e_2
   - r-r.utils=2.12.3=r43hc72bb7e_0
   - r-r6=2.5.1=r43hc72bb7e_2
-  - r-ragg=1.2.6=r43h73ae6e3_0
+  - r-ragg=1.2.7=r43h73ae6e3_0
   - r-rappdirs=0.3.3=r43h57805ef_2
   - r-rcolorbrewer=1.1_3=r43h785f33e_2
   - r-rcpp=1.0.11=r43h7df8631_0
@@ -483,7 +486,7 @@ dependencies:
   - r-rcpptoml=0.2.2=r43ha503ecb_1
   - r-readr=2.1.4=r43ha503ecb_1
   - r-readxl=1.4.3=r43ha5c9fba_0
-  - r-recipes=1.0.8=r43hc72bb7e_0
+  - r-recipes=1.0.9=r43hc72bb7e_0
   - r-rematch=2.0.0=r43hc72bb7e_0
   - r-rematch2=2.1.2=r43hc72bb7e_3
   - r-repr=1.1.6=r43h785f33e_1
@@ -514,7 +517,7 @@ dependencies:
   - r-squarem=2021.1=r43hc72bb7e_2
   - r-stargazer=5.2.3=r43hc72bb7e_2
   - r-statmod=1.5.0=r43hd8f1df9_1
-  - r-stringi=1.8.2=r43h9facbd6_0
+  - r-stringi=1.8.3=r43h9facbd6_0
   - r-stringr=1.5.1=r43h785f33e_0
   - r-survey=4.2_1=r43hc72bb7e_1
   - r-survival=3.5_7=r43h57805ef_0
@@ -530,7 +533,7 @@ dependencies:
   - r-tidyselect=1.2.0=r43hc72bb7e_1
   - r-tidyverse=2.0.0=r43h785f33e_1
   - r-timechange=0.2.0=r43ha503ecb_1
-  - r-timedate=4022.108=r43hc72bb7e_1
+  - r-timedate=4032.109=r43hc72bb7e_0
   - r-tinytex=0.49=r43hc72bb7e_0
   - r-tmb=1.9.6=r43h08d816e_0
   - r-tzdb=0.4.0=r43ha503ecb_1
@@ -545,19 +548,18 @@ dependencies:
   - r-xfun=0.41=r43ha503ecb_0
   - r-xml2=1.3.6=r43h1ad5fc0_0
   - r-xtable=1.8_4=r43hc72bb7e_5
-  - r-yaml=2.3.7=r43h57805ef_1
+  - r-yaml=2.3.8=r43h57805ef_0
   - r-zoo=1.8_12=r43h57805ef_1
-  - rdma-core=28.9=h59595ed_1
-  - re2=2023.03.02=h8c504da_0
+  - re2=2023.06.02=h2873b5e_0
   - readline=8.2=h8228510_1
-  - referencing=0.31.1=pyhd8ed1ab_0
+  - referencing=0.32.0=pyhd8ed1ab_0
   - regex=2023.10.3=py311h459d7ec_0
   - requests=2.31.0=pyhd8ed1ab_0
   - rfc3339-validator=0.1.4=pyhd8ed1ab_0
   - rfc3986-validator=0.1.1=pyh9f0ad1d_0
-  - rpds-py=0.13.2=py311h46250e7_0
-  - s2n=1.3.46=h06160fa_0
-  - sacrebleu=2.3.3=pyhd8ed1ab_0
+  - rpds-py=0.15.2=py311h46250e7_0
