{ "cells": [ { "cell_type": "markdown", "id": "02220643", "metadata": {}, "source": [ "# Tutorial for R Users\n", "\n", "In this tutorial, we will go through CausalBGM workflow with the R package **bayesgm**.\n", "\n", "First of all, you need to install , please refer to the [install page](https://bayesgm.readthedocs.io/en/latest/getting-started/installation.html) to make sure **bayesgm** R package is installed.\n" ] }, { "cell_type": "markdown", "id": "45918c1d", "metadata": {}, "source": [ "
\n", "Notes\n", "\n", "- *bayesgm* R package was developed based on *[reticulate](https://rstudio.github.io/reticulate/)* package, which enables building R APIs based on Python APIs. Make sure the dependency R packages are installed.\n", "- The R APIs are consistent with Python APIs, detailed usage of CausalBGM APIs can be found at **[online document](https://bayesgm.readthedocs.io/en/latest/api/models.html#causalbgm-family)**.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "id": "a18375c0-d4f8-4ea0-a529-d24ea0ff3aa6", "metadata": {}, "outputs": [], "source": [ "library(bayesgm)" ] }, { "cell_type": "markdown", "id": "3c0db7a5-c226-47ed-b496-b8cdf55df377", "metadata": {}, "source": [ "## Dependencies" ] }, { "cell_type": "markdown", "id": "6772b6c0-5895-406f-ab5e-3954bf1cf65a", "metadata": {}, "source": [ "
\n", "Reminder\n", "\n", "- Install the following dependent R packages for running the whole workflow.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "id": "65fabfc9-9b1f-4bb4-af2f-dc727ca7d758", "metadata": {}, "outputs": [], "source": [ "#install.packages(c(\"reticulate\", \"lattice\", \"Matrix\", \"R6\",\"png\"))" ] }, { "cell_type": "markdown", "id": "26ddfaa3-ef55-4a97-abfc-93ab35d30d22", "metadata": {}, "source": [ "
\n", "Notes\n", "\n", "The function **configure_bayesgm()** specifies:\n", "\n", "* **python**: the path to the Python executable used by *reticulate*\n", "* **pythonpath**: the directory containing the *bayesgm* Python source code\n", " \n", "Make sure to replace with your **own paths** here. After configuration, you can verify that the Python backend is available by running:\n", "**stopifnot(bayesgm_available(configure = FALSE))**\n", "\n", "If the configuration is correct, this command will run silently; otherwise it will raise an error indicating that the Python environment or package cannot be located.\n", "\n", "You may also run **reticulate::py_config()** to check which Python environment is currently being used by R.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 3, "id": "dcad5a4d-8583-4910-8d77-6eda512de1ce", "metadata": {}, "outputs": [], "source": [ "configure_bayesgm(\n", " python = \"~/.conda/envs/py3.9/bin/python\",\n", " pythonpath = \"/home/ql339/project_pi_ql339/ql339/bayesgm/src\"\n", ")\n", "stopifnot(bayesgm_available(configure = FALSE))" ] }, { "cell_type": "markdown", "id": "d389c67f", "metadata": {}, "source": [ "## Binary treatment \n", "\n", "We first give a step-by-step tutorial for implementing CausalBGM under binary treatment settings." ] }, { "cell_type": "markdown", "id": "9cc35789", "metadata": {}, "source": [ "### Data generation\n", "\n", "Let's load a ACIC2018 simulation dataset (ufid='629e3d2c63914e45b227cc913c09cebe') with binary treatment.