diff --git a/lectures/live-coding/lecture04-with-answers.ipynb b/lectures/live-coding/lecture04-with-answers.ipynb new file mode 100644 index 0000000..517e564 --- /dev/null +++ b/lectures/live-coding/lecture04-with-answers.ipynb @@ -0,0 +1,7828 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "# **Beyond Linear Models**\n", + "**Lecture 04**\n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "slideshow": { + "slide_type": "skip" + }, + "tags": [], + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Loading required package: ggplot2\n", + "\n", + "Registered S3 method overwritten by 'GGally':\n", + " method from \n", + " +.gg ggplot2\n", + "\n", + "Loading required package: car\n", + "\n", + "Loading required package: carData\n", + "\n", + "Loading required package: lmtest\n", + "\n", + "Loading required package: zoo\n", + "\n", + "\n", + "Attaching package: ‘zoo’\n", + "\n", + "\n", + "The following objects are masked from ‘package:base’:\n", + "\n", + " as.Date, as.Date.numeric\n", + "\n", + "\n", + "Loading required package: sandwich\n", + "\n", + "Loading required package: survival\n", + "\n", + "\n", + "Attaching package: ‘modelr’\n", + "\n", + "\n", + "The following object is masked from ‘package:broom’:\n", + "\n", + " bootstrap\n", + "\n", + "\n", + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ────────────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.4\n", + "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.0 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.5.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.3 \u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.2.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 1.0.2 \u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 1.3.0\n", + "── \u001b[1mConflicts\u001b[22m ──────────────────────────────────────────────── tidyverse_conflicts() ──\n", + "\u001b[31m✖\u001b[39m \u001b[34mmodelr\u001b[39m::\u001b[32mbootstrap()\u001b[39m masks \u001b[34mbroom\u001b[39m::bootstrap()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mrecode()\u001b[39m masks \u001b[34mcar\u001b[39m::recode()\n", + "\u001b[31m✖\u001b[39m \u001b[34mpurrr\u001b[39m::\u001b[32msome()\u001b[39m masks \u001b[34mcar\u001b[39m::some()\n", + "\u001b[31m✖\u001b[39m \u001b[34mlubridate\u001b[39m::\u001b[32mstamp()\u001b[39m masks \u001b[34mcowplot\u001b[39m::stamp()\n", + "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n", + "\n", + "Attaching package: ‘faraway’\n", + "\n", + "\n", + "The following objects are masked from ‘package:survival’:\n", + "\n", + " rats, solder\n", + "\n", + "\n", + "The following objects are masked from ‘package:car’:\n", + "\n", + " logit, vif\n", + "\n", + "\n", + "The following object is masked from ‘package:GGally’:\n", + "\n", + " happy\n", + "\n", + "\n" + ] + } + ], + "source": [ + "# Run this cell before continuing.\n", + "library(repr)\n", + "library(infer)\n", + "library(cowplot)\n", + "library(broom)\n", + "library(GGally)\n", + "library(AER)\n", + "library(modelr)\n", + "library(tidyverse)\n", + "library(palmerpenguins)\n", + "library(titanic)\n", + "library(faraway)\n", + "\n", + "penguins_clean <-\n", + " penguins %>%\n", + " drop_na()\n", + "\n", + "titan <-\n", + " titanic_train %>%\n", + " as_tibble() %>%\n", + " rename(passenger_class = Pclass,\n", + " passenger_id = PassengerId,\n", + " ticket_number = Ticket)\n", + "\n", + "galapagos <- \n", + " gala %>% \n", + " as_tibble(rownames = 'island') %>%\n", + " select(-Endemics)\n", + "\n", + "colnames(galapagos) <- str_to_lower(colnames(galapagos))\n", + "colnames(titan) <- str_to_lower(colnames(titan))\n", + "\n", + "options(repr.plot.width = 10, repr.plot.height = 5) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# From Feedback\n", + "\n", + "- Lectures could use more structure; \n", + " - I agree! Especially based on last lecture. \n", + " - I'll put more structure into the lecture. \n", + "\n", + "
\n", + "\n", + "- Answering questions might go a bit off topic and becomes disruptive;\n", + " - I'll try to keep tabs on this; \n", + " - Also, increased lecture structure might help with this. \n", + "\n", + "
\n", + "\n", + "- More breaks;\n", + " - I could use a little more as well!\n", + " - Let's try to have a 10 min break every 50 minutes of class;" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "# Last class: Review\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "skip" + }, + "tags": [] + }, + "source": [ + "When I label things as optional, I'm just bringing them to your attention. If you ever need them beyond this course, you'll know they exist. You don't need to know these for the course." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "## Assumptions for the linear model" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "\n", + "- **Linear associations:**\n", + " - Diagnostic: \n", + " - Plot of predicted values against the residuals;\n", + " - Check for patterns;\n", + " - Consequence of violation:\n", + " - Dubious model; \n", + " - Remedies:\n", + " - Add transformations of covariates to the models (e.g., $X^2$, $\\sqrt{X}$, $log(X)$)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "- **Independence of erros:**\n", + " - Diagnostic:\n", + " - Frequently, we can tell from the student design whether this is an issue;\n", + " - Consequence of violation:\n", + " - Affects std. errors of coefficients;\n", + " - Confidence interval and hypothesis tests are not valid.\n", + " - Remedies: \n", + " - No simple remedies here; we need to adapt the model to deal with this;\n", + " - These new techniques are whole new courses: e.g., times series analysis, spatial statistics, longitudinal analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "- **Constant variance, $\\sigma^2$ (homoscedasticity)**:\n", + " - Diagnostic: \n", + " - Plot of predicted values against the residuals;\n", + " - Check if there's a funnel shape;\n", + " - Consequence of violation (heteroscedasticity):\n", + " - Affects std. errors of coefficients;\n", + " - Confidence interval and hypothesis tests are affected.\n", + " - Remedies:\n", + " - The simplest approach is to transform the response to stabilize the variance. Typical transformations: $\\sqrt{Y}$ and $log(Y)$ (not that these only work for positive data). \n", + " - **(Optional)** But other transformations are possible [see a bunch here](https://www.ime.usp.br/~abe/lista/pdfm9cJKUmFZp.pdf).\n", + " - Bootstrapping for CIs and hypothesis tests;\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "- **Normality of the residuals**:\n", + " - Diagnostic: \n", + " - Plot the histogram and QQ-plot of residuals;\n", + " - **(Optional)** There are also hypothesis tests available to test for normality;\n", + " - Consequence of violation:\n", + " - Affect the sampling distribution of the coefficients in small samples;\n", + " - CLT gives us some comfort for large samples;\n", + " - Remedies:\n", + " - If the sample is large, we don't need to do anything and could rely on CLT. \n", + " - Transform the response might also help here. \n", + " - Bootstrapping for CIs and hypothesis tests;\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "# **Today's topic: Logistic and Poisson Regression**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "skip" + }, + "tags": [] + }, + "source": [ + "Now that we have covered Multiple Linear Regression, which aims to model the relationship between a dependent variable and multiple independent variables with a quantitative outcome, let's move on to logistic and Poisson regression. These methods are suited for different types of response variables. Logistic regression is used when the dependent variable is categorical, usually binary. It models the probability of an event occurring by fitting data to a logistic curve, transforming linear outputs into probabilities through the logistic function.\n", + "\n", + "On the other hand, Poisson regression is suitable for count data, where the dependent variable represents the number of occurrences of an event within a fixed interval. It assumes that the counts follow a Poisson distribution and models the logarithm of the expected counts as a linear combination of the independent variables. Both logistic and Poisson regression use the familiar framework of linear predictors while expanding the applicability of regression analysis to a wider range of data types and research questions." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "## 1. Logistic Regression\n", + "\n", + "- Logistic regression is a powerful statistical method used for modelling binary outcome variables. \n", + "\n", + "- Unlike linear regression, which predicts continuous values, logistic regression **predicts the probability** of a binary event occurring (e.g., success/failure, yes/no, or true/false). \n", + "\n", + "- Logistic regression not only provides interpretable coefficients but also allows for effective classification and decision-making across various fields, including medicine, finance, and social sciences. \n", + "\n", + "- By understanding logistic regression, we can effectively handle dichotomous data and uncover insights that would be obscured by traditional linear approaches." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "skip" + }, + "tags": [] + }, + "source": [ + "In this sections, we will work with data about the `titanic`. Let's take a look:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "The titanic dataset has information about 891 passengers." + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 5 × 12
passenger_idsurvivedpassenger_classnamesexagesibspparchticket_numberfarecabinembarked
<int><int><int><chr><chr><dbl><int><int><chr><dbl><chr><chr>
65902Eitemiller, Mr. George Floyd male 230029751 13.0000S
57413Kelly, Miss. Mary femaleNA0014312 7.7500Q
