{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< | [Main Contents](https://vectorbite.github.io/VBiTraining2/) | >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Fitting in (Vector-Borne Disease) Ecology and Evolution: Challenge problems <span class=\"tocSkip\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#The-Traits-Challenge\" data-toc-modified-id=\"The-Traits-Challenge-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>The Traits Challenge</a></span><ul class=\"toc-item\"><li><span><a href=\"#The-Data\" data-toc-modified-id=\"The-Data-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>The Data</a></span></li><li><span><a href=\"#Guidelines\" data-toc-modified-id=\"Guidelines-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Guidelines</a></span></li></ul></li><li><span><a href=\"#The-Extended-Traits-Challenge\" data-toc-modified-id=\"The-Extended-Traits-Challenge-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>The <em>Extended</em> Traits Challenge</a></span></li><li><span><a href=\"#An-abundances-challenge\" data-toc-modified-id=\"An-abundances-challenge-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>An abundances challenge</a></span></li><li><span><a href=\"#Time-Series-Challenge\" data-toc-modified-id=\"Time-Series-Challenge-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Time Series Challenge</a></span><ul class=\"toc-item\"><li><span><a href=\"#The-Data\" data-toc-modified-id=\"The-Data-4.1\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>The Data</a></span></li><li><span><a href=\"#Guidelines\" data-toc-modified-id=\"Guidelines-4.2\"><span class=\"toc-item-num\">4.2&nbsp;&nbsp;</span>Guidelines</a></span></li></ul></li><li><span><a href=\"#The-Open-Challenge\" data-toc-modified-id=\"The-Open-Challenge-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>The Open Challenge</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Traits Challenge\n",
    "\n",
    "You will work in groups to tackle this \"Challenge\" problem. \n",
    "\n",
    "The main objective is to fit alternative models to data using Maximum Likelihood and compare/select between them. Your goal is not just to practise model fitting and selection, but also to extract biological insights from it. \n",
    "\n",
    "**_You will present the results of your analysis and biological inferences during the group discussion session_**. \n",
    "\n",
    "Good luck!\n",
    "  \n",
    "## The Data\n",
    "\n",
    "The data for this question consist of thermal traits for *Aedes agypti* mosquitos found in the data file ` AeaegyptiTraitData.csv`. \n",
    "\n",
    "There are four possible traits (as well as some data that are recorded as the inverse trait, which we ignore for now):\n",
    "\n",
    "- pEA: proportion surviving from egg to adulthood  \n",
    "- MDR: mosquito development rate  \n",
    "- PDR: parasite development rate (= 1/EIP the extrinsic incubation period)  \n",
    "- $\\mu$ (mu): death rate (= 1/longevity)\n",
    "\n",
    "You will choose one of these four traits and fit a curve to the data using maximum likelihood. You may also fit  models to data of your choosing.\n",
    "\n",
    "Base your code on what was provided in the lecture/practical portion of the class. You will start with a specific set of tasks to accomplish, starting with easy ones through to more challenging ones. \n",
    "\n",
    "First read in the data and look at the summary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " trait.name       T             trait         \n",
       " 1/mu:18    Min.   : 1.00   Min.   : 0.00000  \n",
       " EIP :27    1st Qu.:20.00   1st Qu.: 0.03044  \n",
       " MDR :29    Median :26.67   Median : 0.13587  \n",
       " mu  :12    Mean   :26.41   Mean   : 5.14394  \n",
       " PDR :12    3rd Qu.:32.00   3rd Qu.: 6.00000  \n",
       " pEA :55    Max.   :52.00   Max.   :40.54000  \n",
       "                                              \n",
       "                                     ref          trait2    trait2.name \n",
       " Eisen_et_al_2014                      :31   Karachi :  6   EIP50 :  4  \n",
       " Beserra_2009                          :18   Surabaya:  6   Strain: 18  \n",
       " Kamimura_et_al_2002_JapanSocMedEnt&Zoo:18   Timor   :  6   NA's  :131  \n",