\n", "\n", "The data contain treatment (*X*), potential outcome (*Y*), and covariates (*V*)." ] }, { "cell_type": "code", "execution_count": 4, "id": "a215a593", "metadata": {}, "outputs": [], "source": [ "data(\"acic_2018_example\", package = \"bayesgm\")\n", "\n", "ufid <- acic_2018_example$ufid\n", "x <- acic_2018_example$x\n", "y <- acic_2018_example$y\n", "v <- acic_2018_example$v\n", "ite_true <- acic_2018_example$ite_true\n", "ate_true <- acic_2018_example$ate_true" ] }, { "cell_type": "markdown", "id": "829d7fed", "metadata": {}, "source": [ "Let's take a look at the simulation data." ] }, { "cell_type": "code", "execution_count": 5, "id": "588d2f27", "metadata": {}, "outputs": [ { "data": { "image/png": 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deH0FJWdinLkw/sQ5ggM0HVJ6m3JhRF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DpAHTrwHSDtT/gR8s/P34MaxzGnGC26ts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\nyYUPJaldAPg6Ntypdy3plra/AscH4U7gAPd5Bxe3PwGPwIZG9c4Afh+EbwQ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"text/plain": [ "Plot with title “Distribution of covariates”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "par(cex=0.7, mai=c(0.1,0.1,0.2,0.1))\n", "par(fig=c(0.1,0.5,0.5,1.0))\n", "slices <- c(sum(x==1), sum(x==0))\n", "lbls <- c(paste(\"T group:\",round(sum(x==1)*100/length(x), 2), \"%\", sep=\"\"), paste(\"C group:\",round(sum(x==0)*100/length(x), 2), \"%\", sep=\"\"))\n", "pie(slices, labels = lbls, main=\"Treatment Variables\")\n", "par(fig=c(0.5,1,0.5,1), new=TRUE)\n", "hist(y, breaks=12, col=\"red\",xlab=\"y values\")\n", "par(fig=c(0.1,1.0,0.1,0.4), new=TRUE)\n", "boxplot(v, main=\"Distribution of covariates\", xlab=\"Covariate index\", ylab=\"Values\")" ] }, { "cell_type": "markdown", "id": "9b2abaf2-2785-4d17-9e17-f59db217501d", "metadata": {}, "source": [ "### Instantiate a CausalBGM model\n", "\n", "Before creating a CausalBGM model, parameters are needed for configing a CausalBGM model, which are described as follows.\n", "\n", "#### General Parameters\n", "| Config Parameter | Description |\n", "|-------------------------|-------------|\n", "| `dataset` | Dataset name to indicate the input data. *Default: 'Sim_Hirano_Imbens'.* |\n", "| `output_dir` | Output directory to save the results during the model training. *Default: '.'.* |\n", "| `save_res` | Whether to save intermediate results. *Default: TRUE.* |\n", "| `save_model` | Whether to save the model after training. *Default: FALSE.* |\n", "| `binary_treatment` | Whether to use binary treatment settings. *Default: FALSE.* |\n", "| `use_bnn` | Whether to use Bayesian neural networks. *Default: TRUE.* |\n", "\n", "#### Parameters for Iterative Updating Algorithm\n", "| Config Parameter | Description |\n", "|-------------------------|-------------|\n", "| `z_dims` | Latent dimensions of `Z`. *Default: c(3L, 6L, 3L, 6L).* |\n", "| `v_dim` | Dimension of covariates. *Default: 200.* |\n", "| `lr_theta` | Learning rate for updating model parameters. *Default: 0.0001.* |\n", "| `lr_z` | Learning rate for updating latent variables. *Default: 0.0001.* |\n", "| `g_units` | Number of units for covariates generative model. *Default: c(64L, 64L, 64L, 64L, 64L).* |\n", "| `f_units` | Number of units for outcome generative model. *Default: c(64L, 32L, 8L).* |\n", "| `h_units` | Number of units for treatment generative model. *Default: c(64L, 32L, 8L).