{ "cells": [ { "cell_type": "markdown", "id": "640f2f18", "metadata": {}, "source": [ "# Practice: Chp. 13" ] }, { "cell_type": "code", "execution_count": 1, "id": "9b9954ef", "metadata": {}, "outputs": [], "source": [ "source(\"iplot.R\")\n", "suppressPackageStartupMessages(library(rethinking))" ] }, { "cell_type": "markdown", "id": "b340ae34", "metadata": {}, "source": [ "**13E1.** Which of the following priors will produce more *shrinkage* in the estimates?\n", "\n", "(a) $\\alpha_{tank} \\sim Normal(0,1)$\n", "\n", "(b) $\\alpha_{tank} \\sim Normal(0,2)$\n", "\n", "**Answer.** We could interpret this question in two ways. The first is that the author meant to\n", "write:\n", "\n", "(a) $\\bar{\\alpha} \\sim Normal(0,1)$\n", "\n", "(b) $\\bar{\\alpha} \\sim Normal(0,2)$\n", "\n", "That is, interpretion #1 is that these are priors for the hyperparameter for the average of all\n", "tanks, with no new prior specified for the hyperparameter for the variability among tanks $\\sigma$.\n", "\n", "The second interpretation is that the author is trying to express in shorthand new priors for both\n", "the $\\bar{\\alpha}$ and $\\sigma$ priors, and only the expected value of these two priors, ignoring\n", "a standard deviation. To use the same terms as the chapter:\n", "\n", "(a) $\\alpha_{tank} \\sim Normal(\\bar{\\alpha},\\sigma),\n", " \\bar{\\alpha} \\sim Normal(0,?),\n", " \\sigma \\sim Exponential(1)$\n", "\n", "(b) $\\alpha_{tank} \\sim Normal(\\bar{\\alpha},\\sigma),\n", " \\bar{\\alpha} \\sim Normal(0,?),\n", " \\sigma \\sim Exponential(\\frac{1}{2})$\n", "\n", "Notice we decrease the $\\lambda$ parameter to the exponential distribution to increase the expected\n", "value.\n", "\n", "Said another way, the first interpretation is that the author meant to specify this prior at the\n", "second level of the model, and the second interpretation is that the author meant to specify this\n", "prior at the first level. The first interpretation makes sense given this prior shows up directly in\n", "models in the chapter already, without much reinterpretation. The second interpretation is supported\n", "by the author's choice of variable name (e.g. see the chapter and question **13M3**). See also\n", "question **13M5**.\n", "\n", "In both interpretations, prior (a) will produce more shrinkage because it is more regularizing. It\n", "has a smaller standard deviation and therefore expects less variability.\n", "\n", "**13E2.** Rewrite the following model as a multilevel model.\n", "\n", "$$\n", "\\begin{align}\n", "y_i & \\sim Binomial(1,p_i) \\\\\n", "logit(p_i) & = \\alpha_{group[i]} + \\beta x_i \\\\\n", "\\alpha_{group} & \\sim Normal(0, 1.5) \\\\\n", "\\beta & \\sim Normal(0, 0.5)\n", "\\end{align}\n", "$$\n", "\n", "**Answer.** The focus of this chapter is on varying intercepts rather than varying effects (see the next\n", "chapter), so we'll only convert the intercept:\n", "\n", "$$\n", "\\begin{align}\n", "y_i & \\sim Binomial(1,p_i) \\\\\n", "logit(p_i) & = \\alpha_{group[i]} + \\beta x_i \\\\\n", "\\alpha_{group} & \\sim Normal(\\bar{\\alpha}, \\sigma) \\\\\n", "\\bar{\\alpha} & \\sim Normal(0, 1.5) \\\\\n", "\\sigma & \\sim Exponential(1) \\\\\n", "\\beta & \\sim Normal(0, 0.5)\n", "\\end{align}\n", "$$\n", "\n", "**13E3.