       " Tun-Lin_et_al_2000_MedVetEnto         :13   NA's    :135               \n",
       " Rueda_et_al_1990_EntSocAm             :12                              \n",
       " Yang_et_al_2008_EpidInfect            :12                              \n",
       " (Other)                               :49                              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dat<-read.csv(file=\"../data/AeaegyptiTraitData.csv\")\n",
    "summary(dat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nexts plot the response output, `trait` across temperature, `T`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jzXja9hEynheeuuKVHOzQ/XeqCB2Ela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\nRAKAA/8H2Va9Jn26xRUAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "traits<-c(\"pEA\", \"MDR\", \"PDR\", \"mu\")\n",
    "par(mfrow=c(2,2), bty=\"o\", mai=c(0.8,0.7,0.1,0.1))\n",
    "for(i in 1:4){ \n",
    "    d.temp<-subset(dat, trait.name==traits[i])\n",
    "    plot(trait ~ T, data=d.temp, xlab=\"Temperature (C)\", ylab=traits[i], xlim=c(5, 45))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Guidelines\n",
    "\n",
    "We suggest the following steps for your analysis. \n",
    "\n",
    "**(1) Fitting a linear model, revisited**\n",
    "\n",
    "* Using the [`nll.slr`](#Implementing-the-Likelihood-in-R) function and the code you wrote above, find the MLEs of the slope and intercept (i.e., find the best fitting line for your chosen trait). \n",
    "* Plot your data with the fitted line.\n",
    "* Plot the likelihood surface for $b_0$ and $b_1$ and indicate the MLEs your likelihood surface. \n",
    "* Obtain confidence intervals for your estimates. \n",
    "\n",
    "**(2) Fitting a non-linear model**\n",
    "\n",
    "* Choose a non-linear model to fit to your trait (e.g., the quadratic, Briere from [above](#Two-thermal-performance-curve-models)). We have implemented some functions in the file `temp_functions.R` that can be found in the `code` directory. \n",
    "* Using the [`nll.slr`](#Implementing-the-Likelihood-in-R) function as an example, write your own function that calculates the negative log likelihood as a function of the parameters describing your trait and any additional parameters you need for an appropriate noise distribution (e.g., $\\sigma$ if you have normal noise).\n",
    "* Use the `optim()` function to find the MLEs of all of your parameters.\n",
    "* Obtain a confidence interval for your estimate.\n",
    "* Plot the fitted function with the data and your fittend line from Task 1.\n",
    "* Do all of these with a second (linear or non-linear) function fited to your trait data. Find the MLEs and fit this curve to your data. \n",
    "* Plot both the fits on the data.\n",
    "\n",
    "**(3) Compare models**\n",
    "\n",
    "Now compare your models (e.g., AIC, BIC, LRT). Optionally, also calculate the relative model probabilities). Which comes out on top? Is this what you expected? What biological inferences can you draw from the results?\n",
    "\n",
    "**_Extra challenge_**\n",
    "\n",
    "If you have the time and the interest you may try to fit curves to all of the 4 traits in the data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The *Extended* Traits Challenge\n",
    "\n",
    "Perform a Bayesian analysis for the same *Aedes agypti* mosquito traut data in ` AeaegyptiTraitData.csv`. \n",
    "\n",
    "Here you will perform model selection with DIC, as explained in the Intro to Bayesian Stats [lecture](https://github.com/vectorbite/VBiTraining2/tree/master/lectures).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An abundances challenge\n",
    "\n",
    "Fit some real data to the population growth models you were [introduced to previously](). These data have been generated/collected by [Tom Smith](https://mhasoba.pythonanywhere.com/pawarlab/default/people), a PhD student at Silwood as part of his Dissertation research. Import the [dataset](https://github.com/vectorbite/VBiTraining2/blob/master/data/example_growth_data.csv) into R: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>ID</th><th scope=col>bacterial_genus</th><th scope=col>replicate</th><th scope=col>trait_name</th><th scope=col>trait_value</th><th scope=col>hour</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Sch_AE103_02  </td><td>Flavobacterium</td><td>1             </td><td>Log(cells/mL) </td><td>5.301030      </td><td> 0            </td></tr>\n",