19313Andersen-Jensen, Miss. Carla Christine Nielsinefemale1910350046 7.8542S
62313Nakid, Mr. Sahid male 20112653 15.7417C
85711Wick, Mrs. George Dennick (Mary Hitchcock) female451136928 164.8667S
\n" + ], + "text/latex": [ + "A tibble: 5 × 12\n", + "\\begin{tabular}{llllllllllll}\n", + " passenger\\_id & survived & passenger\\_class & name & sex & age & sibsp & parch & ticket\\_number & fare & cabin & embarked\\\\\n", + " & & & & & & & & & & & \\\\\n", + "\\hline\n", + "\t 659 & 0 & 2 & Eitemiller, Mr. George Floyd & male & 23 & 0 & 0 & 29751 & 13.0000 & & S\\\\\n", + "\t 574 & 1 & 3 & Kelly, Miss. Mary & female & NA & 0 & 0 & 14312 & 7.7500 & & Q\\\\\n", + "\t 193 & 1 & 3 & Andersen-Jensen, Miss. Carla Christine Nielsine & female & 19 & 1 & 0 & 350046 & 7.8542 & & S\\\\\n", + "\t 623 & 1 & 3 & Nakid, Mr. Sahid & male & 20 & 1 & 1 & 2653 & 15.7417 & & C\\\\\n", + "\t 857 & 1 & 1 & Wick, Mrs. George Dennick (Mary Hitchcock) & female & 45 & 1 & 1 & 36928 & 164.8667 & & S\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 5 × 12\n", + "\n", + "| passenger_id <int> | survived <int> | passenger_class <int> | name <chr> | sex <chr> | age <dbl> | sibsp <int> | parch <int> | ticket_number <chr> | fare <dbl> | cabin <chr> | embarked <chr> |\n", + "|---|---|---|---|---|---|---|---|---|---|---|---|\n", + "| 659 | 0 | 2 | Eitemiller, Mr. George Floyd | male | 23 | 0 | 0 | 29751 | 13.0000 | | S |\n", + "| 574 | 1 | 3 | Kelly, Miss. Mary | female | NA | 0 | 0 | 14312 | 7.7500 | | Q |\n", + "| 193 | 1 | 3 | Andersen-Jensen, Miss. Carla Christine Nielsine | female | 19 | 1 | 0 | 350046 | 7.8542 | | S |\n", + "| 623 | 1 | 3 | Nakid, Mr. Sahid | male | 20 | 1 | 1 | 2653 | 15.7417 | | C |\n", + "| 857 | 1 | 1 | Wick, Mrs. George Dennick (Mary Hitchcock) | female | 45 | 1 | 1 | 36928 | 164.8667 | | S |\n", + "\n" + ], + "text/plain": [ + " passenger_id survived passenger_class\n", + "1 659 0 2 \n", + "2 574 1 3 \n", + "3 193 1 3 \n", + "4 623 1 3 \n", + "5 857 1 1 \n", + " name sex age sibsp parch\n", + "1 Eitemiller, Mr. George Floyd male 23 0 0 \n", + "2 Kelly, Miss. Mary female NA 0 0 \n", + "3 Andersen-Jensen, Miss. Carla Christine Nielsine female 19 1 0 \n", + "4 Nakid, Mr. Sahid male 20 1 1 \n", + "5 Wick, Mrs. George Dennick (Mary Hitchcock) female 45 1 1 \n", + " ticket_number fare cabin embarked\n", + "1 29751 13.0000 S \n", + "2 14312 7.7500 Q \n", + "3 350046 7.8542 S \n", + "4 2653 15.7417 C \n", + "5 36928 164.8667 S " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Let's take a look at the titanic data set\n", + "\n", + "cat(\"\\nThe titanic dataset has information about\", nrow(titan ), \"passengers.\")\n", + "\n", + "titan %>%\n", + " slice_sample(n = 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "source": [ + "- You can find details about the columns by typing `?titan `.\n", + "\n", + "- Given all the information we have about the passengers, I want to calculate the probability of survival (see `Survived` column).\n", + "\n", + "- Let's start by using the model we know, MLR, and see why it is less than adequate for this job. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1.1 Classifying with LR: a range problem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start with the following model: \n", + "$$\n", + " \\text{Survived} = \\beta_0 + \\beta_1\\times\\text{fare} + \\varepsilon_i\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call:\n", + "lm(formula = survived ~ fare, data = titan)\n", + "\n", + "Residuals:\n", + " Min 1Q Median 3Q Max \n", + "-0.9653 -0.3391 -0.3222 0.6044 0.6973 \n", + "\n", + "Coefficients:\n", + " Estimate Std. Error t value Pr(>|t|) \n", + "(Intercept) 0.3026994 0.0187849 16.114 < 2e-16 ***\n", + "fare 0.0025195 0.0003174 7.939 6.12e-15 ***\n", + "---\n", + "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", + "\n", + "Residual standard error: 0.4705 on 889 degrees of freedom\n", + "Multiple R-squared: 0.06621,\tAdjusted R-squared: 0.06516 \n", + "F-statistic: 63.03 on 1 and 889 DF, p-value: 6.12e-15\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "##[1] Fitting the model\n", + "\n", + "model_titanic_lr <- lm(survived ~ fare, data = titan )\n", + "summary(model_titanic_lr)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n" + ] + }, + { + "data": { + "application/pdf": 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BIU/D7CoPKqbpKcooEZO3kKhjSAbIoWgm8ZJn1q9LBOlktUYqFsBC6OLgwgWy0L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zvH43ubto1DLH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\nAOeFv/37FH9pv/zwt/8Av2KAKdT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CDNkG1yImCPQAgAAADEtCNn5KI9avle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\n49FoqzZc9zSitYc9IGk0Gr1eb7PZbuC/0uP/nXu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"\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "application/pdf": { + "height": 300, + "width": 600 + }, + "image/jpeg": { + "height": 300, + "width": 600 + }, + "image/png": { + "height": 300, + "width": 600 + }, + "image/svg+xml": { + "height": 300, + "isolated": true, + "width": 600 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "##[2] Plotting \n", + "titan %>%\n", + " ggplot(aes(fare, survived)) + \n", + " geom_point() + \n", + " geom_smooth(method = lm, se = FALSE) + \n", + " theme(text = element_text(size = 18))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- Remember that the linear regression is model the conditional mean $E[\\text{survived}\\ |\\ \\text{fare}]$, we can show that this is the probability of `survived` given `fare`, $P(\\left.\\text{survived} = 1 \\right| \\text{fare})$. \n", + "\n", + "- However, probabilities are between 0 and 1 (always!), and the model gives us outputs above 1. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1.2 The Logistic Regression Model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- As we saw in the previous section, trying to predict probability using a linear combination of covariates will cause range problems (probabilities outside the interval [0,1]).\n", + "\n", + "- So, the idea here is to use a non-linear model:\n", + "$$\n", + "P(\\left.Y_{i} = 1 \\right| X_{i1}) = \\frac{e^{\\beta_0 + \\beta_1 X_{i1}}}{1 + e^{\\beta_0 + \\beta_1 X_{i1}}}\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad [\\text{Eq. 1}]\n", + "$$\n", + "\n", + "- Under the model above (Eq. 1), the probability is always between 0 and 1. Let's take a look $P(\\left.Y_{i} = 1 \\right| X_{i1})$ as a function of $X$: " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "application/pdf": 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WlgcK/VaU13Wp0+Kk+kwQ8m1gu1fz7u49/EmSipmvycdwkHSSzJJF1KVV16Rzr1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v60D97q371N08furX111QrBKJWsWK3m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\nf3YDsFiGAyyGAJakIgr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"isolated": true, + "width": 600 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting Eq 1 \n", + "# Here the value of z is z = beta_0 + beta_1 * X\n", + "tibble(z = seq(-5, 5, 0.01),\n", + " logistic_function = exp(z)/(1+exp(z))) %>%\n", + " ggplot(aes(z, logistic_function)) + \n", + " geom_line() + \n", + " theme(text = element_text(size = 18)) + \n", + " xlab(expression(paste(beta[0], '+', beta[1], 'X'))) + \n", + " ylab('P(Y = 1 | X)') + \n", + " ggtitle('Logistic Function')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- As you can see above, the value is contained between 0 and 1.\n", + "\n", + "**Odds:**\n", + "\n", + "- But note that Eq. 1 is the same as \n", + "\n", + "$$\n", + "\\frac{P(\\left.Y_{i} = 1 \\right| X_{i1})}{1-P(\\left.Y_{i} = 1 \\right| X_{i1})} = e^{\\beta_0 + \\beta_1 X_{i1}}\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad [\\text{Eq. 2}]\n", + "$$\n", + "\n", + "- The quantity $P(\\left.Y_{i} = 1 \\right| X_{i1})/\\left[1-P(\\left.Y_{i} = 1 \\right| X_{i1})\\right]$ is called **odds**.\n", + "\n", + "
\n", + "\n", + "- For the titanic case:\n", + "$$\n", + "\\frac{P(\\left.\\text{survived} = 1 \\right| \\text{fare})}{1-P(\\left.\\text{survived} = 1 \\right| \\text{fare})}\n", + "$$\n", + " - odds close to 0 -> low chance of survival;\n", + " - as the probability of survival increases, the odds increases (indefinitely).\n", + " \n", + " \n", + "**Numerical Examples:**\n", + "\n", + "- A passenger with an odd of $0.25 = 1/4$ means that the passenger has 1 in 5 chance of surviving.\n", + "- A passenger with an odd of $0.5 = 1/2$ means that the passenger has 1 in 3 chance of surviving.\n", + "- A passenger with an odd of $0.75 = 3/4$ means that the passenger has 3 in 7 chance of surviving.\n", + "- A passenger with an odd of $1$ means that the passenger has 1 in 2 chance of surviving.\n", + "- A passenger with an odd of $2$ means that the passenger has 2 in 3 chance of surviving.\n", + "- A passenger with an odd of $3$ means that the passenger has 3 in 4 chance of surviving." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- If we take the log of Eq. 2 we have: \n", + "$$\n", + "\\log\\left(\\frac{P(\\left.Y_{i} = 1 \\right| X_{i1})}{1-P(\\left.Y_{i} = 1 \\right| X_{i1})}\\right) = \\beta_0 + \\beta_1 X_{i1}\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad [\\text{Eq. 3}]\n", + "$$\n", + "which is called log-odds or logit;\n", + "\n", + "