** Rewrite the following model as a multilevel model.\n", "\n", "$$\n", "\\begin{align}\n", "y_i & \\sim Normal(\\mu_i,\\sigma) \\\\\n", "\\mu_i & = \\alpha_{group[i]} + \\beta x_i \\\\\n", "\\alpha_{group} & \\sim Normal(0, 5) \\\\\n", "\\beta & \\sim Normal(0, 1) \\\\\n", "\\sigma & \\sim Exponential(1)\n", "\\end{align}\n", "$$\n", "\n", "**Answer.** As in the last question, we'll only convert the intercept:\n", "\n", "$$\n", "\\begin{align}\n", "y_i & \\sim Normal(\\mu_i,\\sigma_1) \\\\\n", "\\mu_i & = \\alpha_{group[i]} + \\beta x_i \\\\\n", "\\alpha_{group} & \\sim Normal(\\bar{\\alpha}, \\sigma_2) \\\\\n", "\\bar{\\alpha} & \\sim Normal(0, 5) \\\\\n", "\\sigma_2 & \\sim Exponential\\left(\\frac{1}{2}\\right) \\\\\n", "\\beta & \\sim Normal(0, 1) \\\\\n", "\\sigma_1 & \\sim Exponential(1)\n", "\\end{align}\n", "$$\n", "\n", "**13E4.** Write a mathematical model formula for a Poisson regression with varying intercepts.\n", "\n", "$$\n", "\\begin{align}\n", "y_i & \\sim Poisson(\\lambda) \\\\\n", "log(\\lambda) & = \\alpha_{group[i]} \\\\\n", "\\alpha_{group} & \\sim Normal(\\bar{\\alpha}, \\sigma) \\\\\n", "\\bar{\\alpha} & \\sim Normal(0, 5) \\\\\n", "\\sigma & \\sim Exponential(1)\n", "\\end{align}\n", "$$\n", "\n", "**13E5.** Write a mathematical model formula for a Poisson regression with two different kinds of\n", "varying intercepts, a cross-classified model.\n", "\n", "$$\n", "\\begin{align}\n", "y_i & \\sim Poisson(\\lambda) \\\\\n", "log(\\lambda) & = \\alpha_{x[i]} + \\alpha_{y[i]} \\\\\n", "\\alpha_{x} & \\sim Normal(\\mu_x, \\sigma_x) \\\\\n", "\\mu_x & \\sim Normal(0, 5) \\\\\n", "\\sigma_x & \\sim Exponential(1) \\\\\n", "\\alpha_{y} & \\sim Normal(0, \\sigma_y) \\\\\n", "\\sigma_y & \\sim Exponential(1)\n", "\\end{align}\n", "$$\n", "\n", "**13M1.** Revisit the Reed frog survival data, `data(reedfrogs)`, and add the `predation` and `size`\n", "treatment variables to the varying intercept model. Consider models with either main effect alone,\n", "both main effects, as well as a model including both and their interaction. Instead of focusing on\n", "inferences about these two predictor variables, focus on the inferred variation across tanks.\n", "Explain why it changes as it does across models.\n", "\n", "**ERROR.** The `predation` predictor is actually labeled `pred`.\n", "\n", "**ERROR.** The author duplicated this question in **13H4**, without realizing he had moved it and\n", "primarily only changed wording.\n", "\n", "Compare the second sentences:\n", "\n", "> Consider models with either main effect alone, both main effects, as well as a model including both\n", "> and their interaction.\n", "\n", "> Consider models with either predictor alone, both predictors, as well as a model including their\n", "> interaction.\n", "\n", "One sentence only exists in **13H4**:\n", "\n", "> What do you infer about the causal inference of these predictor variables?\n", "\n", "Compare the last two sentences:\n", "\n", "> Instead of focusing on inferences about these two predictor variables, focus on the inferred\n", "> variation across tanks. Explain why it changes as it does across models.