* |\n", "\n", "#### Parameters for EGM Initialization\n", "| Config Parameter | Description |\n", "|-------------------------|-------------|\n", "| `kl_weight` | Coefficient for KL divergence term in BNNs. *Default: 0.0001.* |\n", "| `lr` | Learning rate for EGM initialization. *Default: 0.0002.* |\n", "| `g_d_freq` | Frequency for updating discriminators and generators. *Default: 5.* |\n", "| `use_z_rec` | Whether to use reconstruction for latent features. *Default: True.* |\n", "| `e_units` | Number of units for the encoder network. *Default: c(64L, 64L, 64L, 64L, 64L).* |\n", "| `dz_units` | Number of units for the discriminator network in latent space. *Default: c(64L, 32L, 8L).* |" ] }, { "cell_type": "code", "execution_count": 6, "id": "08bfcc0e-a806-4f16-8d3c-04cb4fcde3f6", "metadata": {}, "outputs": [], "source": [ "params <- list(\n", " dataset = \"Semi_acic\",\n", " output_dir = tempdir(),\n", " save_res = FALSE,\n", " save_model = FALSE,\n", " binary_treatment = TRUE,\n", " use_bnn = TRUE,\n", " z_dims = c(3L, 6L, 3L, 6L),\n", " v_dim = 177L,\n", " lr_theta = 0.0001,\n", " lr_z = 0.0001,\n", " g_units = c(64L, 64L, 64L, 64L, 64L),\n", " f_units = c(64L, 32L, 8L),\n", " h_units = c(64L, 32L, 8L),\n", " kl_weight = 0.0001,\n", " lr = 0.0002,\n", " g_d_freq = 5L,\n", " use_z_rec = TRUE,\n", " e_units = c(64L, 64L, 64L, 64L, 64L),\n", " dz_units = c(64L, 32L, 8L)\n", ")\n", "\n", "model <- CausalBGM(params = params, random_seed = NULL)" ] }, { "cell_type": "markdown", "id": "4d8db7db", "metadata": {}, "source": [ "### Model training\n", "\n", "Train CausalBGM with an optional EGM warm-start. \n", "\n", "| Config Parameter | Description |\n", "|-------------------------|-------------|\n", "| `x` | Treatment, *Required.* |\n", "| `y` | Outcome, *Required.* |\n", "| `v` | Covariates, *Required.* |\n", "| `batch_size` | Batch size for training. *Default: 32.* |\n", "| `epochs` | Number of epochs for training. *Default: 100.* |\n", "| `epochs_per_eval` | Frequency of evaluations during training (e.g., every 5 epochs). *Default: 5.* |\n", "| `use_egm_init` | Whether to run EGM initialization before iterative training. *Default: True.* |\n", "| `epochs_per_eval` | Frequency of evaluations during training (e.g., every 5 epochs). *Default: 5.* |\n", "| `egm_n_iter` | Number of EGM initialization iterations. *Default: 30000.* |\n", "| `egm_batches_per_eval` | Evaluate EGM initialization every this many iterations. *Default: 500.* |\n", "| `verbose` | Controls verbosity level, showing progress and evaluation metrics. *Default: 1.* |\n" ] }, { "cell_type": "markdown", "id": "4059811a-8a1a-4a3f-9ac4-e24ff05624cd", "metadata": {}, "source": [ "
\n", "Notes\n", " \n", "The training procedure consists of two phases:\n", "- **EGM initialization** (optional) — warm-start to obtain a good starting point for the latent variables and model parameters. This phase is optional and can be skipped by setting *use_egm_init* to False.\n", "- **Stochastic iterative updating** — alternates between updating the generator network parameters \n", " and the per-sample latent variables via stochastic gradient optimization.