\n", + "\n", + "- The logit is linear in $X$! \n", + " - We can use the linear model we are used to to model the **logit** of function;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1.3 Fitting a logistic regression in R" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- To fit a logistic regression we use the Maximum Likelihood Method; \n", + " - You don't need about the details of the method; " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\log\\left(\\frac{P(\\left.\\text{survived} = 1 \\right| \\text{fare})}{1-P(\\left.\\text{survived} = 1 \\right| \\text{fare})}\\right) = \\beta_0 + \\beta_1\\times\\text{fare}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call:\n", + "glm(formula = survived ~ fare, family = \"binomial\", data = titan)\n", + "\n", + "Deviance Residuals: \n", + " Min 1Q Median 3Q Max \n", + "-2.4906 -0.8878 -0.8531 1.3429 1.5942 \n", + "\n", + "Coefficients:\n", + " Estimate Std. Error z value Pr(>|z|) \n", + "(Intercept) -0.941330 0.095129 -9.895 < 2e-16 ***\n", + "fare 0.015197 0.002232 6.810 9.79e-12 ***\n", + "---\n", + "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", + "\n", + "(Dispersion parameter for binomial family taken to be 1)\n", + "\n", + " Null deviance: 1186.7 on 890 degrees of freedom\n", + "Residual deviance: 1117.6 on 889 degrees of freedom\n", + "AIC: 1121.6\n", + "\n", + "Number of Fisher Scoring iterations: 4\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[3] Fitting Logistic Regression\n", + "\n", + "model_titanic_logistic <- glm(formula = survived ~ fare, data = titan, family = 'binomial')\n", + "summary(model_titanic_logistic)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n", + "\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n" + ] + }, + { + "data": { + "application/pdf": 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BIU/DHCoIpWN1lO0cg2O2UKxnwB2RStBF8yTP7Q6EFP1ktUQlF2ApWjixeQactK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UKj3kA/rTf7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IqS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\nbRNE8ZXtnp+n6toNxqS+HNOVZI7LbJtRXmI3S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POLhRybWNesU0hwWrCaniJnpEgxkYrZ\nbO7t1VwoKAiDQyAEAAAAAJgEnC5SVMXnFwtHzwqKxzTAvkKCq+NlVicnAuhDIAQAAAAA8GsX\nr7LZp4SCMrGrV2do6LwZrqxUeZNFDgnCajEwbAiEAAAAAAD+qNtOHSoX9p0Uq+p1LtpNBm19\nopyeIi+NxRRBGDkEQgAAAAAAP6Kq5NQFPrtIOFkhOD2m/9E0sS50ZFrl1QkOjkEhQRgtBEIA\nAAAAAL9Q28Tk2sT8EqGlU6dARHSEkpEibbHKEWYMDYUxg0AIAAAAAOBLvTJ19CyfX6JfSJBn\ntZVLHNuWS8kLnJTOFEKAUUEgBAAAAADwAU0jpy9z2UXiZ+W87BwY9SiKJMY6M1OldYkOkcfQ\nUBgvCIQAAAAAABOquZM+UCJ8UihebdUpEBFuVtOT5a+kSbPClYlvG0w1CIQAAAAAABPBqVDH\nz/F5xUJhJa96TAPkGG1VvCM9RV4e52B0phACjAsEQgAAAACA8XW+ls2xiQfLhB5JZxZgXLQr\nwypttMjBBgwNhYmGQAgAAAAAMC66eqnDZ4SPjouXrulcdQcbtHWJ8q0rpQUzPYpLAEwUBEIA\nAAAAgLHkUsjJCj6nSCys5BWPoaEMTZYvdmRapRWLHazOFEKACYVACAAAAAAwNi43sNlFQkGJ\n0N6jMwswNlLJsErpKXKYCYUEwV8gEAIAAAAAjEqPRB08LeTZhLM1nOezQaK2Kt6xJVlKWeic\n+LYBDA2BEAAAAABgJFSNFFfxOTbh6Fne6Rq4WgxNEcsCZ6ZVumWpg2exWgz4KQRCAAAAAIDh\naeqgC0qFj0+KDW06swAjQtTNFnnbCmlGGAoJgr9DIAQAAAAA8IrTRR0/z+8rFEsucppHnx/H\naquWOLYtl5IXOCmd6hIA/giBEAAAAADgJi7UsZ8UigVlgl3WiXqLol3pyXJ6shRsxNBQmGQQ\nCAEAAAAA9LV00ofLhf2nhMsNOpfN04LVdYnyV9LkeTNQSBAmKwRCAAAAAIAvcSpU0QUuv1g4\nelbwLCTIscS60LElRV4dL6OQIEx2CIQAAAAAANdV1bM5RUJBmdjVqzM0dP4MV2aqvDlZNhtR\nSBACBAIhAAAAAEx1XXbqcLmw76RYVa9zeWwyaOsT5fQUeWksCglCoEEgBAAAAIApSlHJqUo+\n1yaeqOCdHtMAaZpYFzqyUuVV8Q6OwWoxEJgQCAEAAABgyrnSzHxaKuQWiw1ttOez0RHKpiQ5\nI1WOCkUhQQhwCIQAAAAAMFX0SNSh00KuTTxbo3MZbBC0dYlyViqGhsIUgkAIAAAAAAFO1UjZ\nJS63WPysnJedA1eLoSiSONeZaZXWJTpEHkNDYWpBIAQAAACAgNXcQR8oFT4pFK+26hSIiDCr\nm5Plr6RJs8IxNBSmKARCAAAAAAg0Dhd1uJzPs4mllzjVo8+PY7VbEhyZqVLyAietU10CYApB\nIAQAAACAwHGhjs0rFgpKxU69QoKxkUp6ivSVNBQSBLgOgRAAAAAAJr22bjq/WMi1idWNOkND\nQ4PUzclyVqoUG4WhoQBfgkAIAAAAAJOVSyEnK/icIrGwklc8+vxYhqTFObJSpeVxDlYnJwIA\nAiEAAAAATEKfXyV7PxX3nwpu79YpJDhnupJhlTKtcqgJQ0MBhoJACAAAAACTRpedKigVDpQI\n52sJIcKAZ00GbcMyOTNVWjzb5YvWAUw+CIQAAAAA4O9UjRRX8TlFwtFzvNM1cLUYmiKWBc5M\nq3TLUgfPopAgwDAgEAIAAACA/2rqoAtKhY9Pig1tOrMAp4eomyzythXSjDCsFgMwEgiEAAAA\nAOB37A7qcLmQUyScqeY0jz4/g0A2p5D05J742XYKhQQBRgGBEAAAAAD8yIU69pNCsaBMsMs6\nUW9RtCs9Wf7qLUxkuNjR4XI6J76BAAEFgRAAAAAAfK+5g84rEXOLhLoWnaGh4WZ1S4qcYZVm\nRyiEkCBj0IQ3ECAwIRACAAAAgM84FeroWT63SLBd5FWPChEco61c4shKk1MXOmid6hIAMFoI\nhAAAAADgA9UNTH6JmF0kdPToRL3YSCU9RcpKlUOCUEgQYBwhEAIAAADAxOnooQ+UCjlFwufX\ndC5EzUZtk0XKSpXnz0QhQYCJgEAIAAAAAONOUUlhJZ9nE09U8E6PrEfTJHWhIytNXrnEwTEo\nJAgwcRAIAQAAAGAcXWlmPi0VcmxiY7vO0NDoCGVTkpxhlaLCMDQUwAcQCAEAAABg7PVI1MHT\nQq5NPFejc8FpELT1iXJWmpwQg8IRAL6EQAgAAAAAY0bVyLkaLr9YOFAqSA79QoJbl0ubLLKB\nx9BQAN9DIAQAAACAMdDQxuTahFyb0NCuU0gwMlTNsEoZVnlGmDLxbQOAwSAQAgAAAMDIyU7q\ns3I+t1gsu8SpHn1+PKvdstSRaZUsC5y0Tn8hAPgYAiEAAAAAjMSFOjavWCgoFTt79YeGpifL\nm5MlsxFDQwH8FwIhAAAAAAxDaxedXyzkFos1jTpDQ0NNanqynGmVYqMwNBRgEkAgBAAAAICb\nc7rIiQo+1yaequQVjwoRLENWLHZkWqXlix2MTnUJAPBTCIQAAAAAMJTqRia/WMwpEtp7dKJe\nTKSyJUXKtMqhJhQSBJh8KE2biqO6ZVn2dRMG4nmeEOJwOHzdEH/H8zzO0k0JgqCqqtOJyk5D\noSiKZVmcpaHRNM1xnKIoLpfL123xazRN0zSNszQ0hmFYlnW5XIqCkYRDYVlW0zR/OEudPSS3\niPn4BFNRqzNF0Gwk6Vbl1pVKfKwPLiZZlmUYxul0qipS6FA4jnO5XFPzgt97HMfRNO2HAWEM\nCYIw2FNTtIfQbrf7ugkDcRxH/LJh/objOJyloVEU5Q6EOFFDYxiGoiicpaExDOO+mMCJGhrP\n8wzD4CwNjed5lmUdDgfu6w1NFEVVVX14llSNlFSxOTb+8GlOdg6MgjRF4mNcGamODKtT4DRC\niE8++AaDgWEYWZZxI2Zo7pzjD/cX/Jn7pp4kSYGanGmaRiAcyG+/O/y2Yf5D0zScpaFRFEVw\noryDs+QlVVVxoobmvr+AszQ0lmUJPk5eUFXVV93ydc1Mrk3IKxabO3WGhs6cpmSmyltSpOkh\n1zvlfPg36e4YxPiFm3L3NuMsDc2dAwO4K5VhdNZ/6jNFAyEAAAAAuNll6nC5kF0knK3hPK+H\nRV5bl+jItEqJc50UCgkCBBwEQgAAAIAp6kId+0mhWFAq2B36hQS3Lpc2JckGITC7TQCAIBAC\nAAAATDVNHXResZhrE+pbdAaSRZjVLVY5I0WKjsDEM4DAh0AIAAAAMCU4Fer4OT6vWNAtJMgx\nmnWRc0uKvCZBRiFBgKkDgRAAAAAgwFXWsbk28dNSocuuMzR04SxXZqq8KUkKNmJoKMCUg0AI\nAAAAEJjae+iCEiG7SLzcoDM01GxUNyfLmany/BlYghJg6kIgBAAAAAgoqkpKL3H7CsXj5wWn\nR9ajKWJZ4ExPltYvc/AsugQBpjoEQgAAAIAAUd3I5NrE/GKhrVtnFuCc6UqmVUpPkacFe8wg\nBICpCoEQAAAAYHLrkaiDZUJusXiuRufSzihoG5LkTKscH+Oc+LYBgJ9DIAQAAACYlFSNnKvh\n8ouFA6WCNEQhQYts4DE0FAD0IRACAAAATDINbUyuTci1CQ3tOqvFRIWpW1KkTKscFYZCggBw\nEwiEAAAAAJOD00UdP8/nFQuFlbyqV0hwVbwjPUVeEeegUUgQALyDQAgAAADg787WsLk28WCZ\n0CvrDA1dMseVYZU2LJNNBgwNBYDhQSAEAAAA8FOtXXR+sZBjE2ubdIaGhprU9GQ50yrFRmFo\nKACMEAIhAAAAgH9xusjx83x+sXDsnODyyHo0TSzznduWS6vjZVYnJwIADAMCIQAAAIC/uHSN\nLSjjc04xHT06Q0PnRilZqdKmZDk0CIUEAWBsIBACAAAA+Fi3nTpULuTZhLM1nOezQaK2YZmc\nniIvjUUhQQAYYwiEAAAAAL6haqT0IpdXIn5WzsvOgV2CNEWWzHFuscrpybLAYbUYABgXCIQA\nAAAAE62umcktFvNsQnOnToGI6Ah1S4q0JUWaHoKhoQAwvhAIAQAAACaIw0WdOM/vKxRLLnKa\nR58fx2qrljh2rCOW+Q6HQ/ZFAwFgykEgBAAAABhfmkbKq7mcIvFwOS85Bg4NpSiSEOPMSpXX\nJcoGQTMajQqqSADAREEgBAAAABgvTR10XrGYUyRcbdUpEBFhVrekSBmpcnQ4IiAA+AYCIQAA\nAMAYcyrU8XN8XrFwqpJXPKYBcoxmXeTckiKvSZAZnSmEAAATB4EQAAAAYMxUXmFzbOLBMqHL\nrlNIcOEsV2aqvClJCjZi1VAA8AsIhAAAAACj1WWnDpcLH58QL17VubgKNmjrEuVtK6SFs1wT\n3zYAgCEgEAIAAACMkEshpyr57CKxsJJ3eUwDZGiSFufIsEorFzs4XHMBgF/ClxMAAADAsFU3\nMDk2Mb9EaO/WmQUYE6lkpEjpKfK0YBQSBAC/hkAIAAAA4K0eiTp2js8vEYurOM9njYK2OsGx\nJVlKXuCkdKYQAgD4HQRCAAAAgJtQNVJ6kcuxiUfO8A7XwKhHUyRpvjPDKq1d6hA4rBYDAJMJ\nAiEAAADAoK61Mbk2IdcmNrbrDA2NClUyrHJGqhwVikKCADApIRACAAAADOR0UcfP8/sKxZKL\nnObR58ex2qoljvQUeUWcg0YhQQCYzBAIAQAAAL5wtobLKRIOnRZ6ZZ1ZgPExrgyrtGGZHCRi\naCgABAIEQgAAAADS2kUfOi1kFwmfX9O5OgozqeuXyVlp8vwZKCQIAAEFgRAAAACmLqdCnTjP\nZ58Siqp41aNCBMeSFYsdGVZpeZyDwdBQAAhECIQAAAAwFV26ymYXCQWlYmevztDQeTNcmany\nZoscEoRCggAQyBAIAQAAYArptlOHyoVPCsULdTpXQSaDtj5RTk+Rl8Y6J75tAAATD4EQAAAA\nAp+qkqIqPvuUcOI871Q8CgnSxLrAkZEqr0lwcAxWiwGAKQSBEAAAAAJZXTNTUCrkFosNbTqz\nACND1Y1J8q0rJRQSBICpCYEQAAAAApBdpg6VC9mnhLM1nOezBl5blyhnpspLY52UzhRCAICp\nAoEQAAAAAoemkdOXuZwi8bMzvOQYGPUoiiyNdWalymsTZQOPoaEAAAiEAAAAEBCaO+kDJcL+\nU2J9C+P5bLhZTU+Ws9Kk6HAMDQUA+AICIQAAAExiThd15CyfUySWXORUjz4/jtXWxDsyU+WU\nhQ4aQ0MBADwgEAIAAMCkVHmFzbGJn5YJ3XadqLco2pVhlTZZ5GADhoYCAAwKgRAAAAAmky47\ndbhc+OiEeOmqzmVMsEFblyjfulJaMNM18W0DAJh0EAgBAABgEnAp5FQln10kFlbyLo9pgAxN\n0uIcmVZpxWIHh6sbAACv4SsTAAAA/FptE5NrE3NsQnu3TiHB2RHKxiQ5M1WKDFUnvm0AAJMd\nAiEAAAD4o2479WmZkGsTK67oXK4EidqGZXKGVYqPwdBQAICRQyAEAAAAP6JqpOQil2sTPzvD\nO10DV4uhKZI035lhldYudQgcVosBABgtBEIAAADwC00ddEGp8PFJsaFNp5BgRIi62SJvXS7N\nnIZCggAAYwaBEAAAAHxJclCfneGzi8Tyy5zm0efHs9q6REeGVUqa70QhQQCAMYdACAAAAL5x\noY79pFAsKBPssn4hwfRkeXOyZDZiaCgAwHhBIAQAAIAJ1dpFHzot7D8lXG7QuQ4JM6nrl8lZ\nafL8GVgtBgBg3CEQAgAAwERwuEi+jfztkOFkhUn1qBDBsWTlYkeGVUqLczA61SUAAGBcIBAC\nAADA+KpuYPJLxByb2N5NCBm4YExspJKeImWmyqFBKCQIADDREAgBAABgXHT2UgWlYnaRcOmq\nzvVGsFHbZJEzrdLCWRgaCgDgMwiEAAAAMJZUlZy6wOcUCScqBKdH1qNpYl3gyEyVVyc4OAar\nxQAA+BgCIQAAAIyNumamoFTILRYb2nRmAUaFaV9ZQW1d3htq6J34tgEAgC4EQgAAABiVXpk6\ndFrILhLO1XCezxp4bV2inJkqpy5mgoNN3d2qJE18GwEAQB8CIQAAAIzQ9UKCpd+WETgAACAA\nSURBVILdoV9IcOtyaVOSbBA0QghFDVxOBgAAfA6BEAAAAIanuZM+UCJ8UihebdXJeOFmNT1Z\nzkqTosOViW8bAAAMCwIhAAAAeMXhoo6c4XNsYulFTvVYDoZjtTUJjkyrnLLQQev0FwIAgD9C\nIAQAAICbuFDH5hULBaViZ69O1HMXEvxKmmw2opAgAMAkg0AIAAAA+tq76bxiIdcmVjfqDA0N\nDVI3JctZqdLcKAwNBQCYrPwlECqKsn///s7OzuXLly9cuND7F/b29paWll69epWm6Tlz5iQl\nJXGczhJnAAAA4CWXQk5W8Dk2sbCCVzz6/BiaLI9zZKZKKxY7WCwTAwAwyflFIKyrq9u1a1dV\nVRUhJDQ01PtAeODAgT/96U89PT19WyIiIh577LHExMRxaSgAAEBAq2lk8orFHJvQ3q1TSHDO\ndCXDKmVY5TAThoYCAAQI3wfC7Ozs1157TVGUkJCQjo4O71948uTJ3//+9zRN79ixIyUlRVGU\nI0eO5Obm/uxnP3vhhReio6PHr80AAACBpMtOfVoq5NrEyjqdC4MgUduQJGdapSVzXBPfNgAA\nGFc+DoS5ubl//OMfo6Ojn3zyyT//+c82m83LF2qa9uqrr2qa9tBDD2VkZLg3Wq1Wk8n0t7/9\n7Y033nj66afHrdUAAACBQNXIuRouv1jILxFk58DVYmiKLJnj3GKVN1tkkfdYVBQAAAKCjwOh\n3W7ftGnTgw8+KIrisF549uzZa9euRUREbNmypf/2u+666x//+EdRUVFHR0dISMiYNhYAACBA\n1LcwuTYhr1hs6tAZGhoVpmRY5YwUKSoMQ0MBAAKcjwPhpk2bvvrVr47gheXl5YSQpKQkivrS\nHc3g4OAFCxZUVlaePXt29erVY9PKcdba2vqb3/zm1KlThJC0tLTHH388PDxcd8+//vWv3//+\n90f5dhzHKYqiqgN/x1MUpWla//81Go3952f2bSeE9N+z/3aGYZYsWfLtb3/7l7/8ZXd3t3s7\nwzBGozEuLq60tNThcBBCaJq2WCwtLS3Xrl1jWdZqtb722mvTpk0brM2apv3Hf/zHu+++29PT\nExISYrFYDh8+7D5U37tPnz69vb29/0Y397uHh4eHhIRs2LDh0UcfNZvNhJCysrLf/e53FRUV\ngiA0NjZ2dnZSFGU2m93NSE1N/X//7/+98MILH3zwQW9vb1BQkMFgaG9v1zRt/vz5u3btSktL\nI4T09PT8/ve/z8/Pr62t7ejo8DyrbizLxsfH19bWdnV1Kcr1tfhCQkLefvvtJUuW3HbbbZWV\nlaqqiqL41FNPVVVV/f3vf+/u7nafZIqiaJqOiop6+OGH//d//7eyslLTtLlz577yyisJCQmD\nnbGb+uijj958880rV67ExMTcf//9jY2N7733XkNDw7x58yorK+vq6tztue+++/Lz8y9fvkxR\nVFxc3Kuvvjp37lzPo125ciU9Pb21tdX9wz7xxBOPPfbYiNtGCKmtrf3ud79bXl7udDrJjU8X\nz/OLFi16/fXXddswGFVVn3zySfffY0hIyCOPPPLggw/2PStJ0v33319QUCDLcmhoqMFgaGxs\n1DQtJibm5ZdfTkpKGm7Ln3vuuTfffLOrq8tkMt1zzz3PPPPMcI8QYI4fP75z5862tjaKosLC\nwt55552UlJQxPP577733xBNP9PT0UBQ1e/bsf/zjHxMwX0CW5Zdffnn//v1dXV1JSUmPPfbY\nokWLxuTI//Ef/7Fnz57e3l6Koniev/XWW3fv3s3z/Jgc3M3uoD4rF3KKhPJqzuOLnAictjbR\nkWmVkuY5KRQSBAAYjn/6p386dOiQoigsy37jG9944YUXfN0ib1GeV/a+8tOf/tRmsz344INb\nt2696c6//vWvP/vss3vvvfeuu+4a8NQLL7xw4MCBu+++++677x7s5c3NzaNt7hhpb2/fvHlz\nbW1t35bZs2cXFBSEhoYO2DM3N/eb3/zmxLZu4phMpnPnzg3WUfzVr3712LFjY/JGS5Ysyc3N\ntdls27dvH3pPlmVdrkFny7z77rtr1qzZtm1baWnpaNrDcZw78wwXTdOHDh1avHix51MURYWH\nhzudzsEm5e7evfvnP//5CN6U47ji4uKoqKj+GyVJiomJGfBN8tBDD/3sZz8bwVsQQlpbW5ct\nW+aZ7d1YlrXZbDNnzvTyaFlZWQPGot93332/+tWv3IdKSUm5fPmy7gtpms7Pzx/WClX//M//\n/NFHH/XfkpGR8fbbb3t/BD/EsmxoaKjdbve8PXRTZWVl6enp/bdQFPXpp5+O5l5Gf2+//faj\njz7afwtN0xcuXHDf9Bknqqp+4xvfOHjwYN8WURT3799vtVpZlh3BWeqzffv2o0ePDtg4f/78\nEydOjPiY/V2oYz8pFAvKBLusE/UWRbvSk+X0ZCnYOI5XBaIomkym7u5uSZLG710CgNFoVBRF\nlmVfN8Svue/VdnR0jOzX6NRhNpt7e3uHuKQBQojZbOZ5vqWlZcTJKCUl5cqVK/23rFix4uOP\nPx6L1o0BhmHCwsIGe9b3i8qMjPtKV/cHc0epzs7OiW7TiPzmN7/pnwYJIVeuXPnVr3713HPP\nDdjzW9/61gS2a6J1d3c/8sgj//3f/+351OHDh8cqDRJCzp8//8c//vHdd9+96Z5Df3U++OCD\n3//+90eZBgkhI/41pqrqzp07jx8/PtwXXrt27fnnnx/Zmzqdzp07d+7fv7//xvT0dM9vz5df\nfnnEgfC+++4bLA0SQlwu186dO3Nycrw51CeffOI5M/mNN9740Y9+FBoaunv37sHSICFEVdXv\nfOc77q57b1y8eHFAGiSE5ObmlpaWWiwWLw8SYL7+9a8P2KJp2te+9rVz586NyfEff/zxAVtU\nVb3zzjvz8/PH5Pi69u7d2z8NEkIkSXriiSdG+aZHjx71TIOEkEuXLr366qvf/e53R3zk5k46\nr1jMLRLqWnQKRISb1fRkOcMqzZmOQoIAgc7lorq7h96F6u2lbnploihUV5c3b0jJMrHbvWwd\n5XJRI7inJknUSG8wUb295Mb1BiOKhGEMvb0jCISU01lhsz18Iw1+RMhnhBBCTp48eeHChbEa\nQjKuJmsgdN9c1B1IIwgCIcT+5c9fZmZm3/X99u3bH3nkkfFvo1d019E5derUgFGjra2t/tOX\nO05sNpvuWNns7OyxfaNjx45dvHhxlAdpbm4ew5g6MrW1tYONLiaEcByn++yhQ4eGiFs3VVlZ\nOeCw1dXVnrtpmqZpWkRExAje4vz580PvcOHChSF+8P50c6OmaYcPH/7Od75z4MCBoV9eV1fn\n5RsRQl566SXd7dnZ2Zs3b/byIH7LYDAMd6Y3IaS9vd1zY2trq/dndWi691OqqqrG6vi6ysrK\nPDcWFRUJgsBx3AjOktuA+yz95efnP/XUU8M9oMNFjp8ln5ygCoqJZyFBjiWrEsi2ldrGZIpl\nREJG2OyRCQoKCgoKmsh3nKRMJpOvm+B/VJXcGPxCSRLp6TH3HwvT79nrenpI/195ikIGdBg4\nHGRACJEkzwxDeX6byTLp7R240ekkuomrvZ3oXsV1dBDdySaDHYfo/Qj9dXcTvS/GsRx3HtCM\nI31hCiF90yEabgRCQsjbb7/9hz/8YbTNGguDTWtym6yBcAi6wclkMvXN3RJFceiTMpFoWmc2\nP8MwA1pITYHJHJ4/dd/2sX0jlh2bj/2YN2y4KIoa7JPMMIymabrP6n7kvEfTtJf/fHieH9k/\ntJt+2of4wQcY7O+I4zhVVW/6SfD+jcjgnyuWZf3nC2cEKIpyTzAeq59iWGfVD4+v+y+Ipmn3\n53bEbz3E98lg342DqailPjxGZRdSnXq32hfN1m5frWUt10JvZI2J/Hj2fZwC/hbnKNE0PaFn\nqa3t+oMb+YSSJOLudXG5SF9fUF966Z+F+iWQL1JT/zwz2OP+RyaE6uz84rM4IJL1NU9P4F8e\nwWTT/zMpCIKfXAMM/X0yWQOhwWAghOgOr3f3frh36PP+++/3/1//mUO4du3akydPDti4bt26\nNo+vP+8vxCep9evXe/7UhJA77rhjsL6Xkdm0aVNTU5PubX7vzZkzJz093bdDw+Pi4nTPmHsO\nocvl0p1DmJCQYDQaez3va3onOTl5wJsmJiYWFRV5tsHpdOo276bS0tKG6C0hhFgsFi+PvGPH\njj//+c8DNtI07f6wbd++PS8vb4iXL1iwwPsf4dZbb3366ac9v3C3b98+svPgJ9xzCCVJGsHs\nuMjIyGvXrg3YOHPmzLE6IaIoek5F8/yIjq1Vq1Z5fiOtW7dOkqTRzCG84447XnzxRd2nvPwI\ndfbSB0qEnCLh0jWdbGk2ahuTpKw0ecFMFyFEcw59jT1e3HMIe3t7MYdQh6ZRHR2EEKq728Bx\nam+vs7OT3EhZlCy7x8VRHR1E0/pG4tGdnUTT+obw9W2nenool6tv/76DE02jb/Qv6fR6AcCY\n+s53vuMn1wCBOYfQ/SPpjkdqaWkhhAyxZKVf+cEPfrB///6zZ8/2bYmPj9ddoTE3N3fA8gyB\nZPr06e51PjylpKRs377973//+5i80apVq+6///61a9du27Zt6FBkMBjsgwx8Zxjm9ddfT0pK\n+sc//vHpp5+OuDEURZlMpi7vBuIPwPP8O++8M4IXTps27fnnnx/ZqGmj0fjmm28O2Lh///4Z\nM2b09cC7PfvssyM4vtsrr7yydOnS7kFGyxgMBs+MN5g1a9ZkZWUNGHX81FNPGY1GQsg999zz\nxhtvDFb+lGXZYa0HEx0dff/997/66qv9N95zzz0LFizw/iABZt++fampqf1DMk3Tn3zyyVgd\n/6233vrGN77RfwvP83v37h2r4+vaunXrjh07+t9kDAsL+81vfjPKw1osljvuuOODDz4YsD01\nNdVzKmZ/qkZKL3J5JeLh07zDpVNI0LLAmZ4srUt0CBw65cYA1d1NXC66q4soCtXR4U5i1+c+\nyTJltxOHg+rtvb7FPWXLndZUle7q+iL1dXYSVaXsdsrhIE7nSKZOgT9gGC042HOzGhxMPEcT\n8Lxm1BuTyLLaIMODNZ7XvtzD8QWa1gZfQEszGIgg3Hhb3uVyDehU0IKCtJsNk9FMJnLTQVUU\npXld5k0LDtaGM0xJCwkhIxgiN+SZGYzJZOI4rr29XTUab3pmdN1xxx1nzpwhhPRdO95+++0z\nZswYwaEm3mQNhLGxsYSQmpoaz6fcG+fNmzfRbRoRURSzs7NfffXVkydPapq2YsWKBx54QHcW\nSlJS0tGjR2+55ZbRjCGhaTokJKSnp8dzFtmAASosy0ZHR9fU1AyoRcEwDMMwDodjwEWee7wT\nz/Nr16599NFHH3jggcbGRkIIwzCCIISFhd1yyy379u1zV24QBGH79u2XLl2qqqoSRXHDhg0v\nvPDCEEMZX3311VWrVr3yyiutra0zZ87MzMzcs2dP/zsugiAkJCRcunSpu7tbVdW+tlEUFRQU\nFBoaOnv27JCQkI0bN+7cuZNl2aVLlx45cuSll146d+5cUFBQbW3ttWvXGIaJjIycOXOmy+Va\nsWLF9773vT179rz22mttbW0RERGhoaHuj9ayZct++9vfxsTEEELeeeedPXv2HDhw4MKFCzU1\nNX0zmgb8HZnN5i1bthQXFzc0NEiSpGkaRVGxsbF79+6dM2fO3XfffeTIEafTGRoa+uKLL549\ne/aNN96or69XVdU9vMpgMMydO/eXv/zlK6+8curUKUVRkpKSXn755ZHN0COE3H333XFxcW++\n+WZ1dfW8efPuu+++5ubm//u//2toaIiLi6uoqCguLna359lnn33nnXfKysooikpLS3v55Zd1\n57RcuXJl/fr1ly5dUlXVaDS+8sorWVlZI2sbIcRoNJaXlz/88MNHjhxxp2WGYdzhOTU19aWX\nXhrWGpJ79ux56aWXXn/99ba2thkzZjzzzDP923bs2LEnnnhi79693d3ds2bNmjZtWmVlpaIo\niYmJL7300oD1VG/queees1qtu3btampqCg8Pf/TRRwN7LaibmjNnTnFx8V133VVdXU1R1Ny5\ncz/44IPp06eP1fE3bdqUn5//7W9/u7GxkWXZZcuW7d27dwLGcv/Xf/3X5s2bs7Oz29vbLRbL\nQw89NCY/1J/+9KdVq1a98MIL7i/PsLCwnTt3/uhHPxps/9omJscm5hcLrV06X57REUpGirTF\nKkeYA3loiZeonh5KlqmuLqq3l0gS1dlJSRIly1R7O+VwkN5ed38a1d7uzmbunEZ1dhKHg+ru\nvr5zv/UnwBtav/XSVbO578q+/1W+Zjb3BacB4af/yzVBIP2fEgRNFHme5zhOkiSF57Ub4YcQ\nQjhO+/Ik1YHxzGMHjefJl6Oa+y0G/kT9WjuJMGazHauM3oxmNhOeV0axyujfPv306aef3rNn\nj1OSQkymxx577KGHHhrbRo6fyVp2oqqq6rHHHgsLC3v99df7//pvbm6+//77OY576623jLq3\nYW7sNjaNHjvuLk13JTcYQlhYmJ90vvutm5adADeWZY1G42RZkdhXRlN2YkoRBGGUZSe81CtT\nB8uEXJt4tkbnlq5B0NYnypmp8tJYf1yIf8RlJ6iuLqqnh+rupnp6qPZ2qreXstup7m6qu5uy\n26neXqqjg7LbSW8v3dVF9fRcz3hdXZQsT5XOtxu9TH1JRgsKIhxH+gUw9UZPTl/W+uKpG4Gt\nr1Poi4xEUeqN23B9x+zfCdM/O3nVpzRGUHbCSyg74Y3Rl53wc4EwZFSSJIfD4b56c29ZuHDh\n3LlzL1++vG/fvttvv71vz7ffflvTtFtuuWWINAgAADC5qBo5V8PlFwsFpYLdoV9IcOtyaZNF\nNvB+fDWjqqStja6vZ5ubqa4uqquL6ux0/0m7H7gjX3c31dHxRQKczHdt3F1b1/u+3CMGb3RP\nueOZO0Fd341h3KGOmz5d1TQnxxFB+CKPGY0az/eN0NMMBo3nyZd70gAARkA/EO7YsUO3IJI3\nVFW12+0ff/zx+vXrb7pzcXFx3x0Ld29GdXV1YWGhe0tsbGxkZCQh5H/+538+/PBDi8Xyi1/8\nou+1//Iv//KTn/zktddeu3btWmpqqsvlKigoOHLkSHBw8L333juyxgMAAPiVhnYm1ybk2oSG\nNp3RsNND1AyrlGGVZ07zRSFBl4vu6KA6O6mODqqjg+7ooG78R9/Y+MVjd98dIcZRrO0+vnhe\nMxo1o1HjOC0khHCcZjJpoqgJghYcTBhGCwkhNK2azddnjnGcFhR0PewZDJogaEYj4fnrUc1g\n+NI4xuGgUJgeACaQfiBsbW1taGgYzXG9XA/zt7/97YAVNfbt27dv3z7343/913+99dZbB3tt\nYmLiD3/4wxdffPHDDz/88MMP3RvnzJnz+OOPj2sRKgAAgPHmdFHHz/N5xUJhJe/5G5VjtFXx\njvQUeXmcgxnrOU2U3U61ttLt7VRbG93eTvU9aGuj2tvdW65vH9GaWOOC5zWjUTWbidGoGQya\n2awFBbmDnGY0EkFQzebrmS001D3EUTObiShqRqMWFHQ9AQIATEn6gXDFihWe65pQFNXZ2enu\nOTQajXFxcaGhoTRNd3V1VVVVuad1zZ07d82aNcHBwe4lN27qa1/72hA3wBYtWuR+kJqaajKZ\nPBd4WLlypcViKSkpqa+vp2l6wYIFS5cuHWWZNQAAAB86V8PmFosHy4QeSWdoaNxsV6ZV2pgk\nmwzDHhpK9fZSLS10UxPd1ka1tn7pz5aWvseUr2pCMIwWHKyazVpQEDGZtKAg1WzWTCbNZNKC\ngjSTSQsJuf7AYNBCQzWDQTMYtODgiZy3BgAQePS/QH/96197biwsLLzzzjuTkpKef/75zMzM\nASu5lZaW/u53v3vrrbd27Nixa9cuL99+x44d3uxmtVqtVqvuU6Iorlq1ysu3AwAA8E9t3XR+\nsZBrE6sbdYaGhgapm5PlrFQpNkp/aCglSXRTE9XQQLe00K2tVFMT3dxMt7ZSLS10Swvd1ES1\ntFCDlNIZFzyvBgdrISHu/1SzWTObmbAwLjxcFgSnwaAFB6shIZrZrAUHX/8Pk/8BAHzB2ztq\nbW1td9xxR1hY2JEjR3TXnbdYLG+++WZ0dPSzzz4bExPz6KOPjmk7AQAAApCqktJL3L5C8dg5\nweWR9WiaWOY7ty2X1sS28S2NdE0TVdRENzbSTU10Swt97dr14NfQMAFrabr75dTQUC00VAsL\nU0NCtLAwLTRUvZH6rgc/92O94mmiKHImk3P4q4wCAMD48TYQ/vWvf62vr//lL3+pmwb7/PjH\nP961a9euXbu+//3vY+gmAADAYGoambxiMccmtHfThJAgR+ec3rppvQ1RPVem2Rvma1fi+frZ\n8hU+r5H+aT3V2zte7eA4NSxMmzbtiz8jIq4/Dg3tnwBHvEQKAAD4M28DoXvq4LJly4beLSgo\nKC4u7vTp05cvX54/f/5oWwcAABAwXC66sdFxqa6isOVKaaNWW2/prc/ovhLRe3V6b73oGvvI\npwUHq5GR6rRpWni4Om2aGhmphYer4eFaeLgaFnb9z+DgMX9fAACYRLwNhI2NjYQQb0p/utcX\nbWhoQCAEAIApx+Wir11j6uro2lq6vp6+epWpr6evXaPr66nGRkpVCSEzxuSNeF4ND1cjI9XI\nSDU8XJsxQ42IUN15LzJSnTZNDQ8nPD8mbwUAAAHM20AYHBxMCDlw4MDq1auH2K2hoaGioqJv\nfwAAgIBEdXXRdXVMbS195QpTX8/W1zNXrgjV1XRDA7lRX3eU3NFOmTlTi4xUZszQIiPViAg1\nKkoND1enT9emTRuTdwEAgCnO20CYlpa2d+/e5557Li0tLSsrS3efjo6Oe++91+VyBQUFLVy4\ncOwaCQAA4BuU3U5XVzM1NUxNjfsBXV3NXLlCdXSM/uDOkGnUrCg1OlqdPl2dNUuNiFBnzbr+\nePp09O8BAMAE8DYQfvvb3/7P//zP7u7ur3zlK6tXr87MzFywYEFISAjLsna7va6uzmazffDB\nBx0dHYSQb33rW55lDAEAAPyXojBXrnwR+W4kQLqpaTRHVSm6xTCj0TS7yTirwTSn0RjNxcxY\nsCJq6epwYe5MDb8rAQDA17wNhNHR0X/+85/vvvtuh8Nx7NixY8eODbZncnLy888/P0bNAwAA\nGGtOJ1NTw1y+zHz+OX3xovsBU1tLHI4RH1ILDXXNnHMlaM5Zbd5FNvaaac41U8w1U0yLYYZC\ns4SQcLOanixnpkqzI64Xlxh2XXkAAIBx4G0gJITs2LGjqKjomWee2bdvnyzLnjvMnDnzu9/9\n7pNPPjl0aQoAAIAJ4nIxtbVMVRVTVcV8/jlz+TJ96RJTVzfCaX4UpUZFKTExamysEh2tRker\ns2fLs+YUSfPyqiIPn2YVdeArOJakLXRsSZFXx8usTsF5AAAAHxtGICSEJCYmvv/++11dXcXF\nxRcuXGhvb3c6nUajMTIyMiEhYdmyZRRFjVNDAQAAhkZ1dDCXLzPV1cz580xFBVNdzVRWUnb7\nCA6lhYaqUVHqjBlKbKwSG6vOnavExioLF2pBQX37XKhjc4vFgr8JXb06v/vmz3RlpcqbLLLZ\n6BETAQAA/MbwAqFbcHDw+vXr169fP+atAQAA8IqmMVeuMBUVzPnz1zsAL1ygW1uHfRyaVmfN\nUubNU+bNU+bOVebNU+fOVWJiNLN5sFd09NAHSoWcIuHzazq/Q81GbWOSlJUmL5g5NmuNAgAA\njKuRBEIAAIAJRl+7xlRUsBUV7hDInj1LdXcP9yBqVJSyZMmXOv0WLdKMRq9eq5HSi9y+QvH4\necHpkfVoiljj1I3LetYvc/AspgcCAMCkMZJAWFtbe+jQoXPnzrW1tT388MPx8fHu7ZIkYXFR\nAAAYPbqujj13jjl3jq2sZM6fZyorqd7eYR1BDQ9XFi1SFi5UFixQFi5UFi1SYmIIx42gMTWN\nTK5NzC8RWrtoz2dnRygZVmnbSm1GONPTozPBHgAAwJ8NLxBWVVU9+uijn3zyiaZdv/155513\n9gXCjRs3pqSk/Pa3vw3qN8UCAADgJhwO5tIltrTUHf/Y4uLhFXvgOGXWLHXuXFdc3PUOwPh4\nNTJylI3qlamjZ/n8ErHkIqd59PkZBW11gmNLspS8wElRRBCEUb4dAACATwwjEJ4+fXrjxo2t\ng8zQqKurO3ny5IkTJ8rLywsKClgWg1EBAEAfU1vLnDnDnj17/c/PPyeK4uVrNUFQFi1S4uKU\n+HjXokVKfLwSG0uYMVvBU9VI2SUu1yYeLucdroGrxVAUWTbXmZkqrV3qEHkMDQUAgEnP29im\nKMo999zT2tpqMpm+973vbdu27Yc//OHJkyf7djCZTA8//PDu3bs/++yzP/7xj48++uj4NBgA\nACYf+to1trT0+n9FRXRLi7ev5Dhl/nzX4sXK4sXKkiWuuDhl0aIxjH/9NbQzuTYht0hoaNc5\nfmSouiVFykyVZ4R5m10BAAD8n7eBMCcnp6ysTBTF48ePL126lBBiMBj67xASEvKHP/zBYDD8\n+te/fvnllxEIAQCmLpeLvXCBKS1ly8rYsjL2zBlvF4ChKCUmRklMdCUkKAkJrqVLlZiYcYp/\nfZwu6vh5Pq9YKKzkVc9Cgoy2Kt6RniIvj3MwOlMIAQAAJjdvA2F2djYh5JFHHnGnwcH86Ec/\nevHFFysqKhobGyNHPX8DAAAmB1VlKiu54mK2uJgtK2POnKEkyZvXacHBrvh4ZelS19KlroQE\nJT5eM5nGu7F9ztWwuTbx4GmhR9IpJLh4tivDKm1Mkk0GDA0FAICA5W0grKmpIYSsW7du6N1C\nQ0MXLVpUWlpaW1uLQAgAEMDoq1dZm40rLmaLitiSEi/7ANXZs11JSa6kJFdCguLuAJxwbd30\nwTIhp0i4pFdIMNiorVsq37ZSmo9CggAAMAV4Gwi7uroIITNmzLjpnqGhXL1qYQAAIABJREFU\noYQQh8MxmmYBAIC/obq62JIStqjI3RNIX73qxWsoJTb2egJMSlIsFnXatPFvqT6ni5yo4HNt\n4qlKXvEYGsoyZHmcIzNVWh7nYMd3jCoAAIAf8TYQhoWFEULq6urS0tKG2E3TtKqqKkLINN/9\nygcAgLHCXLhAysv5gwf548eZCxeI5xy7AWhaWbjQtWxZXwjUzOYJaelQPr/GZhcJBaVCR4/O\nLMDYKCUrVdqcLIcG3eynAwAACDjeBkKLxfLuu+9+8MEH27dvH2K3vXv31tXVmUym+fPnj0Xz\nAABgQlGSxJaUsCdPcidPsoWFdGsrIWToDjN11iyX1eq0Wl1Wq8timchJgEPrtlOHyoU8m3C2\nRqcefZCobVgmp6fIS2OdE982AAAAP+FtILzzzjt/8pOfvPXWW5mZmXfffbfuPu+///79999P\nCLnttts4Tue3LwAA+CG6qYm12djSUu7kSfb4cUqWh95fM5lcCQkui8VlsbhWr/bJPMAhqCqx\nXeRzioRjZ3mnMnC1GJoiKQudGVbplgQHx2K1GAAAmOq8DYQJCQnf+ta39uzZ881vfnPPnj1b\nt25tbGwkhBw6dOj8+fO1tbXZ2dmlpaWEEFEUn3nmmXFsMgAAjBpdW8sdPcodOcIdO8ZcvnyT\nvRnGFR/vWrHCmZLislqVhQsJ7Y8VGOpamNwiIa9EbO7Qad7MaUpmqrwlRZoegqGhAAAA13kb\nCAkhL7/8cm1t7cGDB/ft27dv3z73xl/84hf99xFF8S9/+Ut8fPxYthEAAMYCU119PQQePUrX\n1g69sxYc7EpLU1auFNPT7UlJPX6ZAN0cLurEeX5foVhykdM8+vw4Vlu1xLFtuZS8wEnpVJcA\nAACY0oYRCE0mU15e3h/+8Iddu3bV19cPPBDLbt++/ec//3lCQsKYthAAAEaOqa5mjx/nTp7k\nCgqYm4VANSrKuXKla+VKl8XitFoJx7EsK4aGErud9PRMTIO9p2nkTDWXUyQcLhfsDp2olxDj\nzEqT1yfKBgFDQwEAAPQNIxASQliWfeyxx37wgx+Ul5efPn26paXF6XSazeb58+enpaWZ/WAp\nOQAAoK9c4Q8d4g4d4j77jG5oGGpXhnElJjpXr3atXOlcvlyNipqoNo5KSyedXyJknxLrWnTW\nu5kWrK5LlLcul+dGoZAgAADATXgbCB0OB8/z7scURS1btmzZsmXj1ioAABgeqqeHPXWKP3SI\nO3iQLS0dald3CFyxwrVqlWPdOi0sbKLaOFpOF3X0HJ9TJBRX8arn0FBGWxXvyEyVUxc6/Hh8\nKwAAgH/xNhDefvvtJpPp3nvv3bZtG1YQBQDwB5TDwZ44wR06xB86xJaWEkUZdFeOcyYnu9as\nca5Z41yxwn8qQ3ipso7Ns4kFpUKXXWdo6IKZrsxUeZNFMhsxNBQAAGB4vA2Esizn5OS8//77\nERERd999986dO1NTU8e1ZQAAoEPT2DNnuE8/5Q8dYo8fp+z2QfdkWafV6ly71rl6tWvFCs1o\nnMBWjo0uO3W4XPj4hHjxqs5vK5NBW58ob10uLYrG0FAAAIAR8jYQxsfHHz58WFXV5ubm3bt3\n7969OyEhYefOnffcc8+sWbPGtYkAAED19nKHD/M5OXx+Pl1XN8SeSmysc8MG54YNjg0btJCQ\nCWvhGFJUUljJ5xSJJyt4l0evJ02TtEWOzFR55WKZG95EeAAAABiI0jyX6B7E1atX/+//s3ff\n8VFV+f/Hz71T7p2ZEBJ6LypVShKaWBAIBASx/RBFEXZdGzbW9nVXpSjYXXVFXXVxVRRlVXDF\ngiRAaIoIKRQJJYD0npA2c++0+/tjdnFIhjBAkplkXs8/fIRz78x85jqZzHvuuefz+edz585d\ns2bNyVvJsjxkyJDx48dff/319trz9fOxY8ciXUJ5DRo0EEIUFBREupBol5iYWFhYGOkqopok\nSQ0bNvR4PEVFRZGuJaqZzWa73V5cXBzpQk7PMMybNlmWLLEuWWJZt054T3sezN+ihWfAAPeA\nAZ4rr/Q3aVKFJZjN5oSEBJfLVVYjq4zuPWrKyFYzspXC0hBXAbZq5BvYQx+aojVNjLpGgoqi\nmM3mmjlKtZeqqnFxcaWlpZqmRbqWqGa3230+n67rkS4kqjkcDpvNVlRU5PF4Il1LVIuPj3c6\nnd7T/wWBECI+Pt5qtR4/fjz8ZFS7mEymxNMvGXAWX642b9580qRJkyZN2r1799y5c+fOnZub\nm+v3+9PT09PT0+vVqzd69OgJEyYMGDBAotMTAJyr308GLl4sV+jxc5Jht3v79AmEQG+PHqI2\nv/E6demnzdYluaEbCdoVo39X95AkGgkCAFD1zuIMYUXbtm377LPP/v3vf+fl5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DKZqiAQrlu3bvny5c2bN6+iqgBACCHkQ4ds//yn+vHH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sel7gGdFH699FN7NqFwAAAGqzCC+QPWzY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\n5xNp98TR0fHMmTN9+vTR07127dppN3bs2FH7l+Xw4cOXLFmi0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"\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "application/pdf": { + "height": 300, + "width": 600 + }, + "image/jpeg": { + "height": 300, + "width": 600 + }, + "image/png": { + "height": 300, + "width": 600 + }, + "image/svg+xml": { + "height": 300, + "isolated": true, + "width": 600 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "#[4] Plotting \n", + "titan %>%\n", + " ggplot(aes(fare, survived)) + \n", + " geom_point() + \n", + " geom_smooth(method = lm, se = FALSE) + \n", + " geom_smooth(method = \"glm\", method.args = list(family = \"binomial\"), se = FALSE, color = 'red') + \n", + " theme(text = element_text(size = 18))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1.4 **Logistic Regression and Interpretation**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In LR, we were modelling \n", + "\n", + "$$\n", + "E[Y|X] = \\beta_0 + \\beta_1 X\n", + "$$\n", + "\n", + "but in logistic regression, we are modelling the **logit**\n", + "\n", + "$$\n", + "\\log\\left(\\frac{P(\\left.Y = 1 \\right| X)}{1-P(\\left.Y = 1 \\right| X)}\\right) = \\beta_0 + \\beta_1 X\n", + "$$\n", + "\n", + "therefore, we need to adjust our interpretation." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "#### 1.4.1 **One numeric covariate**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see the output of our logistic model for the Titanic data again:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\log\\left(\\frac{P(\\left.\\text{survived} = 1 \\right| \\text{fare})}{1-P(\\left.\\text{survived} = 1 \\right| \\text{fare})}\\right) = \\beta_0 + \\beta_1\\times\\text{fare}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call: glm(formula = survived ~ fare, family = \"binomial\", data = titan)\n", + "\n", + "Coefficients:\n", + "(Intercept) fare \n", + " -0.9413 0.0152 \n", + "\n", + "Degrees of Freedom: 890 Total (i.e. Null); 889 Residual\n", + "Null Deviance:\t 1187 \n", + "Residual Deviance: 1118 \tAIC: 1122" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "model_titanic_logistic" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "\n", + "**Interpretation:**\n", + "\n", + "- Intercept - $\\beta_0 = -0.9413$: if the `fare` paid was 0 dollars, the logit is expected to be -0.9413.\n", + "- Slope - $\\beta_1 = 0.0152$: an increase of 1 dollar in the `fare` paid is associated with an increase in the logit of 0.0152." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But interpreting the `logit` function itself is hard. So, we usually interpret the exponential of the coefficients, so we can talk in terms of **odds** instead of logits. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 2 × 5
termestimatestd.errorstatisticp.value
<chr><dbl><dbl><dbl><dbl>
(Intercept)0.39010870.095129144-9.8952844.363702e-23
fare 1.01531290.002231678 6.8096149.786127e-12
\n" + ], + "text/latex": [ + "A tibble: 2 × 5\n", + "\\begin{tabular}{lllll}\n", + " term & estimate & std.error & statistic & p.value\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\t (Intercept) & 0.3901087 & 0.095129144 & -9.895284 & 4.363702e-23\\\\\n", + "\t fare & 1.0153129 & 0.002231678 & 6.809614 & 9.786127e-12\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 2 × 5\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> |\n", + "|---|---|---|---|---|\n", + "| (Intercept) | 0.3901087 | 0.095129144 | -9.895284 | 4.363702e-23 |\n", + "| fare | 1.0153129 | 0.002231678 | 6.809614 | 9.786127e-12 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value \n", + "1 (Intercept) 0.3901087 0.095129144 -9.895284 4.363702e-23\n", + "2 fare 1.0153129 0.002231678 6.809614 9.786127e-12" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[5] Coefficients for the odds\n", + "tidy(model_titanic_logistic, exponentiate = TRUE)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- Intercept: $e^{\\beta_0} = e^{-0.9413} = 0.3901$, if the `fare` paid was 0 dollars, the **odds** is expected to be 0.3901.\n", + "- Slope: $e^{\\beta_1} = e^{0.0152} = 1.0153$, it **multiplies** the **odds** by 1.0153, i.e., it increases the odds in $1.53\\%$ of its value." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "#### 1.4.2 **One categorical covariate**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's fit a logistic regression now using `sex` as covariate. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\log\\left(\\frac{P(\\left.\\text{survived} = 1 \\right| \\text{fare})}{1-P(\\left.\\text{survived} = 1 \\right| \\text{fare})}\\right) = \\beta_0 + \\beta_1 X_\\text{male}\n", + "$$\n", + "\n", + "where $X_\\text{male} = 1$ if passenger is male and 0 if female. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call: glm(formula = survived ~ sex, family = binomial, data = titan)\n", + "\n", + "Coefficients:\n", + "(Intercept) sexmale \n", + " 1.057 -2.514 \n", + "\n", + "Degrees of Freedom: 890 Total (i.e. Null); 889 Residual\n", + "Null Deviance:\t 1187 \n", + "Residual Deviance: 917.8 \tAIC: 921.8" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[6] Fit Logistic Regression with Sex as covariate\n", + "model_titanic_logistic_sex <- glm(survived ~ sex, family = binomial, data = titan ) \n", + "model_titanic_logistic_sex" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 2 × 5
termestimatestd.errorstatisticp.value
<chr><dbl><dbl><dbl><dbl>
(Intercept)2.876543210.1289864 8.1914772.580394e-16
sexmale 0.080967320.1671782-15.0361074.258662e-51
\n" + ], + "text/latex": [ + "A tibble: 2 × 5\n", + "\\begin{tabular}{lllll}\n", + " term & estimate & std.error & statistic & p.value\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\t (Intercept) & 2.87654321 & 0.1289864 & 8.191477 & 2.580394e-16\\\\\n", + "\t sexmale & 0.08096732 & 0.1671782 & -15.036107 & 4.258662e-51\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 2 × 5\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> |\n", + "|---|---|---|---|---|\n", + "| (Intercept) | 2.87654321 | 0.1289864 | 8.191477 | 2.580394e-16 |\n", + "| sexmale | 0.08096732 | 0.1671782 | -15.036107 | 4.258662e-51 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value \n", + "1 (Intercept) 2.87654321 0.1289864 8.191477 2.580394e-16\n", + "2 sexmale 0.08096732 0.1671782 -15.036107 4.258662e-51" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[7] Get the coefficients for the odds\n", + "tidy(model_titanic_logistic_sex, exponentiate = TRUE)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "**Interpretation:**\n", + "\n", + "- Reference level: `female`\n", + "- Intercept: $e^{\\beta_0} = e^{1.057} = 2.8765$, a female passenger had a 2.8765 odds of surviving (i.e., the proportion of survivals relative to the proportion of deaths in the sample)\n", + "- Slope: $e^{\\beta_1} = e^{-2.514} = 0.08097$, it **multiplies** the female passenger **odds** by 0.08097; or, alternatively, is male passangers's **odds** of **dying** were $e^{2.514} = 12.3542$ higher than of that of females. \n", + " - Not a good time to be a male in a ship, eh?" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A grouped_df: 4 × 3
sexsurvivedn
<chr><int><int>
female0 81
female1233
male 0468
male 1109