       "\t<tr><td>Sch_AE103_02  </td><td>Flavobacterium</td><td>1             </td><td>Log(cells/mL) </td><td>5.301030      </td><td> 5            </td></tr>\n",
       "\t<tr><td>Sch_AE103_02  </td><td>Flavobacterium</td><td>1             </td><td>Log(cells/mL) </td><td>6.991226      </td><td>10            </td></tr>\n",
       "\t<tr><td>Sch_AE103_02  </td><td>Flavobacterium</td><td>1             </td><td>Log(cells/mL) </td><td>8.094820      </td><td>15            </td></tr>\n",
       "\t<tr><td>Sch_AE103_02  </td><td>Flavobacterium</td><td>1             </td><td>Log(cells/mL) </td><td>8.358316      </td><td>20            </td></tr>\n",
       "\t<tr><td>Sch_AE103_02  </td><td>Flavobacterium</td><td>1             </td><td>Log(cells/mL) </td><td>8.460296      </td><td>25            </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       " ID & bacterial\\_genus & replicate & trait\\_name & trait\\_value & hour\\\\\n",
       "\\hline\n",
       "\t Sch\\_AE103\\_02 & Flavobacterium   & 1                & Log(cells/mL)    & 5.301030         &  0              \\\\\n",
       "\t Sch\\_AE103\\_02 & Flavobacterium   & 1                & Log(cells/mL)    & 5.301030         &  5              \\\\\n",
       "\t Sch\\_AE103\\_02 & Flavobacterium   & 1                & Log(cells/mL)    & 6.991226         & 10              \\\\\n",
       "\t Sch\\_AE103\\_02 & Flavobacterium   & 1                & Log(cells/mL)    & 8.094820         & 15              \\\\\n",
       "\t Sch\\_AE103\\_02 & Flavobacterium   & 1                & Log(cells/mL)    & 8.358316         & 20              \\\\\n",
       "\t Sch\\_AE103\\_02 & Flavobacterium   & 1                & Log(cells/mL)    & 8.460296         & 25              \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "ID | bacterial_genus | replicate | trait_name | trait_value | hour | \n",
       "|---|---|---|---|---|---|\n",
       "| Sch_AE103_02   | Flavobacterium | 1              | Log(cells/mL)  | 5.301030       |  0             | \n",
       "| Sch_AE103_02   | Flavobacterium | 1              | Log(cells/mL)  | 5.301030       |  5             | \n",
       "| Sch_AE103_02   | Flavobacterium | 1              | Log(cells/mL)  | 6.991226       | 10             | \n",
       "| Sch_AE103_02   | Flavobacterium | 1              | Log(cells/mL)  | 8.094820       | 15             | \n",
       "| Sch_AE103_02   | Flavobacterium | 1              | Log(cells/mL)  | 8.358316       | 20             | \n",
       "| Sch_AE103_02   | Flavobacterium | 1              | Log(cells/mL)  | 8.460296       | 25             | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  ID           bacterial_genus replicate trait_name    trait_value hour\n",
       "1 Sch_AE103_02 Flavobacterium  1         Log(cells/mL) 5.301030     0  \n",
       "2 Sch_AE103_02 Flavobacterium  1         Log(cells/mL) 5.301030     5  \n",
       "3 Sch_AE103_02 Flavobacterium  1         Log(cells/mL) 6.991226    10  \n",
       "4 Sch_AE103_02 Flavobacterium  1         Log(cells/mL) 8.094820    15  \n",
       "5 Sch_AE103_02 Flavobacterium  1         Log(cells/mL) 8.358316    20  \n",
       "6 Sch_AE103_02 Flavobacterium  1         Log(cells/mL) 8.460296    25  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>ID</th><th scope=col>bacterial_genus</th><th scope=col>replicate</th><th scope=col>trait_name</th><th scope=col>trait_value</th><th scope=col>hour</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>963</th><td>Wil_SP04_02  </td><td>Bacillus     </td><td>4            </td><td>Log(cells/mL)</td><td>7.086360     </td><td>25           </td></tr>\n",
       "\t<tr><th scope=row>964</th><td>Wil_SP04_02  </td><td>Bacillus     </td><td>4            </td><td>Log(cells/mL)</td><td>7.322219     </td><td>30           </td></tr>\n",
       "\t<tr><th scope=row>965</th><td>Wil_SP04_02  </td><td>Bacillus     </td><td>4            </td><td>Log(cells/mL)</td><td>7.361728     </td><td>35           </td></tr>\n",
       "\t<tr><th scope=row>966</th><td>Wil_SP04_02  </td><td>Bacillus     </td><td>4            </td><td>Log(cells/mL)</td><td>7.322219     </td><td>40           </td></tr>\n",