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 7, "id": "063096bf", "metadata": {}, "outputs": [], "source": [ "model <- model$fit(\n", " x = x,\n", " y = y,\n", " v = v,\n", " epochs = 100L,\n", " epochs_per_eval = 10L,\n", " batch_size = 32L,\n", " use_egm_init = TRUE,\n", " egm_n_iter = 30000L,\n", " egm_batches_per_eval = 500L,\n", " verbose = 1L\n", ")" ] }, { "cell_type": "markdown", "id": "c95ac08a-0fe2-4b24-9590-a63eaf4a96b8", "metadata": {}, "source": [ "### Model Prediction\n", "\n", "Estimate causal effects with posterior intervals from latent MCMC samples.\n", "\n", "| Config Parameter | Description |\n", "|-------------------------|-------------|\n", "| `x` | Treatment, *Required.* |\n", "| `y` | Outcome, *Required.* |\n", "| `v` | Covariates, *Required.* |\n", "| `alpha` | Significance level for the posterior interval. *Default: 0.01.* |\n", "| `n_mcmc` | Number of posterior MCMC samples to draw. *Default: 3000.* |\n", "| `burn_in` | Number of burn-in MCMC samples before drawing. *Default: 5000.* |\n", "| `q_sd` | Standard deviation for the proposal distribution used in Metropolis-Hastings (MH) sampling. *Default: 1.0.* |\n", "| `sample_y` | Whether to consider the variance function in the outcome generative model. *Default: True.* |\n", "| `bs` | Batch size in inference stage, denoting number of test subjects processed per batch prediction. *Default: 10000.* |\n", "\n", "| Return | Type | Description | Shape |\n", "|------------|---------------|---------------------------------------------------------------------------------------------------------|-------------|\n", "| `res$effect` | `numeric vector` | Point estimates of the Individual Treatment Effect (ITE). | `(length(x))` |\n", "| `res$interval` | `numeric matrix` | Posterior intervals for the ITEs, representing `[lower bound, upper bound]` | `(length(x), 2)` " ] }, { "cell_type": "code", "execution_count": 8, "id": "9a31c4d4-2176-4a61-89bc-cecad0352c9f", "metadata": {}, "outputs": [], "source": [ "res <- model$predict(\n", " x = x,\n", " y = y,\n", " v = v,\n", " alpha = 0.01,\n", " n_mcmc = 3000L,\n", " burn_in = 5000L,\n", " q_sd = 1.0\n", ")\n", "pred_ite <- as.numeric(res$effect)\n", "pred_interval <- as.matrix(res$interval)" ] }, { "cell_type": "markdown", "id": "1c5b1445-e4b7-4e68-b045-9790b1506f09", "metadata": {}, "source": [ "### Model Evaluation\n", "\n", "For this ACIC example, the package dataset includes the ground-truth\n", "counterfactual outcomes, so the true individual treatment effects and average\n", "treatment effect are available directly." ] }, { "cell_type": "code", "execution_count": 9, "id": "324b64dc-602f-4747-96d3-7951e72334c5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Delta ATE (Absolute Error in Average Treatment Effect): 0.0037\n", "Delta PEHE (Precision in Estimation of Heterogeneous Effect): 0.0002\n" ] } ], "source": [ "pred_ate <- mean(pred_ite)\n", "delta_ate <- abs(pred_ate - ate_true)\n", "delta_pehe <- mean((pred_ite - ite_true)^2)\n", "\n", "\n", "cat(sprintf(\n", " \"Delta ATE (Absolute Error in Average Treatment Effect): %.4f\\n\",\n", " delta_ate\n", "))\n", "cat(sprintf(\n", " \"Delta PEHE (Precision in Estimation of Heterogeneous Effect): %.4f\\n\",\n", " delta_pehe\n", "))" ] }, { "cell_type": "markdown", "id": "6d56a3f0", "metadata": {}, "source": [ "## Continuous treatment\n", "\n", "We first give a step-by-step tutorial for implementing CausalBGM under continuous treatment settings. We use the Hirano and Imbens simulation dataset for an example." ] }, { "cell_type": "code", "execution_count": 