\n" + ], + "text/latex": [ + "A grouped\\_df: 4 × 3\n", + "\\begin{tabular}{lll}\n", + " sex & survived & n\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\t female & 0 & 81\\\\\n", + "\t female & 1 & 233\\\\\n", + "\t male & 0 & 468\\\\\n", + "\t male & 1 & 109\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A grouped_df: 4 × 3\n", + "\n", + "| sex <chr> | survived <int> | n <int> |\n", + "|---|---|---|\n", + "| female | 0 | 81 |\n", + "| female | 1 | 233 |\n", + "| male | 0 | 468 |\n", + "| male | 1 | 109 |\n", + "\n" + ], + "text/plain": [ + " sex survived n \n", + "1 female 0 81\n", + "2 female 1 233\n", + "3 male 0 468\n", + "4 male 1 109" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[8] Let's check these numbers with the sample\n", + "titan %>%\n", + " group_by(sex) %>%\n", + " count(survived)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "2.87654320987654" + ], + "text/latex": [ + "2.87654320987654" + ], + "text/markdown": [ + "2.87654320987654" + ], + "text/plain": [ + "[1] 2.876543" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[9] Odds of surviving - female\n", + "233/81 # This is our beta 0" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "0.232905982905983" + ], + "text/latex": [ + "0.232905982905983" + ], + "text/markdown": [ + "0.232905982905983" + ], + "text/plain": [ + "[1] 0.232906" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[10] Odds of surviving - male\n", + "109/468" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "0.232913703703704" + ], + "text/latex": [ + "0.232913703703704" + ], + "text/markdown": [ + "0.232913703703704" + ], + "text/plain": [ + "[1] 0.2329137" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[11] Odds of surving - male: using beta_1 times odds_surving_female\n", + "233/81 * 0.08097" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "0.347639484978541" + ], + "text/latex": [ + "0.347639484978541" + ], + "text/markdown": [ + "0.347639484978541" + ], + "text/plain": [ + "[1] 0.3476395" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[12] Odds of dying - female\n", + "81/233 # This is our beta 0" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "4.29357798165138" + ], + "text/latex": [ + "4.29357798165138" + ], + "text/markdown": [ + "4.29357798165138" + ], + "text/plain": [ + "[1] 4.293578" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[13] Odds of dying - male\n", + "468/109 # This is our beta 0" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "sexmale: 4.29357798163834" + ], + "text/latex": [ + "\\textbf{sexmale:} 4.29357798163834" + ], + "text/markdown": [ + "**sexmale:** 4.29357798163834" + ], + "text/plain": [ + " sexmale \n", + "4.293578 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[14] Odds of dying - male: using exp(-beta_1) times odds_dying_female\n", + "81/233 * exp(-model_titanic_logistic_sex$coefficients[2])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "#### 1.4.2 **One categorical one numerical covariate**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's fit a logistic regression using `Sex` and `Fare`:\n", + "\n", + "$$\n", + "\\log\\left(\\frac{P(\\left.\\text{survived} = 1 \\right| \\text{fare})}{1-P(\\left.\\text{survived} = 1 \\right| \\text{fare})}\\right) = \\beta_0 + \\beta_1 X_\\text{male} + \\beta_2\\times\\text{fare}\n", + "$$\n", + "\n", + "where $X_\\text{male} = 1$ if passenger is male and 0 if female. " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call: glm(formula = survived ~ sex + fare, family = binomial, data = titan)\n", + "\n", + "Coefficients:\n", + "(Intercept) sexmale fare \n", + " 0.64710 -2.42276 0.01121 \n", + "\n", + "Degrees of Freedom: 890 Total (i.e. Null); 888 Residual\n", + "Null Deviance:\t 1187 \n", + "Residual Deviance: 884.3 \tAIC: 890.3" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[15] Fit Logistic Regression with Sex and Fare as covariates\n", + "\n", + "model_titanic_logistic_multiple <- glm(survived ~ sex + fare, family = binomial, data = titan ) \n", + "model_titanic_logistic_multiple" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, we have two logistic curves with different intercepts for the `logit` function, but the same slope. \n", + "\n", + "\\begin{equation*}\n", + " \\text{logit}(p_\\text{survival}) = \\beta_0 + \\beta_1\\times X_\\text{male} + \\beta_2 \\times \\text{fare} = \\begin{cases}\n", + " \\beta_0 + \\beta_2 \\times \\text{fare}, \\quad\\quad\\quad \\text{if } X_\\text{male} = 0\\\\\n", + " \\beta_0 + \\beta_1 + \\beta_2 \\times \\text{fare}, \\quad \\text{ if } X_\\text{male} = 1\n", + " \\end{cases}\n", + "\\end{equation*}\n", + " \n", + "Therefore, for the odds: \n", + "\n", + "\\begin{equation*}\n", + " \\frac{p_\\text{survival}}{1-p_\\text{survival}} = \\begin{cases}\n", + " e^{\\beta_0}e^{\\beta_2\\text{fare}}, \\quad\\quad\\quad \\text{if } X_\\text{male} = 0\\\\\n", + " e^{\\beta_0 + \\beta_1}e^{\\beta_2 \\text{fare}}, \\quad\\quad \\text{if } X_\\text{male} = 1\n", + " \\end{cases}\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "application/pdf": 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epNCN07a38PYKTOYltdKJdHS9qOesbM0gr67Aj+meavDwptQ97eFuYtxhDbU+p0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\ncmVmCjcxNTc5CiUlRU9GCg==", 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S4BCMgLEEEAkHLHtz7Y56j4deHJPh/4bTTIboyu0jTzSBcBnIA4HYYUD8M1uUVz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\nmIf+eaTzuPzKiu8oo9ul8NOK+9/m2H9mVJfxcVUl84x/9IjF/ic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TfZGxEOh8Phie/UfAmzAQBAiWC2TUZeskzK5yXLJCMvmSaZBjMNZpnMMMg0JMsi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hYSHfVfBAqVSKRKKCgoKyK1P5CalUSgix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\nOAVudCKKiopSZihSqVQ6nS4YDCpzu+t0OmWuuHRB2Ov1hs5CK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Fw+bWp6sKSCERGjx4uJY9y7/ZPG6vTPVtV8arN7W/xa44jUmtKGhq/8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\nrZUhKHo9qctoq9e0ez2j0ejz+RR4h4nUZdTtdkfeZbQ3sVgsDQ3t7g7dC0h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+ }, + "image/svg+xml": { + "height": 300, + "isolated": true, + "width": 600 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "#[16] Plotting the logistic curves\n", + "\n", + "# Don't worry about this part of the code\n", + "data_for_plotting <- \n", + " tibble(fare = rep(seq(0, 499.99, 0.1), 2), \n", + " sex = c(rep('female', 5000), rep('male', 5000))) %>%\n", + " add_predictions(model = model_titanic_logistic_multiple, var = 'pred', type = 'response')\n", + "##############################################\n", + "\n", + "titan %>%\n", + " ggplot(aes(fare, survived, color = sex)) + \n", + " geom_point() + \n", + " geom_line(aes(y = pred), data = data_for_plotting) + \n", + " theme(text = element_text(size = 18))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 3 × 5
termestimatestd.errorstatisticp.value
<chr><dbl><dbl><dbl><dbl>
(Intercept)1.909994190.148502397 4.3575071.315524e-05
sexmale 0.088676520.170515090-14.2084808.116863e-46
fare 1.011277190.002295331 4.8856051.031115e-06
\n" + ], + "text/latex": [ + "A tibble: 3 × 5\n", + "\\begin{tabular}{lllll}\n", + " term & estimate & std.error & statistic & p.value\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\t (Intercept) & 1.90999419 & 0.148502397 & 4.357507 & 1.315524e-05\\\\\n", + "\t sexmale & 0.08867652 & 0.170515090 & -14.208480 & 8.116863e-46\\\\\n", + "\t fare & 1.01127719 & 0.002295331 & 4.885605 & 1.031115e-06\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 3 × 5\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> |\n", + "|---|---|---|---|---|\n", + "| (Intercept) | 1.90999419 | 0.148502397 | 4.357507 | 1.315524e-05 |\n", + "| sexmale | 0.08867652 | 0.170515090 | -14.208480 | 8.116863e-46 |\n", + "| fare | 1.01127719 | 0.002295331 | 4.885605 | 1.031115e-06 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value \n", + "1 (Intercept) 1.90999419 0.148502397 4.357507 1.315524e-05\n", + "2 sexmale 0.08867652 0.170515090 -14.208480 8.116863e-46\n", + "3 fare 1.01127719 0.002295331 4.885605 1.031115e-06" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[17] Getting the coefficients for the odds\n", + "tidy(model_titanic_logistic_multiple, exponentiate = TRUE)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- Note that we are controlling for `fare`. For any constant `fare` value, being male changes the `odds` of surviving by a factor of $e^{-2.42276} = 0.0887$, or in other words, it increases the odds of dying by $11.2769$ times. \n", + "\n", + "- Another way to look at this is that male passengers have only $8.87\\%$ of the odds of surviving a female passenger. " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
1
520.161725278468
2
46.1261298230157
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[1] 520.161725278468\n", + "\\item[2] 46.1261298230157\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "1\n", + ": 520.1617252784682\n", + ": 46.1261298230157\n", + "\n" + ], + "text/plain": [ + " 1 2 \n", + "520.16173 46.12613 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[18] For example, for a fare of 500, the odds for females and males are: \n", + "exp(predict(model_titanic_logistic_multiple, \n", + " newdata = tibble(fare = c(500, 500), sex = c('female', 'male'))))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "- Considering `sex` constant, increasing the fare in 1 dollar increases the odds of surviving in approx. $1.1\\%$ for either `male` or `female`.\n", + " - Considering `sex` constant, increasing the fare in 1 dollar changes the odds of surviving by a factor of $1.0113$." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "For female passengers, increasing the fare from 500 to 501 increases the odds of surviving from 520.1617 to 526.0277 .\n", + "\n", + "For male passengers, increasing the fare from 500 to 501 increases the odds of surviving from 46.12613 to 46.6463 .\n" + ] + } + ], + "source": [ + "#[19] For example, females and males passenger, increasing the fare from 500 to 501:\n", + "aux <- exp(predict(model_titanic_logistic_multiple, newdata = tibble(fare = c(500, 501, 500, 501), sex=c('female', 'female', 'male','male'))))\n", + "\n", + "cat(\"\\nFor female passengers, increasing the fare from 500 to 501 increases the odds of surviving from\", aux[1], 'to', aux[2], '.