\n", "\n", "> Also focus on the inferred variation across tanks (the $\\sigma$ across tanks). Explain why it\n", "> changes as it does across models with different predictors included.\n", "\n", "We could treat **13H4** as a separate question that expands on **13M1** by adding causal inference,\n", "but this answer will combine the two.\n", "\n", "**Answer.** First, let's reproduce results from model `m13.2` in the chapter:" ] }, { "cell_type": "code", "execution_count": 2, "id": "7aaf6a11", "metadata": {}, "outputs": [ { "data": { "image/png": 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ELgl9xABWgA0wyCA1SA4NAMggNUgOpAzSA4QAVoANMMggNUgODQDIIDVEBeHbit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\nAElFTkSuQmCC" }, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-13_3_0.png" } }, "output_type": "display_data" } ], "source": [ "data(reedfrogs)\n", "rf_df <- reedfrogs\n", "rf_df$tank <- 1:nrow(rf_df)\n", "\n", "rf_dat <- list(\n", " S = rf_df$surv,\n", " N = rf_df$density,\n", " tank = rf_df$tank\n", ")\n", "\n", "## R code 13.3\n", "m13.2 <- ulam(\n", " alist(\n", " S ~ dbinom(N, p),\n", " logit(p) <- a[tank],\n", " a[tank] ~ dnorm(a_bar, sigma),\n", " a_bar ~ dnorm(0, 1.5),\n", " sigma ~ dexp(1)\n", " ),\n", " data = rf_dat, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "\n", "iplot(function() {\n", " plot(precis(m13.2, depth=2), main='m13.2')\n", "}, ar=1.0)" ] }, { "cell_type": "markdown", "id": "2b285a33", "metadata": {}, "source": [ "Raw data (preceding plot):" ] }, { "cell_type": "code", "execution_count": 3, "id": "7dae40c3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a[1] 2.123895005 0.8800029 0.88324287 3.60357846 3135.042 0.9993171\n", "a[2] 3.069417613 1.0879816 1.53213514 4.97198488 2880.482 0.9991000\n", "a[3] 1.025435079 0.6859747 -0.01876991 2.11478208 4086.947 0.9992862\n", "a[4] 3.045003704 1.0904417 1.44463933 4.93253177 3026.895 0.9986501\n", "a[5] 2.133584064 0.8865480 0.82569033 3.69185945 3242.085 0.9996229\n", "a[6] 2.129875960 0.8622741 0.85550909 3.51833473 4101.535 0.9983410\n", "a[7] 3.042309196 1.0803602 1.50263737 4.89527573 3300.782 0.9992896\n", "a[8] 2.143396095 0.8774313 0.87912951 3.65976593 4755.805 0.9987193\n", "a[9] -0.181523811 0.6239130 -1.20279368 0.81605579 3355.371 0.9989467\n", "a[10] 2.160446881 0.8868395 0.90286995 3.69858829 2919.991 1.0002489\n", "a[11] 0.982944595 0.6409224 -0.01787153 2.03912637 4340.708 0.9989579\n", "a[12] 0.587181118 0.6201083 -0.37215354 1.60414730 5487.450 0.9985093\n", "a[13] 1.013060494 0.6513388 0.04314274 2.09267998 4561.709 0.9991331\n", "a[14] 0.208921393 0.5888650 -0.77247363 1.13103679 3773.708 0.9990913\n", "a[15] 2.112968097 0.8671883 0.85145433 3.61051924 4976.691 0.9991278\n", "a[16] 2.153449499 0.9001026 0.84944705 3.64511067 3623.187 0.9985997\n", "a[17] 2.922906230 0.8207311 1.72786343 4.31192056 2727.910 1.0017675\n", "a[18] 2.391108593 0.6594986 1.42438049 3.46904519 3825.827 0.9988642\n", "a[19] 2.016368646 0.5883191 1.14001978 3.00910079 4198.075 0.9993717\n", "a[20] 3.696619684 1.0349830 2.22233524 5.54831067 2697.947 0.9997244\n", "a[21] 2.392176052 0.6338009 1.49698276 3.49281857 3195.078 0.9992764\n", "a[22] 2.380392651 