       "\t<tr><th scope=row>967</th><td>Wil_SP04_02  </td><td>Bacillus     </td><td>4            </td><td>Log(cells/mL)</td><td>7.260071     </td><td>45           </td></tr>\n",
       "\t<tr><th scope=row>968</th><td>Wil_SP04_02  </td><td>Bacillus     </td><td>4            </td><td>Log(cells/mL)</td><td>7.292256     </td><td>50           </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllll}\n",
       "  & ID & bacterial\\_genus & replicate & trait\\_name & trait\\_value & hour\\\\\n",
       "\\hline\n",
       "\t963 & Wil\\_SP04\\_02 & Bacillus        & 4               & Log(cells/mL)   & 7.086360        & 25             \\\\\n",
       "\t964 & Wil\\_SP04\\_02 & Bacillus        & 4               & Log(cells/mL)   & 7.322219        & 30             \\\\\n",
       "\t965 & Wil\\_SP04\\_02 & Bacillus        & 4               & Log(cells/mL)   & 7.361728        & 35             \\\\\n",
       "\t966 & Wil\\_SP04\\_02 & Bacillus        & 4               & Log(cells/mL)   & 7.322219        & 40             \\\\\n",
       "\t967 & Wil\\_SP04\\_02 & Bacillus        & 4               & Log(cells/mL)   & 7.260071        & 45             \\\\\n",
       "\t968 & Wil\\_SP04\\_02 & Bacillus        & 4               & Log(cells/mL)   & 7.292256        & 50             \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | ID | bacterial_genus | replicate | trait_name | trait_value | hour | \n",
       "|---|---|---|---|---|---|\n",
       "| 963 | Wil_SP04_02   | Bacillus      | 4             | Log(cells/mL) | 7.086360      | 25            | \n",
       "| 964 | Wil_SP04_02   | Bacillus      | 4             | Log(cells/mL) | 7.322219      | 30            | \n",
       "| 965 | Wil_SP04_02   | Bacillus      | 4             | Log(cells/mL) | 7.361728      | 35            | \n",
       "| 966 | Wil_SP04_02   | Bacillus      | 4             | Log(cells/mL) | 7.322219      | 40            | \n",
       "| 967 | Wil_SP04_02   | Bacillus      | 4             | Log(cells/mL) | 7.260071      | 45            | \n",
       "| 968 | Wil_SP04_02   | Bacillus      | 4             | Log(cells/mL) | 7.292256      | 50            | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "    ID          bacterial_genus replicate trait_name    trait_value hour\n",
       "963 Wil_SP04_02 Bacillus        4         Log(cells/mL) 7.086360    25  \n",
       "964 Wil_SP04_02 Bacillus        4         Log(cells/mL) 7.322219    30  \n",
       "965 Wil_SP04_02 Bacillus        4         Log(cells/mL) 7.361728    35  \n",
       "966 Wil_SP04_02 Bacillus        4         Log(cells/mL) 7.322219    40  \n",
       "967 Wil_SP04_02 Bacillus        4         Log(cells/mL) 7.260071    45  \n",
       "968 Wil_SP04_02 Bacillus        4         Log(cells/mL) 7.292256    50  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BacData <- read.csv(\"../data/example_growth_data.csv\")\n",
    "\n",
    "head(BacData)\n",
    "tail(BacData)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The column `trait_value` and `hour` are your variables of interest (log cell density and time), respectively. Note that the `ID` column will tell you which rows represent one separate growth experiment.  Make sure you have a good look at the data first by plotting them up (idealy, in a loop).  \n",
    "\n",
    "1. Fit the above population growth rate models, and perform model selection on them. Which model fits best? \n",
    "* Can you think of a difefrent model to fit? If so, implement it, and compare that as well. \n",
    "* Write the analysis as a single self-standing R script, which will run and return the results in a `*.csv` file and plot(s) ins pdf.\n",
    "* Again, consider using ggplot insted of base plotting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time Series Challenge\n",
    "\n",
    "Just like the [traits challenge](#The-Traits-Challenge), will work in groups to tackle this second \"Challenge\" problem. \n",
    "\n",
    "The main objective is to perform a time series analysis on some a disease incidence dataset and compare different models. Your goal is not just to practise model fitting and selection, but also to extract biological insights from it. \n",
    "\n",
    "**_You will present the results of your analysis and biological inferences during the group discussion session_**. \n",
    "\n",