\\n')\n", + "cat(\"\\nFor male passengers, increasing the fare from 500 to 501 increases the odds of surviving from\", aux[3], 'to', aux[4], '.\\n')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "#### 1.4.3 **One categorical and one numerical covariate with interaction term**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's fit a logistic regression using `Sex` and `Fare`:\n", + "\n", + "$$\n", + "\\log\\left(\\frac{P(\\left.\\text{survived} = 1 \\right| \\text{fare})}{1-P(\\left.\\text{survived} = 1 \\right| \\text{fare})}\\right) = \\beta_0 + \\beta_1 X_\\text{male} + \\beta_2\\times\\text{fare} + \\beta_3 X_\\text{male}\\times\\text{fare}\n", + "$$\n", + "\n", + "where $X_\\text{male} = 1$ if passenger is male and 0 if female. " + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call:\n", + "glm(formula = survived ~ sex * fare, family = binomial, data = titan)\n", + "\n", + "Deviance Residuals: \n", + " Min 1Q Median 3Q Max \n", + "-2.6280 -0.6279 -0.5991 0.8172 1.9288 \n", + "\n", + "Coefficients:\n", + " Estimate Std. Error z value Pr(>|z|) \n", + "(Intercept) 0.408428 0.189999 2.150 0.031584 * \n", + "sexmale -2.099345 0.230291 -9.116 < 2e-16 ***\n", + "fare 0.019878 0.005372 3.701 0.000215 ***\n", + "sexmale:fare -0.011617 0.005934 -1.958 0.050252 . \n", + "---\n", + "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", + "\n", + "(Dispersion parameter for binomial family taken to be 1)\n", + "\n", + " Null deviance: 1186.66 on 890 degrees of freedom\n", + "Residual deviance: 879.85 on 887 degrees of freedom\n", + "AIC: 887.85\n", + "\n", + "Number of Fisher Scoring iterations: 5\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[20] Fit the model with interaction\n", + "model_titanic_logistic_interaction <- glm(survived ~ sex * fare, family = binomial, data = titan ) \n", + "summary(model_titanic_logistic_interaction)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, we have two logistic curves with different intercepts and slopes for the `logit`. \n", + "\n", + "\\begin{equation*}\n", + " \\text{logit}(p_\\text{survival}) = \\beta_0 + \\beta_1\\times X_\\text{male} + \\beta_2 \\times \\text{fare} + \\beta_3 \\times \\text{fare}\\times X_\\text{male}= \\begin{cases}\n", + " \\beta_0 + \\beta_2 \\times \\text{fare}, \\quad\\quad\\quad \\text{if } X_\\text{male} = 0\\\\\n", + " \\beta_0 + \\beta_1 + \\left(\\beta_2 +\\beta_3\\right)\\times \\text{fare}, \\quad \\text{ if } X_\\text{male} = 1\n", + " \\end{cases}\n", + "\\end{equation*}\n", + " \n", + "Therefore, for the odds: \n", + "\n", + "\\begin{equation*}\n", + " \\frac{p_\\text{survival}}{1-p_\\text{survival}} = \\begin{cases}\n", + " e^{\\beta_0}e^{\\beta_2\\text{fare}}, \\quad\\quad\\quad \\ \\ \\text{if } X_\\text{male} = 0\\\\\n", + " e^{\\beta_0 + \\beta_1} e^{\\left(\\beta_2+\\beta_3\\right) \\text{fare}}, \\quad \\text{if } X_\\text{male} = 1\n", + " \\end{cases}\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "application/pdf": 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wBG6axsqwvl6mhBm6lnzKysoM+B4J/p/vqg1Dap29vCvMUYYntKnc7APOlzk1HE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", 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9rp31XQSiszxP4ksfB+h3WranIYbS3A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\nwCPZYGPxV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4Oc4HsVuk69exs/EuO0ziPctqnbVZFG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\n0aJFXq9XK+natesvf/nL888/v+GzJVkN7crevXtnzZoViUSmTJny61//uuE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+ }, + "image/svg+xml": { + "height": 300, + "isolated": true, + "width": 600 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "#[21c] Plotting \n", + "\n", + "# Don't worry about this part of the code\n", + "data_for_plotting <- \n", + " tibble(fare = rep(seq(0, 499.99, 0.1), 2), \n", + " sex = c(rep('female', 5000), rep('male', 5000))) %>%\n", + " add_predictions(model = model_titanic_logistic_interaction, var = 'pred', type = 'response')\n", + "##############################################\n", + "\n", + "titan %>%\n", + " ggplot(aes(fare, survived, color = sex)) + \n", + " geom_point() + \n", + " geom_line(aes(y = pred), data = data_for_plotting) + \n", + " theme(text = element_text(size = 18))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the coefficient estimates here are the same as if a model with `fare` as covariate only for women passenger and a model only for male passengers:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call:\n", + "glm(formula = survived ~ fare, family = binomial, data = titan %>% \n", + " filter(sex == \"female\"))\n", + "\n", + "Deviance Residuals: \n", + " Min 1Q Median 3Q Max \n", + "-2.6280 -1.4224 0.6451 0.8901 0.9537 \n", + "\n", + "Coefficients:\n", + " Estimate Std. Error z value Pr(>|z|) \n", + "(Intercept) 0.408428 0.190018 2.149 0.031602 * \n", + "fare 0.019878 0.005374 3.699 0.000216 ***\n", + "---\n", + "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", + "\n", + "(Dispersion parameter for binomial family taken to be 1)\n", + "\n", + " Null deviance: 358.53 on 313 degrees of freedom\n", + "Residual deviance: 334.05 on 312 degrees of freedom\n", + "AIC: 338.05\n", + "\n", + "Number of Fisher Scoring iterations: 6\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "summary(glm(survived ~ fare, family = binomial, data = titan %>% filter(sex == 'female')))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call:\n", + "glm(formula = survived ~ fare, family = binomial, data = titan %>% \n", + " filter(sex == \"male\"))\n", + "\n", + "Deviance Residuals: \n", + " Min 1Q Median 3Q Max \n", + "-1.3877 -0.6273 -0.5997 -0.5976 1.9288 \n", + "\n", + "Coefficients:\n", + " Estimate Std. Error z value Pr(>|z|) \n", + "(Intercept) -1.690918 0.130132 -12.994 < 2e-16 ***\n", + "fare 0.008261 0.002521 3.277 0.00105 ** \n", + "---\n", + "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", + "\n", + "(Dispersion parameter for binomial family taken to be 1)\n", + "\n", + " Null deviance: 559.27 on 576 degrees of freedom\n", + "Residual deviance: 545.80 on 575 degrees of freedom\n", + "AIC: 549.8\n", + "\n", + "Number of Fisher Scoring iterations: 4\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# the slope for males in the model with interaction is given by: 0.019878-0.011617 = 0.008261\n", + "summary(glm(survived ~ fare, family = binomial, data = titan %>% filter(sex == 'male')))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 4 × 5
termestimatestd.errorstatisticp.value
<chr><dbl><dbl><dbl><dbl>
(Intercept) 1.50445060.189998621 2.1496353.158407e-02
sexmale 0.12253660.230290839-9.1160617.790454e-20
fare 1.02007740.005371548 3.7006982.150071e-04
sexmale:fare0.98845010.005933729-1.9578095.025241e-02
\n" + ], + "text/latex": [ + "A tibble: 4 × 5\n", + "\\begin{tabular}{lllll}\n", + " term & estimate & std.error & statistic & p.value\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\t (Intercept) & 1.5044506 & 0.189998621 & 2.149635 & 3.158407e-02\\\\\n", + "\t sexmale & 0.1225366 & 0.230290839 & -9.116061 & 7.790454e-20\\\\\n", + "\t fare & 1.0200774 & 0.005371548 & 3.700698 & 2.150071e-04\\\\\n", + "\t sexmale:fare & 0.9884501 & 0.005933729 & -1.957809 & 5.025241e-02\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 4 × 5\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> |\n", + "|---|---|---|---|---|\n", + "| (Intercept) | 1.5044506 | 0.189998621 | 2.149635 | 3.158407e-02 |\n", + "| sexmale | 0.1225366 | 0.230290839 | -9.116061 | 7.790454e-20 |\n", + "| fare | 1.0200774 | 0.005371548 | 3.700698 | 2.150071e-04 |\n", + "| sexmale:fare | 0.9884501 | 0.005933729 | -1.957809 | 5.025241e-02 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value \n", + "1 (Intercept) 1.5044506 0.189998621 2.149635 3.158407e-02\n", + "2 sexmale 0.1225366 0.230290839 -9.116061 7.790454e-20\n", + "3 fare 1.0200774 0.005371548 3.700698 2.150071e-04\n", + "4 sexmale:fare 0.9884501 0.005933729 -1.957809 5.025241e-02" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[22c]\n", + "tidy(model_titanic_logistic_interaction, exponentiate = TRUE)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The reasoning for interpretation is the same. \n", + "Just remember that now, we have an interaction term, so different slopes for `fare`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1.5 Inference \n", + "\n", + "The results in this section are theorectical results based on large samples. \n", + "\n", + "For confidence intervals of $1-\\alpha$%, we can use\n", + "\n", + "$$\n", + "CI\\left(\\hat{\\beta}_j, 1-\\alpha\\right) = \\hat{\\beta}_j \\pm z_{\\alpha/2}\\hat{\\text{SE}}(\\hat{\\beta}_j)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To test $H_0: \\hat{\\beta}_j = 0$ vs $H_1: \\hat{\\beta}_j \\neq 0$, we have that, under the null hypothesis:\n", + "\n", + "$$\n", + "\\frac{\\hat{\\beta}_j}{\\hat{\\text{SE}}(\\hat{\\beta}_j)} \\sim N(0, 1)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But again, R will do all this for you." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 4 × 7
termestimatestd.errorstatisticp.valueconf.lowconf.high
<chr><dbl><dbl><dbl><dbl><dbl><dbl>
(Intercept) 0.408427760.189998621 2.1496353.158407e-02 0.09366300 0.719563508
sexmale -2.099345290.230290839-9.1160617.790454e-20-2.47894577-1.720679671
fare 0.019878480.005371548 3.7006982.150071e-04 0.01183919 0.029554655
sexmale:fare-0.011617110.005933729-1.9578095.025241e-02-0.02204941-0.002425457