10, "id": "17e556b7", "metadata": {}, "outputs": [], "source": [ "sim_data <- load_sim_hirano_imbens(N = 20000L, v_dim = 200L, seed = 0L)\n", "\n", "x <- sim_data$x\n", "y <- sim_data$y\n", "v <- sim_data$v\n", "grid_val <- seq(0, 3, length.out = 20)\n", "true_effect <- grid_val + 2 * (1 + grid_val)^(-3)" ] }, { "cell_type": "markdown", "id": "59e2b0b6", "metadata": {}, "source": [ "Let's take a look at the simulation data." ] }, { "cell_type": "code", "execution_count": 11, "id": "ee636384", "metadata": {}, "outputs": [ { "data": { "image/png": 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EnlmA2sQ7EJ3VJgBsU5MyH6JT1S27AkSVozJkiSpHLMBf6bqDG6KJU9lpZbAz8F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o9UnfmZCP4D2JyvT/JbufusphPjLSjTo1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\nbXTbiy++SFtb2xXAd/osGgy0Dx06tC7rPvO9996jqSnbceV33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"text/plain": [ "Plot with title “First 20 covariates”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "par(cex=0.7, mai=c(0.1,0.1,0.2,0.1))\n", "par(fig=c(0.1,0.5,0.5,1.0))\n", "hist(x, breaks=\"FD\", xlim=c(0,7), col=\"blue\",xlab=\"x values\")\n", "par(fig=c(0.5,1,0.5,1), new=TRUE)\n", "hist(y, breaks=\"FD\", xlim=c(0,7), col=\"red\",xlab=\"y values\")\n", "par(fig=c(0.1,1.0,0.1,0.4), new=TRUE)\n", "boxplot(v[,1:20],main=\"First 20 covariates\", xlab=\"Covariate index\", ylab=\"v values\")\n" ] }, { "cell_type": "markdown", "id": "d8a026b6-2013-4777-9236-9d9cec576071", "metadata": {}, "source": [ "### Instantiate a CausalBGM model" ] }, { "cell_type": "code", "execution_count": 12, "id": "e75ad9ea-1df4-44c0-a002-1ab360538781", "metadata": {}, "outputs": [], "source": [ "params <- list(\n", " dataset = \"Sim_Hirano_Imbens\",\n", " output_dir = tempdir(),\n", " save_res = FALSE,\n", " save_model = FALSE,\n", " binary_treatment = FALSE,\n", " use_bnn = TRUE,\n", " z_dims = c(1L, 1L, 1L, 7L),\n", " v_dim = 20L,\n", " lr_theta = 0.0001,\n", " lr_z = 0.0001,\n", " g_units = c(64L, 64L, 64L, 64L, 64L),\n", " f_units = c(64L, 32L, 8L),\n", " h_units = c(64L, 32L, 8L),\n", " kl_weight = 0.0001,\n", " lr = 0.0002,\n", " g_d_freq = 5L,\n", " use_z_rec = TRUE,\n", " e_units = c(64L, 64L, 64L, 64L, 64L),\n", " dz_units = c(64L, 32L, 8L)\n", ")\n", "\n", "model <- CausalBGM(params = params, random_seed = NULL)" ] }, { "cell_type": "markdown", "id": "d79df242", "metadata": {}, "source": [ "### Model Training\n", "\n", "Train CausalBGM with an optional EGM warm-start. \n", "\n", "| Config Parameter | Description |\n", "|-------------------------|-------------|\n", "| `x` | Treatment, *Required.* |\n", "| `y` | Outcome, *Required.* |\n", "| `v` | Covariates, *Required.* |\n", "| `batch_size` | Batch size for training. *Default: 32.* |\n", "| `epochs` | Number of epochs for training. *Default: 100.* |\n", "| `epochs_per_eval` | Frequency of evaluations during training (e.g., every 5 epochs). *Default: 5.* |\n", "| `use_egm_init` | Whether to run EGM initialization before iterative training. *Default: True.* |\n", "| `epochs_per_eval` | Frequency of evaluations during training (e.g., every 5 epochs). *Default: 5.* |\n", "| `egm_n_iter` | Number of EGM initialization iterations. *Default: 30000.* |\n", "| `egm_batches_per_eval` | Evaluate EGM initialization every this many iterations. *Default: 500.