+  - s2n=1.4.0=h06160fa_0
+  - sacrebleu=2.4.0=pyhd8ed1ab_0
   - scikit-learn=1.3.2=py311hc009520_2
   - scipy=1.11.4=py311h64a7726_0
   - seaborn=0.13.0=hd8ed1ab_0
@@ -593,7 +595,7 @@ dependencies:
   - sqlalchemy=2.0.23=py311h459d7ec_0
   - sqlite=3.44.2=h2c6b66d_0
   - stack_data=0.6.2=pyhd8ed1ab_0
-  - statsmodels=0.14.0=py311h1f0f07a_2
+  - statsmodels=0.14.1=py311h1f0f07a_0
   - sysroot_linux-64=2.12=he073ed8_16
   - tabulate=0.9.0=pyhd8ed1ab_1
   - tenacity=8.2.3=pyhd8ed1ab_0
@@ -613,12 +615,11 @@ dependencies:
   - types-python-dateutil=2.8.19.14=pyhd8ed1ab_0
   - types-pytz=2023.3.1.1=pyhd8ed1ab_0
   - typing=3.10.0.0=pyhd8ed1ab_0
-  - typing-extensions=4.8.0=hd8ed1ab_0
-  - typing_extensions=4.8.0=pyha770c72_0
+  - typing-extensions=4.9.0=hd8ed1ab_0
+  - typing_extensions=4.9.0=pyha770c72_0
   - typing_utils=0.1.0=pyhd8ed1ab_0
   - tzdata=2023c=h71feb2d_0
   - uc-micro-py=1.0.1=pyhd8ed1ab_0
-  - ucx=1.14.1=h64cca9d_5
   - ukkonen=1.0.1=py311h9547e67_4
   - uri-template=1.3.0=pyhd8ed1ab_0
   - urllib3=1.26.18=pyhd8ed1ab_0
@@ -630,7 +631,7 @@ dependencies:
   - websockets=10.4=py311hd4cff14_1
   - wheel=0.42.0=pyhd8ed1ab_0
   - widgetsnbextension=4.0.9=pyhd8ed1ab_0
-  - xarray=2023.11.0=pyhd8ed1ab_0
+  - xarray=2023.12.0=pyhd8ed1ab_0
   - xorg-kbproto=1.0.7=h7f98852_1002
   - xorg-libice=1.1.1=hd590300_0
   - xorg-libsm=1.2.4=h7391055_0
diff --git a/environment.yml b/environment.yml
index 7b336bd..612259f 100644
--- a/environment.yml
+++ b/environment.yml
@@ -45,6 +45,7 @@ dependencies:
   - r-effects
   - r-sjPlot
   - r-patchwork
+  - r-R.cache
   - pip
   - pip:
     - -e ./
diff --git a/jupyter-book/R-MixedModel.py b/jupyter-book/R-MixedModel.py
index 152234c..5a93a2e 100644
--- a/jupyter-book/R-MixedModel.py
+++ b/jupyter-book/R-MixedModel.py
@@ -35,6 +35,7 @@
 library(purrr)
 library(memoise)
 library(patchwork)
+library(R.cache)
 