    "Good luck!\n",
    "\n",
    "\n",
    "## The Data\n",
    "\n",
    "The data consist of time series of dengue case data from San Juan, Puerto Rico together with environmental data for each location across a number of transmission seasons. The file is `combined_sanjuan_new.csv`. Detailed descriptions of the data are available [here]( http://dengueforecasting.noaa.gov/). \n",
    "\n",
    "To operate effectively, health departments must be able to predict weekly cases, as this will correspond to hospital demand and resources. \n",
    "\n",
    "Your task is to provide a fitted model for forecasting weekly total dengue cases in San Juan. You can use autoregressive components and sine/cosine trends to build your model. You can also use the environmental covariates. Remember that you want to be able to predict into the future so you will only include lagged predictors into your prediction model. Below we suggest a series of steps for the analysis and then you'll have the opportunity to develop your own model(s) and choose which components that you want to keep. We'll compare models during the group discussion. \n",
    "\n",
    "Here is some code to get you started.\n",
    "\n",
    "First read in the data and look at the summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>season</th><th scope=col>season_week</th><th scope=col>year_week</th><th scope=col>week_start_date</th><th scope=col>weekID</th><th scope=col>monthID</th><th scope=col>year</th><th scope=col>denv1_cases</th><th scope=col>denv2_cases</th><th scope=col>denv3_cases</th><th scope=col>⋯</th><th scope=col>tmin</th><th scope=col>tmax</th><th scope=col>prec</th><th scope=col>dtr</th><th scope=col>tavg</th><th scope=col>nino12</th><th scope=col>nino34</th><th scope=col>soi</th><th scope=col>pop</th><th scope=col>adjpop</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1990/1991</td><td>1        </td><td>18       </td><td>4/30/1990</td><td>199018   </td><td>199004   </td><td>1990     </td><td>0        </td><td>0        </td><td>0        </td><td>⋯        </td><td>296.4    </td><td>300.7    </td><td>16.64    </td><td>2.385714 </td><td>298.2643 </td><td>25.22    </td><td>28.93    </td><td>0.3      </td><td>2217968  </td><td>2226511  </td></tr>\n",
       "\t<tr><td>1990/1991</td><td>2        </td><td>19       </td><td>5/7/1990 </td><td>199019   </td><td>199005   </td><td>1990     </td><td>0        </td><td>0        </td><td>0        </td><td>⋯        </td><td>297.3    </td><td>300.9    </td><td>22.90    </td><td>2.242857 </td><td>298.9929 </td><td>24.05    </td><td>28.96    </td><td>2.0      </td><td>2217968  </td><td>2227014  </td></tr>\n",
       "\t<tr><td>1990/1991</td><td>3        </td><td>20       </td><td>5/14/1990</td><td>199020   </td><td>199005   </td><td>1990     </td><td>0        </td><td>0        </td><td>0        </td><td>⋯        </td><td>297.0    </td><td>301.1    </td><td>18.50    </td><td>2.442857 </td><td>299.0643 </td><td>24.05    </td><td>28.96    </td><td>2.0      </td><td>2217968  </td><td>2227516  </td></tr>\n",
       "\t<tr><td>1990/1991</td><td>4        </td><td>21       </td><td>5/21/1990</td><td>199021   </td><td>199005   </td><td>1990     </td><td>0        </td><td>0        </td><td>0        </td><td>⋯        </td><td>297.5    </td><td>301.9    </td><td> 7.30    </td><td>3.085714 </td><td>299.6857 </td><td>24.05    </td><td>28.96    </td><td>2.0      </td><td>2217968  </td><td>2228019  </td></tr>\n",
       "\t<tr><td>1990/1991</td><td>5        </td><td>22       </td><td>5/28/1990</td><td>199022   </td><td>199005   </td><td>1990     </td><td>0        </td><td>0        </td><td>0        </td><td>⋯        </td><td>298.1    </td><td>302.4    </td><td>25.19    </td><td>2.200000 </td><td>299.8714 </td><td>24.05    </td><td>28.96    </td><td>2.0      </td><td>2217968  </td><td>2228521  </td></tr>\n",
       "\t<tr><td>1990/1991</td><td>6        </td><td>23       </td><td>6/4/1990 </td><td>199023   </td><td>199006   </td><td>1990     </td><td>1        </td><td>0        </td><td>0        </td><td>⋯        </td><td>297.7    </td><td>301.1    </td><td>44.70    </td><td>1.900000 </td><td>299.0929 </td><td>22.68    </td><td>28.94    </td><td>0.5      </td><td>2217968  </td><td>2229024  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllllllllllllllllllll}\n",