0.6348463 1.44870379 3.44691853 3352.341 0.9986587\n", "a[23] 2.387766858 0.6677886 1.38891610 3.52825066 3481.055 0.9992638\n", "a[24] 1.707655898 0.5241377 0.91766718 2.60417300 5142.443 0.9981182\n", "a[25] -0.991016689 0.4439675 -1.72522983 -0.28233503 4224.010 0.9982751\n", "a[26] 0.162679937 0.3803444 -0.44872939 0.76593787 5110.381 0.9991206\n", "a[27] -1.428071502 0.4897130 -2.22955461 -0.68573472 3306.490 0.9985784\n", "a[28] -0.470549934 0.4166839 -1.15849296 0.19914758 4359.714 0.9992520\n", "a[29] 0.156650932 0.4082734 -0.48325866 0.81498354 3888.688 0.9992465\n", "a[30] 1.441025015 0.4863160 0.70097745 2.24540124 3645.397 0.9990923\n", "a[31] -0.633425518 0.4092424 -1.29825277 0.01788939 3807.050 0.9988602\n", "a[32] -0.307137176 0.4049534 -0.96427001 0.31531593 4200.218 0.9989423\n", "a[33] 3.196570698 0.7447295 2.10154436 4.49980149 2880.864 0.9990879\n", "a[34] 2.712794013 0.6433201 1.74888220 3.78643188 3095.331 0.9988198\n", "a[35] 2.731620944 0.6664324 1.77676015 3.83311873 2992.938 0.9990613\n", "a[36] 2.051060489 0.5000432 1.28411900 2.86453520 3690.270 0.9992633\n", "a[37] 2.065591183 0.5017172 1.30591712 2.92647140 3638.510 0.9989189\n", "a[38] 3.891461657 0.9699415 2.47805339 5.58549440 2735.887 1.0004954\n", "a[39] 2.705455255 0.6495701 1.77860035 3.84518415 2741.298 0.9996879\n", "a[40] 2.354011311 0.5506689 1.50543484 3.26092214 4252.637 0.9991978\n", "a[41] -1.799497041 0.4835684 -2.57131168 -1.07337199 3708.538 0.9989449\n", "a[42] -0.576316697 0.3417616 -1.12795518 -0.03377259 5124.122 0.9981467\n", "a[43] -0.450266837 0.3399222 -0.99046630 0.08640756 5109.116 0.9986930\n", "a[44] -0.333124738 0.3317197 -0.84461886 0.18941723 2979.151 0.9985858\n", "a[45] 0.585451130 0.3402349 0.04255837 1.14995230 4701.920 0.9993146\n", "a[46] -0.569382107 0.3518077 -1.14556430 -0.01996810 6426.916 0.9987633\n", "a[47] 2.070103142 0.5140356 1.30579740 2.93810996 3331.361 0.9987141\n", "a[48] -0.002109234 0.3203171 -0.52018692 0.50742515 3988.177 0.9981734\n", "a_bar 1.346620398 0.2500101 0.96140376 1.74271963 3215.743 0.9989353\n", "sigma 1.610600906 0.2106371 1.30392541 1.97048034 1805.981 1.0002795" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(precis(m13.2, depth = 2), mimetypes=\"text/plain\")\n", "\n", "rf_df$Predator <- as.integer(as.factor(rf_df$pred))\n", "rf_df$Size <- as.integer(as.factor(rf_df$size))\n", "rf_df$Treatment <- 1 + ifelse(rf_df$Predator == 1, 0, 1) + 2*ifelse(rf_df$Size == 1, 0, 1)" ] }, { "cell_type": "markdown", "id": "2a3d8030", "metadata": {}, "source": [ "The `reedfrogs` data.frame is small enough to show in its entirety. Notice several new preprocessed\n", "variables (columns) this solution will introduce later as they are used in models:" ] }, { "cell_type": "code", "execution_count": 4, "id": "ea9822fa", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
density | pred | size | surv | propsurv | tank | Predator | Size | Treatment |
---|---|---|---|---|---|---|---|---|
<int> | <fct> | <fct> | <int> | <dbl> | <int> | <int> | <int> | <dbl> |
10 | no | big | 9 | 0.9000000 | 1 | 1 | 1 | 1 |
10 | no | big | 10 | 1.0000000 | 2 | 1 | 1 | 1 |
10 | no | big | 7 | 0.7000000 | 3 | 1 | 1 | 1 |