 # %%
 options(repr.plot.width = 20, repr.plot.height = 10)
@@ -105,12 +106,23 @@
 
 # %%
 results.clean$Participant_group <- relevel(results.clean$Participant_group, ref='Control')
-results.clean$Partner_condition <- relevel(results.clean$Partner_condition, ref='T4TD')
+results.clean$Partner_condition <- relevel(results.clean$Partner_condition, ref='D')
 results.clean$Model <- relevel(results.clean$Model, ref='gpt-3.5-turbo-0613')
 results.clean$Participant_pronoun <- relevel(results.clean$Participant_pronoun, ref='they')
 results.clean$Participant_case <- relevel(results.clean$Participant_case, ref='standard')
 results.clean$Particpant_label <- relevel(results.clean$Participant_label, ref='colors')
 
+# %%
+levels(results.clean$Partner_condition)
+
+# %%
+results.clean$Partner_condition <- 
+    factor(results.clean$Partner_condition, 
+           levels = c('D', 'T4TD', 'T4TC', 'C'))
+
+# %%
+levels(results.clean$Partner_condition)
+
 # %%
 names(results.clean)
 
@@ -211,6 +223,54 @@
 # %%
 xtable(coef(summary(model.pd))$cond, digits=3)
 
+# %%
+theoretical.altruistic <- list(D=1, C=1, T4TD=1, T4TC=1)
+theoretical.altruistic
+
+# %%
+theoretical.data <- function(group, frequencies) {
+    result <- data.frame(x = as.factor(c('D', 'T4TD', 'T4TC', 'C')), 
+                                      predicted = frequencies, 
+                                      std.error = rep(0, 4),
+                                      conf.low = frequencies,
+                                      conf.high = frequencies,
+                                      group = as.factor(rep('theoretical', 4)),
+                                      facet = as.factor(rep(group, 4))
+                                     )
+    return(result)
+}
+
+theoretical.df <- function(group) {
+    case_when(
+        group == 'Selfish'     ~ theoretical.data('Selfish',     c(0, 0, 0, 0)),
+        group == 'Cooperative' ~ theoretical.data('Cooperative', c(1/6, 3/6, 1, 1)),
+        group == 'Competitive' ~ theoretical.data('Competitive', c(1/6, 1/6, 1/6, 1/6)),
+        group == 'Altruistic'  ~ theoretical.data('Altruistic',  c(1, 1, 1, 1)),
+        group == 'Control'     ~ theoretical.data('Control',     c(NA, NA, NA, NA))
+    )
+}
+
+# %%
+x.df <- theoretical.df("Selfish")
+x.df
+
+# %%
+y.df <- predictions.for.m("gpt-3.5-turbo-1106", "Selfish")
+y.df
+
+# %%
+names(x.df)
+
+# %%
+names(y.df)
+
+# %%
+merged.df <- rbind(x.df, y.df)
+levels(merged.df$group)
+
+# %%
+levels(merged.df$x)
+
 # %%
 predictions.for <- function(model, participant.group) {
     ggpredict(model.pd.1, c("Partner_condition", 
@@ -218,7 +278,7 @@
                             sprintf("Participant_group [%s]", participant.group)))
 }
 
-predictions.for.m <- memoise(predictions.for)
+predictions.for.m <- addMemoization(predictions.for)
 
 # %%
 interaction.plots <- function(participant.group, legend) {    
@@ -226,17 +286,23 @@
                             function(model) predictions.for.m(model, participant.group), 
                             mc.cores=12) 
     combined <- reduce(predictions, rbind)
-    names(combined)[6] <- 'model'
+    combined <- rbind(combined, theoretical.df(participant.group))
+    names(combined)[6] <- 'Model'
     
     p <- ggplot(combined) +
-        aes(x = x, y = predicted, group = model) + 
+        aes(x = x, y = predicted, group = Model) + 
         geom_errorbar(aes(ymin = conf.low, ymax = conf.high), width = .1, position = position_dodge(0.06)) +
-        geom_line(aes(color=model), size = 1) + scale_y_continuous(limits = c(0.1, 1)) +
+        geom_line(aes(color=Model), size = 1) + scale_y_continuous(limits = c(0, 1)) +
         scale_color_brewer(palette = "Dark2", direction = -1) +       
         labs(title = sprintf("Group: %s", participant.group), 
-             x = "Partner condition", y = "Probability of cooperation")
+             x = "Partner condition", y = "Probability of cooperation") +
+         theme(legend.title = element_text(size=16), 
+                legend.text = element_text(size=14)) 
     if (!legend) {
         p <- p + theme(legend.position = "none")
+    } else {
+        p <- p + theme(legend.title = element_text(size=16), 
+                        legend.text = element_text(size=14))
     }
     return(p)
 }
@@ -256,7 +322,7 @@
 
 # %%
 combined.plots <- all.interaction.plots()
-pdf("figs/interaction-plots-all.pdf", width=9, height=10)
+pdf("figs/interaction-plots-all.pdf", width=8, height=11)
 print(combined.plots)
 dev.off()
 combined.plots