       " season & season\\_week & year\\_week & week\\_start\\_date & weekID & monthID & year & denv1\\_cases & denv2\\_cases & denv3\\_cases & ⋯ & tmin & tmax & prec & dtr & tavg & nino12 & nino34 & soi & pop & adjpop\\\\\n",
       "\\hline\n",
       "\t 1990/1991 & 1         & 18        & 4/30/1990 & 199018    & 199004    & 1990      & 0         & 0         & 0         & ⋯         & 296.4     & 300.7     & 16.64     & 2.385714  & 298.2643  & 25.22     & 28.93     & 0.3       & 2217968   & 2226511  \\\\\n",
       "\t 1990/1991 & 2         & 19        & 5/7/1990  & 199019    & 199005    & 1990      & 0         & 0         & 0         & ⋯         & 297.3     & 300.9     & 22.90     & 2.242857  & 298.9929  & 24.05     & 28.96     & 2.0       & 2217968   & 2227014  \\\\\n",
       "\t 1990/1991 & 3         & 20        & 5/14/1990 & 199020    & 199005    & 1990      & 0         & 0         & 0         & ⋯         & 297.0     & 301.1     & 18.50     & 2.442857  & 299.0643  & 24.05     & 28.96     & 2.0       & 2217968   & 2227516  \\\\\n",
       "\t 1990/1991 & 4         & 21        & 5/21/1990 & 199021    & 199005    & 1990      & 0         & 0         & 0         & ⋯         & 297.5     & 301.9     &  7.30     & 3.085714  & 299.6857  & 24.05     & 28.96     & 2.0       & 2217968   & 2228019  \\\\\n",
       "\t 1990/1991 & 5         & 22        & 5/28/1990 & 199022    & 199005    & 1990      & 0         & 0         & 0         & ⋯         & 298.1     & 302.4     & 25.19     & 2.200000  & 299.8714  & 24.05     & 28.96     & 2.0       & 2217968   & 2228521  \\\\\n",
       "\t 1990/1991 & 6         & 23        & 6/4/1990  & 199023    & 199006    & 1990      & 1         & 0         & 0         & ⋯         & 297.7     & 301.1     & 44.70     & 1.900000  & 299.0929  & 22.68     & 28.94     & 0.5       & 2217968   & 2229024  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "season | season_week | year_week | week_start_date | weekID | monthID | year | denv1_cases | denv2_cases | denv3_cases | ⋯ | tmin | tmax | prec | dtr | tavg | nino12 | nino34 | soi | pop | adjpop | \n",
       "|---|---|---|---|---|---|\n",
       "| 1990/1991 | 1         | 18        | 4/30/1990 | 199018    | 199004    | 1990      | 0         | 0         | 0         | ⋯         | 296.4     | 300.7     | 16.64     | 2.385714  | 298.2643  | 25.22     | 28.93     | 0.3       | 2217968   | 2226511   | \n",
       "| 1990/1991 | 2         | 19        | 5/7/1990  | 199019    | 199005    | 1990      | 0         | 0         | 0         | ⋯         | 297.3     | 300.9     | 22.90     | 2.242857  | 298.9929  | 24.05     | 28.96     | 2.0       | 2217968   | 2227014   | \n",
       "| 1990/1991 | 3         | 20        | 5/14/1990 | 199020    | 199005    | 1990      | 0         | 0         | 0         | ⋯         | 297.0     | 301.1     | 18.50     | 2.442857  | 299.0643  | 24.05     | 28.96     | 2.0       | 2217968   | 2227516   | \n",
       "| 1990/1991 | 4         | 21        | 5/21/1990 | 199021    | 199005    | 1990      | 0         | 0         | 0         | ⋯         | 297.5     | 301.9     |  7.30     | 3.085714  | 299.6857  | 24.05     | 28.96     | 2.0       | 2217968   | 2228019   | \n",
       "| 1990/1991 | 5         | 22        | 5/28/1990 | 199022    | 199005    | 1990      | 0         | 0         | 0         | ⋯         | 298.1     | 302.4     | 25.19     | 2.200000  | 299.8714  | 24.05     | 28.96     | 2.0       | 2217968   | 2228521   | \n",
       "| 1990/1991 | 6         | 23        | 6/4/1990  | 199023    | 199006    | 1990      | 1         | 0         | 0         | ⋯         | 297.7     | 301.1     | 44.70     | 1.900000  | 299.0929  | 22.68     | 28.94     | 0.5       | 2217968   | 2229024   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  season    season_week year_week week_start_date weekID monthID year\n",
       "1 1990/1991 1           18        4/30/1990       199018 199004  1990\n",
       "2 1990/1991 2           19        5/7/1990        199019 199005  1990\n",
       "3 1990/1991 3           20        5/14/1990       199020 199005  1990\n",
       "4 1990/1991 4           21        5/21/1990       199021 199005  1990\n",
       "5 1990/1991 5           22        5/28/1990       199022 199005  1990\n",
       "6 1990/1991 6           23        6/4/1990        199023 199006  1990\n",