\n" + ], + "text/latex": [ + "A tibble: 4 × 7\n", + "\\begin{tabular}{lllllll}\n", + " term & estimate & std.error & statistic & p.value & conf.low & conf.high\\\\\n", + " & & & & & & \\\\\n", + "\\hline\n", + "\t (Intercept) & 0.40842776 & 0.189998621 & 2.149635 & 3.158407e-02 & 0.09366300 & 0.719563508\\\\\n", + "\t sexmale & -2.09934529 & 0.230290839 & -9.116061 & 7.790454e-20 & -2.47894577 & -1.720679671\\\\\n", + "\t fare & 0.01987848 & 0.005371548 & 3.700698 & 2.150071e-04 & 0.01183919 & 0.029554655\\\\\n", + "\t sexmale:fare & -0.01161711 & 0.005933729 & -1.957809 & 5.025241e-02 & -0.02204941 & -0.002425457\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 4 × 7\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> | conf.low <dbl> | conf.high <dbl> |\n", + "|---|---|---|---|---|---|---|\n", + "| (Intercept) | 0.40842776 | 0.189998621 | 2.149635 | 3.158407e-02 | 0.09366300 | 0.719563508 |\n", + "| sexmale | -2.09934529 | 0.230290839 | -9.116061 | 7.790454e-20 | -2.47894577 | -1.720679671 |\n", + "| fare | 0.01987848 | 0.005371548 | 3.700698 | 2.150071e-04 | 0.01183919 | 0.029554655 |\n", + "| sexmale:fare | -0.01161711 | 0.005933729 | -1.957809 | 5.025241e-02 | -0.02204941 | -0.002425457 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value conf.low \n", + "1 (Intercept) 0.40842776 0.189998621 2.149635 3.158407e-02 0.09366300\n", + "2 sexmale -2.09934529 0.230290839 -9.116061 7.790454e-20 -2.47894577\n", + "3 fare 0.01987848 0.005371548 3.700698 2.150071e-04 0.01183919\n", + "4 sexmale:fare -0.01161711 0.005933729 -1.957809 5.025241e-02 -0.02204941\n", + " conf.high \n", + "1 0.719563508\n", + "2 -1.720679671\n", + "3 0.029554655\n", + "4 -0.002425457" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[23c]\n", + "tidy(model_titanic_logistic_interaction, conf.int = TRUE, conf.level = 0.9)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 4 × 7
termestimatestd.errorstatisticp.valueconf.lowconf.high
<chr><dbl><dbl><dbl><dbl><dbl><dbl>
(Intercept) 1.50445060.189998621 2.1496353.158407e-021.098189592.0535367
sexmale 0.12253660.230290839-9.1160617.790454e-200.083831560.1789445
fare 1.02007740.005371548 3.7006982.150071e-041.011909551.0299957
sexmale:fare0.98845010.005933729-1.9578095.025241e-020.978191910.9975775
\n" + ], + "text/latex": [ + "A tibble: 4 × 7\n", + "\\begin{tabular}{lllllll}\n", + " term & estimate & std.error & statistic & p.value & conf.low & conf.high\\\\\n", + " & & & & & & \\\\\n", + "\\hline\n", + "\t (Intercept) & 1.5044506 & 0.189998621 & 2.149635 & 3.158407e-02 & 1.09818959 & 2.0535367\\\\\n", + "\t sexmale & 0.1225366 & 0.230290839 & -9.116061 & 7.790454e-20 & 0.08383156 & 0.1789445\\\\\n", + "\t fare & 1.0200774 & 0.005371548 & 3.700698 & 2.150071e-04 & 1.01190955 & 1.0299957\\\\\n", + "\t sexmale:fare & 0.9884501 & 0.005933729 & -1.957809 & 5.025241e-02 & 0.97819191 & 0.9975775\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 4 × 7\n", + "\n", + "| term <chr> | estimate <dbl> | std.error <dbl> | statistic <dbl> | p.value <dbl> | conf.low <dbl> | conf.high <dbl> |\n", + "|---|---|---|---|---|---|---|\n", + "| (Intercept) | 1.5044506 | 0.189998621 | 2.149635 | 3.158407e-02 | 1.09818959 | 2.0535367 |\n", + "| sexmale | 0.1225366 | 0.230290839 | -9.116061 | 7.790454e-20 | 0.08383156 | 0.1789445 |\n", + "| fare | 1.0200774 | 0.005371548 | 3.700698 | 2.150071e-04 | 1.01190955 | 1.0299957 |\n", + "| sexmale:fare | 0.9884501 | 0.005933729 | -1.957809 | 5.025241e-02 | 0.97819191 | 0.9975775 |\n", + "\n" + ], + "text/plain": [ + " term estimate std.error statistic p.value conf.low \n", + "1 (Intercept) 1.5044506 0.189998621 2.149635 3.158407e-02 1.09818959\n", + "2 sexmale 0.1225366 0.230290839 -9.116061 7.790454e-20 0.08383156\n", + "3 fare 1.0200774 0.005371548 3.700698 2.150071e-04 1.01190955\n", + "4 sexmale:fare 0.9884501 0.005933729 -1.957809 5.025241e-02 0.97819191\n", + " conf.high\n", + "1 2.0535367\n", + "2 0.1789445\n", + "3 1.0299957\n", + "4 0.9975775" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[24c]\n", + "tidy(model_titanic_logistic_interaction, conf.int = TRUE, conf.level = 0.9, exponentiate = TRUE)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 1.09818959365696
  2. 2.05353666266515
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 1.09818959365696\n", + "\\item 2.05353666266515\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 1.09818959365696\n", + "2. 2.05353666266515\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 1.098190 2.053537" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[25c] Note that the exponentiate will exponentiate the boundaries \n", + "# of the interval as well\n", + "# Look for the interval of the intercept\n", + "exp(c(0.09366300, 0.719563508))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2. Poisson Regression\n", + "\n", + "- Poisson regression is a regression analysis designed for modelling **count data**, where the response variable represents the number of times an event occurs within a fixed interval of time or space. \n", + "\n", + "- Since **counts are nonnegative integers**, if we use linear regression, we might have a range problem by predicting negative counts. \n", + "\n", + "- By employing Poisson regression, we can analyze and predict event counts, such as the number of customer arrivals, disease occurrences, or traffic accidents, providing valuable insights into the factors influencing these events and enabling better decision-making.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In Poisson regression, the response variable $Y$ is a count, and the conditional distribution of $Y$ is \n", + "\n", + "$$\n", + "Y_i | X_i \\sim Poisson(\\lambda_i)\n", + "$$\n", + "\n", + "If you never heard of the Poisson distribution it is ok. Here's what you need to know: \n", + "\n", + "- Only takes values $0, 1, 2, 3,...$\n", + "- The mean value is $\\lambda$, i.e., $E\\left[Y_i | X_i \\right] = \\lambda_i$\n", + "- Interestingly, the variance is also $\\lambda$!\n", + "\n", + "Again, instead of modelling the mean directly, it models the logarithm of the expected count as a linear combination of predictor variables:\n", + " \n", + "$$\n", + "\\log(\\lambda_i) = \\beta_0 + \\beta_1X_i\n", + "$$\n", + "\n", + "This log-linear relationship allows Poisson regression to effectively handle the nonnegative integer nature of count data.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the following dataset from the `faraway` package that contains information about different island and the number of plant species found in each island. " + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 5 × 7
islandspeciesareaelevationnearestscruzadjacent
<chr><dbl><dbl><dbl><dbl><dbl><dbl>
SanSalvador 237572.33 906 0.219.8 4.89
Daphne.Major 18 0.34 119 8.0 8.0 1.84
SanCristobal280551.62 71645.266.6 0.57
Enderby 2 0.18 112 2.650.2 0.10
Fernandina 93634.491494 4.395.34669.32
\n" + ], + "text/latex": [ + "A tibble: 5 × 7\n", + "\\begin{tabular}{lllllll}\n", + " island & species & area & elevation & nearest & scruz & adjacent\\\\\n", + " & & & & & & \\\\\n", + "\\hline\n", + "\t SanSalvador & 237 & 572.33 & 906 & 0.2 & 19.8 & 4.89\\\\\n", + "\t Daphne.Major & 18 & 0.34 & 119 & 8.0 & 8.0 & 1.84\\\\\n", + "\t SanCristobal & 280 & 551.62 & 716 & 45.2 & 66.6 & 0.57\\\\\n", + "\t Enderby & 2 & 0.18 & 112 & 2.6 & 50.2 & 0.10\\\\\n", + "\t Fernandina & 93 & 634.49 & 1494 & 4.3 & 95.3 & 4669.32\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 5 × 7\n", + "\n", + "| island <chr> | species <dbl> | area <dbl> | elevation <dbl> | nearest <dbl> | scruz <dbl> | adjacent <dbl> |\n", + "|---|---|---|---|---|---|---|\n", + "| SanSalvador | 237 | 572.33 | 906 | 0.2 | 19.8 | 4.89 |\n", + "| Daphne.Major | 18 | 0.34 | 119 | 8.0 | 8.0 | 1.84 |\n", + "| SanCristobal | 280 | 551.62 | 716 | 45.2 | 66.6 | 0.57 |\n", + "| Enderby | 2 | 0.18 | 112 | 2.6 | 50.2 | 0.10 |\n", + "| Fernandina | 93 | 634.49 | 1494 | 4.3 | 95.3 | 4669.32 |\n", + "\n" + ], + "text/plain": [ + " island species area elevation nearest scruz adjacent\n", + "1 SanSalvador 237 572.33 906 0.2 19.8 4.89 \n", + "2 Daphne.Major 18 0.34 119 8.0 8.0 1.84 \n", + "3 SanCristobal 280 551.62 716 45.2 66.6 0.57 \n", + "4 Enderby 2 0.18 112 2.6 50.2 0.10 \n", + "5 Fernandina 93 634.49 1494 4.3 95.3 4669.32 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[26c]\n", + "galapagos %>% \n", + " slice_sample(n = 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's fit the following model:\n", + "\n", + "$$\n", + "\\log(\\lambda_i) = \\beta_0 + \\beta_1\\times\\text{elevation}_i\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "application/pdf": 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mJhYWDooaFODSyKGDtEAuARMKOwqC8zKeaFsNgrtok7BVkKhunaqHsULy84Q/H5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\nZW5kc3RyZWFtCmVuZG9iagpzdGFydHhyZWYKMTAwNTAKJSVFT0YK", 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ZiIYCL/gvFnCXOck4xgIoKJGCwL5yQi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\nw8Ng6mBNH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" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To fit a Poisson model: " + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "Call: glm(formula = species ~ elevation, family = poisson, data = galapagos)\n", + "\n", + "Coefficients:\n", + "(Intercept) elevation \n", + " 3.664649 0.001436 \n", + "\n", + "Degrees of Freedom: 29 Total (i.e. Null); 28 Residual\n", + "Null Deviance:\t 3511 \n", + "Residual Deviance: 1826 \tAIC: 1991" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#[28] Fit a poisson regression with elevation as covariate.\n", + "model_galapagos <- glm(species ~ elevation, family = poisson, data = galapagos)\n", + "model_galapagos" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Interpretation:**\n", + "\n", + "An increase of 1 meter in the maximum elevation of an island is associated with a change in the average number of plant species found by a factor of $e^{0.0014} = 1.00144$, i.e., an increase of $0.14\\%$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You'll do more on Poisson Regression in the worksheet! " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Cheers! " + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.2.3" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}