* |\n", "| `verbose` | Controls verbosity level, showing progress and evaluation metrics. *Default: 1.* |" ] }, { "cell_type": "code", "execution_count": 13, "id": "c0835f43", "metadata": {}, "outputs": [], "source": [ "model <- model$fit(\n", " x = x,\n", " y = y,\n", " v = v,\n", " epochs = 100L,\n", " epochs_per_eval = 10L,\n", " batch_size = 32L,\n", " use_egm_init = TRUE,\n", " egm_n_iter = 30000L,\n", " egm_batches_per_eval = 500L,\n", " verbose = 1L\n", ")" ] }, { "cell_type": "markdown", "id": "8fe9b2ee-f30d-4f18-ab0d-b05cda43ddb3", "metadata": {}, "source": [ "### Model Prediction\n", "\n", "Estimate causal effects with posterior intervals from latent MCMC samples.\n", "\n", "| Config Parameter | Description |\n", "|-------------------------|-------------|\n", "| `x` | Treatment, *Required.* |\n", "| `y` | Outcome, *Required.* |\n", "| `v` | Covariates, *Required.* |\n", "| `alpha` | Significance level for the posterior interval. *Default: 0.01.* |\n", "| `n_mcmc` | Number of posterior MCMC samples to draw. *Default: 3000.* |\n", "| `burn_in` | Number of burn-in MCMC samples before drawing. *Default: 5000.* |\n", "| `x_values` | Treatment value(s) for dose-response function to be predicted. *Examples: 1.0 or c(1.0, 2.0)* |\n", "| `q_sd` | Standard deviation for the proposal distribution used in Metropolis-Hastings (MH) sampling. *Default: 1.0.* |\n", "| `sample_y` | Whether to consider the variance function in the outcome generative model. *Default: True.* |\n", "| `bs` | Batch size in inference stage, denoting number of test subjects processed per batch prediction. *Default: 10000.* |\n", "\n", "\n", "| Return | Type | Description | Shape |\n", "|------------|---------------|---------------------------------------------------------------------------------------------------------|-------------|\n", "| `res$effect` | `numeric vector` | Point estimates of the Average Dose-Response Function. | `(length(x_values))` |\n", "| `res$interval` | `numeric matrix` | Posterior intervals for the ADRF, representing `[lower bound, upper bound]` | `(length(x_values), 2)` " ] }, { "cell_type": "code", "execution_count": 14, "id": "7a4c0393-680c-41b1-9836-034543dc020f", "metadata": {}, "outputs": [], "source": [ "res <- model$predict(\n", " x = x,\n", " y = y,\n", " v = v,\n", " alpha = 0.05,\n", " x_values = grid_val,\n", " n_mcmc = 3000L,\n", " burn_in = 5000L,\n", " q_sd = 1.0\n", ")\n", "\n", "pred_effect <- as.numeric(res$effect)\n", "pred_interval <- as.matrix(res$interval)\n", "pred_lower <- pred_interval[, 1]\n", "pred_upper <- pred_interval[, 2]" ] }, { "cell_type": "markdown", "id": "c3c9ca59-d23f-4ea3-9559-babefddefb0e", "metadata": {}, "source": [ "### Model Evaluation" ] }, { "cell_type": "code", "execution_count": 15, "id": "215524f1-9856-45fb-b1d4-0ec2c511d81b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMSE (Root Mean Squared Error): 0.0289\n", "MAPE (Mean Absolute Percentage Error): 0.0110\n" ] } ], "source": [ "rmse <- sqrt(mean((true_effect - pred_effect)^2))\n", "mape <- mean(abs((true_effect - pred_effect) / true_effect))\n", "\n", "cat(sprintf(\n", " \"RMSE (Root Mean Squared Error): %.4f\\n\",\n", " rmse\n", "))\n", "cat(sprintf(\n", " \"MAPE (Mean Absolute Percentage Error): %.4f\\n\",\n", " mape\n", "))" ] }, { "cell_type": "markdown", "id": "9096fd91-cf1f-4c9b-a113-c82b508d94c8", "metadata": {}, "source": [ "### Plot of the average dose-response function (ADRF)\n", "\n", "We now compare plot of the true ADRF and the ADRF estimated by our model." ] }, { "cell_type": "code", "execution_count": 16, "id": "0397ea2d-9fcd-4f90-8081-f1ce3115abbe", "metadata": {}, "outputs": [ { "data": { "image/png": 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7IY/wGOHmk0A5IkSZIa1fLqfkeF1/T2Jjs2NTUDxBg/E7Psx2A40pYMSJIkSWpE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\nK1bsgzUnyfQx8EesnfnCVn6UiEhXEd0grxVOR2PNqU8A3gNux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"text/plain": [ "Plot with title “Predicted and True ADRF”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(\n", " grid_val,\n", " true_effect,\n", " type = \"n\",\n", " ylim = range(c(true_effect, pred_lower, pred_upper), finite = TRUE),\n", " xlab = \"Treatment level\",\n", " ylab = \"ADRF\",\n", " main = \"Predicted and True ADRF\"\n", ")\n", "polygon(\n", " x = c(grid_val, rev(grid_val)),\n", " y = c(pred_lower, rev(pred_upper)),\n", " border = NA,\n", " col = grDevices::adjustcolor(\"firebrick\", alpha.f = 0.2)\n", ")\n", "lines(grid_val, true_effect, col = \"black\", lwd = 2)\n", "lines(grid_val, pred_effect, col = \"firebrick\", lwd = 2)\n", "legend(\n", " \"bottomright\",\n", " legend = c(\"True ADRF\", \"Predicted ADRF\", \"Predicted 95% interval\"),\n", " col = c(\"black\", \"firebrick\", NA),\n", " lty = c(1, 1, NA),\n", " lwd = c(2, 2, NA),\n", " pch = c(NA, NA, 15),\n", " pt.cex = c(NA, NA, 2),\n", " pt.bg = c(NA, NA, grDevices::adjustcolor(\"firebrick\", alpha.f = 0.2)),\n", " bty = \"n\"\n", ")" ] }, { "cell_type": "code", "execution_count": 17, "id": "8f20ccae", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "R version 4.4.2 (2024-10-31)\n", "Platform: x86_64-pc-linux-gnu\n", "Running under: Red Hat Enterprise Linux 8.10 (Ootpa)\n", "\n", "Matrix products: default\n", "BLAS/LAPACK: FlexiBLAS OPENBLAS; LAPACK version 3.12.0\n", "\n", "locale:\n", " [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C \n", " [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8 \n", " [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8 \n", " [7] LC_PAPER=en_US.UTF-8 LC_NAME=C \n", " [9] LC_ADDRESS=C LC_TELEPHONE=C \n", "[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C \n", "\n", "time zone: America/New_York\n", "tzcode source: system (glibc)\n", "\n", "attached base packages:\n", "[1] stats graphics grDevices utils datasets methods base \n", "\n", "other attached packages:\n", "[1] bayesgm_0.1.0\n", "\n", "loaded via a namespace (and not attached):\n", " [1] crayon_1.5.3 vctrs_0.6.5 cli_3.6.3 rlang_1.1.4 \n", " [5] png_0.1-8 jsonlite_1.8.9 glue_1.8.0 htmltools_0.5.8.1\n", " [9] IRdisplay_1.1 IRkernel_1.3.2 fansi_1.0.6 grid_4.4.2 \n", "[13] evaluate_1.0.1 fastmap_1.2.0 base64enc_0.1-3 lifecycle_1.0.4 \n", "[17] compiler_4.4.2 Rcpp_1.0.13-1 pbdZMQ_0.3-14 lattice_0.22-9 \n", "[21] digest_0.6.37 R6_2.6.1 repr_1.1.7 reticulate_1.45.0\n", "[25] utf8_1.2.4 pillar_1.9.0 Matrix_1.7-4 uuid_1.2-2 \n", "[29] tools_4.4.2 withr_3.0.2 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sessionInfo()" ] } ], "metadata": { "kernelspec": { "display_name": "R 4.4.2 (cluster)", "language": "R", "name": "ir442_cluster" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.4.2" } }, "nbformat": 4, "nbformat_minor": 5 }