10 | no | big | 10 | 1.0000000 | 4 | 1 | 1 | 1 |
10 | no | small | 9 | 0.9000000 | 5 | 1 | 2 | 3 |
10 | no | small | 9 | 0.9000000 | 6 | 1 | 2 | 3 |
10 | no | small | 10 | 1.0000000 | 7 | 1 | 2 | 3 |
10 | no | small | 9 | 0.9000000 | 8 | 1 | 2 | 3 |
10 | pred | big | 4 | 0.4000000 | 9 | 2 | 1 | 2 |
10 | pred | big | 9 | 0.9000000 | 10 | 2 | 1 | 2 |
10 | pred | big | 7 | 0.7000000 | 11 | 2 | 1 | 2 |
10 | pred | big | 6 | 0.6000000 | 12 | 2 | 1 | 2 |
10 | pred | small | 7 | 0.7000000 | 13 | 2 | 2 | 4 |
10 | pred | small | 5 | 0.5000000 | 14 | 2 | 2 | 4 |
10 | pred | small | 9 | 0.9000000 | 15 | 2 | 2 | 4 |
10 | pred | small | 9 | 0.9000000 | 16 | 2 | 2 | 4 |
25 | no | big | 24 | 0.9600000 | 17 | 1 | 1 | 1 |
25 | no | big | 23 | 0.9200000 | 18 | 1 | 1 | 1 |
25 | no | big | 22 | 0.8800000 | 19 | 1 | 1 | 1 |
25 | no | big | 25 | 1.0000000 | 20 | 1 | 1 | 1 |
25 | no | small | 23 | 0.9200000 | 21 | 1 | 2 | 3 |
25 | no | small | 23 | 0.9200000 | 22 | 1 | 2 | 3 |
25 | no | small | 23 | 0.9200000 | 23 | 1 | 2 | 3 |
25 | no | small | 21 | 0.8400000 | 24 | 1 | 2 | 3 |
25 | pred | big | 6 | 0.2400000 | 25 | 2 | 1 | 2 |
25 | pred | big | 13 | 0.5200000 | 26 | 2 | 1 | 2 |
25 | pred | big | 4 | 0.1600000 | 27 | 2 | 1 | 2 |
25 | pred | big | 9 | 0.3600000 | 28 | 2 | 1 | 2 |
25 | pred | small | 13 | 0.5200000 | 29 | 2 | 2 | 4 |
25 | pred | small | 20 | 0.8000000 | 30 | 2 | 2 | 4 |
25 | pred | small | 8 | 0.3200000 | 31 | 2 | 2 | 4 |
25 | pred | small | 10 | 0.4000000 | 32 | 2 | 2 | 4 |
35 | no | big | 34 | 0.9714286 | 33 | 1 | 1 | 1 |
35 | no | big | 33 | 0.9428571 | 34 | 1 | 1 | 1 |
35 | no | big | 33 | 0.9428571 | 35 | 1 | 1 | 1 |
35 | no | big | 31 | 0.8857143 | 36 | 1 | 1 | 1 |
35 | no | small | 31 | 0.8857143 | 37 | 1 | 2 | 3 |
35 | no | small | 35 | 1.0000000 | 38 | 1 | 2 | 3 |
35 | no | small | 33 | 0.9428571 | 39 | 1 | 2 | 3 |
35 | no | small | 32 | 0.9142857 | 40 | 1 | 2 | 3 |
35 | pred | big | 4 | 0.1142857 | 41 | 2 | 1 | 2 |
35 | pred | big | 12 | 0.3428571 | 42 | 2 | 1 | 2 |
35 | pred | big | 13 | 0.3714286 | 43 | 2 | 1 | 2 |
35 | pred | big | 14 | 0.4000000 | 44 | 2 | 1 | 2 |
35 | pred | small | 22 | 0.6285714 | 45 | 2 | 2 | 4 |
35 | pred | small | 12 | 0.3428571 | 46 | 2 | 2 | 4 |
35 | pred | small | 31 | 0.8857143 | 47 | 2 | 2 | 4 |
35 | pred | small | 17 | 0.4857143 | 48 | 2 | 2 | 4 |
reedfrogs {rethinking} | R Documentation |
Data on lab experiments on the density- and size-dependent\n", "predation rate of an African reed frog, Hyperolius\n", "spinigularis,\n", "from Vonesh and Bolker 2005 \n", "
\n", "\n", "\n", "data(reedfrogs)\n", "\n", "\n", "
Various data with variables:\n", "
\n", "\n", "density
initial tadpole density (number of tadpoles\n", "in a 1.2 x 0.8 x 0.4 m tank) [experiment 1]
\n", "pred
factor: predators present or absent [experiment 1]
\n", "size
factor: big or small tadpoles [experiment 1]
\n", "surv
number surviving
\n", "propsurv
proportion surviving (=surv/density) [experiment 1]
\n", "Vonesh and Bolker (2005) Compensatory larval responses shift\n", "trade-offs associated with predator-induced hatching plasticity.\n", "Ecology 86:1580-1591\n", "
\n", "\n", "\n", "\n", "data(reedfrogs)\n", "boxplot(propsurv~size*density*pred,data=reedfrogs)\n", "\n", "\n", "