       "  denv1_cases denv2_cases denv3_cases ⋯ tmin  tmax  prec  dtr      tavg    \n",
       "1 0           0           0           ⋯ 296.4 300.7 16.64 2.385714 298.2643\n",
       "2 0           0           0           ⋯ 297.3 300.9 22.90 2.242857 298.9929\n",
       "3 0           0           0           ⋯ 297.0 301.1 18.50 2.442857 299.0643\n",
       "4 0           0           0           ⋯ 297.5 301.9  7.30 3.085714 299.6857\n",
       "5 0           0           0           ⋯ 298.1 302.4 25.19 2.200000 299.8714\n",
       "6 1           0           0           ⋯ 297.7 301.1 44.70 1.900000 299.0929\n",
       "  nino12 nino34 soi pop     adjpop \n",
       "1 25.22  28.93  0.3 2217968 2226511\n",
       "2 24.05  28.96  2.0 2217968 2227014\n",
       "3 24.05  28.96  2.0 2217968 2227516\n",
       "4 24.05  28.96  2.0 2217968 2228019\n",
       "5 24.05  28.96  2.0 2217968 2228521\n",
       "6 22.68  28.94  0.5 2217968 2229024"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "       season     season_week      year_week      week_start_date\n",
       " 1990/1991: 52   Min.   : 1.00   Min.   : 1.00   10/1/1990:  1   \n",
       " 1991/1992: 52   1st Qu.:13.75   1st Qu.:13.75   10/1/1991:  1   \n",
       " 1992/1993: 52   Median :26.50   Median :26.50   10/1/1993:  1   \n",
       " 1993/1994: 52   Mean   :26.50   Mean   :26.50   10/1/1994:  1   \n",
       " 1994/1995: 52   3rd Qu.:39.25   3rd Qu.:39.25   10/1/1995:  1   \n",
       " 1995/1996: 52   Max.   :52.00   Max.   :52.00   10/1/1997:  1   \n",
       " (Other)  :676                                   (Other)  :982   \n",
       "     weekID          monthID            year       denv1_cases    \n",
       " Min.   :199018   Min.   :199004   Min.   :1990   Min.   : 0.000  \n",
       " 1st Qu.:199505   1st Qu.:199501   1st Qu.:1995   1st Qu.: 0.000  \n",
       " Median :199944   Median :199910   Median :1999   Median : 0.000  \n",
       " Mean   :199959   Mean   :199939   Mean   :1999   Mean   : 1.389  \n",
       " 3rd Qu.:200430   3rd Qu.:200407   3rd Qu.:2004   3rd Qu.: 1.000  \n",
       " Max.   :200917   Max.   :200904   Max.   :2009   Max.   :27.000  \n",
       "                                                                  \n",
       "  denv2_cases      denv3_cases      denv4_cases      other_positive_cases\n",
       " Min.   : 0.000   Min.   : 0.000   Min.   : 0.0000   Min.   :  0.00      \n",
       " 1st Qu.: 0.000   1st Qu.: 0.000   1st Qu.: 0.0000   1st Qu.:  5.00      \n",
       " Median : 1.000   Median : 0.000   Median : 0.0000   Median : 13.00      \n",
       " Mean   : 1.951   Mean   : 2.172   Mean   : 0.7915   Mean   : 19.71      \n",
       " 3rd Qu.: 2.000   3rd Qu.: 2.000   3rd Qu.: 1.0000   3rd Qu.: 25.00      \n",
       " Max.   :30.000   Max.   :74.000   Max.   :17.0000   Max.   :148.00      \n",
       "                                                                         \n",
       " additional_cases   total_cases     NDVI.18.45.66.14.  NDVI.18.50..66.14.\n",
       " Min.   :  0.000   Min.   :  0.00   Min.   :-0.06346   Min.   :-0.45610  \n",
       " 1st Qu.:  0.000   1st Qu.:  9.00   1st Qu.: 0.12914   1st Qu.: 0.01666  \n",
       " Median :  1.000   Median : 19.00   Median : 0.16591   Median : 0.06867  \n",
       " Mean   :  7.415   Mean   : 33.43   Mean   : 0.16569   Mean   : 0.06817  \n",
       " 3rd Qu.:  3.000   3rd Qu.: 37.00   3rd Qu.: 0.20226   3rd Qu.: 0.11432  \n",
       " Max.   :337.000   Max.   :461.00   Max.   : 0.38142   Max.   : 0.64900  \n",
       "                                                                         \n",
       "   satprecip           tmin            tmax            prec       \n",
       " Min.   :  0.00   Min.   :292.6   Min.   :297.7   Min.   :  0.00  \n",
       " 1st Qu.:  0.00   1st Qu.:296.3   1st Qu.:300.4   1st Qu.: 10.29  \n",
       " Median : 20.04   Median :297.5   Median :301.5   Median : 21.11  \n",
       " Mean   : 34.70   Mean   :297.3   Mean   :301.4   Mean   : 30.03  \n",
       " 3rd Qu.: 50.76   3rd Qu.:298.3   3rd Qu.:302.4   3rd Qu.: 38.11  \n",
       " Max.   :389.60   Max.   :299.8   Max.   :304.3   Max.   :574.30  \n",
       "                                                                  \n",
       "      dtr             tavg           nino12          nino34     \n",
       " Min.   :1.443   Min.   :295.2   Min.   :18.57   Min.   :26.43  \n",
       " 1st Qu.:2.171   1st Qu.:298.3   1st Qu.:21.00   1st Qu.:28.18  \n",
       " Median :2.464   Median :299.4   Median :22.75   Median :28.84  \n",
       " Mean   :2.529   Mean   :299.3   Mean   :23.11   Mean   :28.63  \n",
       " 3rd Qu.:2.800   3rd Qu.:300.3   3rd Qu.:25.15   3rd Qu.:29.17  \n",
       " Max.   :4.471   Max.   :301.8   Max.   :29.15   Max.   :29.83  \n",
       "                                                                \n",
       "      soi                pop              adjpop       \n",
       " Min.   :-5.20000   Min.   :2217968   Min.   :2226511  \n",
       " 1st Qu.:-1.02500   1st Qu.:2348629   1st Qu.:2350513  \n",
       " Median :-0.10000   Median :2389397   Median :2390718  \n",
       " Mean   :-0.01376   Mean   :2365620   Mean   :2369177  \n",
       " 3rd Qu.: 1.10000   3rd Qu.:2403420   3rd Qu.:2403322  \n",
       " Max.   : 4.40000   Max.   :2453157   Max.   :2453157  \n",
       "                                                       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sanjuan<-read.csv(file=\"../data/combined_sanjuan_new.csv\")\n",
    "head(sanjuan)\n",
    "summary(sanjuan)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next plot the response output, `total_cases` across time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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m/RdhDiICFxoPhrN1D3a/wp2g5CHCQk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\n1WfF4B0+XbrhUgxwbaw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/GRn7g+ccdE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\nEhJBGAAJiSAMgIREEAbwfxSlXV27JXuoAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t<-seq(1, length(sanjuan$total_cases))\n",
    "plot(t, sanjuan$total_cases, type=\"l\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It may be a little hard to tell, but when you have a lot of cases, the variance is higher, too. As in the [airline time series example](#Airline_TS), we need to make a data transformation. However, we have zeros in the total cases, so instead of a log we'll use a square-root:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H6MkHi8J6Tt8GU3lnM8G4uQenrDsVechdTUyTvFlhzm3pp0+Ni5dvzQfKLyBYeF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\nUl5YeARhJOgZMqzFH+i62NYtAh8VUZxspDqyYn+X5fi9qk9yS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ZSAKUNWQyHfN2M+xWjk0988xjmzsCgARpHBVTlq3ArBULajrGeGP5qa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\nIYAyQAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t<-seq(1, length(sanjuan$total_cases))\n",
    "plot(t, sqrt(sanjuan$total_cases), type=\"l\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the ACF plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAANKebYnc5nTt37ty5s9YpAAAAtKf7Yue8CxcuWM/AaFBFRUWrhQEAAHCYPMWu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\nJEGxAwAAkMR/AF4Pd5vgzGjgAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Series  sqrt(sanjuan$total_cases)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf(sqrt(sanjuan$total_cases))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*What do you notice about the ACF? What does this tell you about terms you might want to include in your regression analysis?*\n",
    "\n",
    "If you were to look at your covariates, you'd notice that there's a lot of correlation between things like average and max or min temperature and population and the adjusted population. Thus, we don't want to include absolutely everything here. Instead, we're going to select a subset of covariates here. As always, it's a good idea to build a new data frame with the subset of covariates that you want to explore. We start with the sqrt of cases as your response, AR1 of the sqrt response, a trend, and sine/cosine with a 52 week period together with a subset of the environmental covariates at 1 week lags. (As an aside, temperature, precipitation, etc, will be correlated with the sine/cosine terms.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "n<-max(t)\n",
    "YX <- data.frame(sqrty=sqrt(sanjuan$total_cases)[2:n],\n",
    "                 sqrty.m1=sqrt(sanjuan$total_cases)[1:(n-1)],\n",
    "                 t=t[2:n],\n",
    "                 sin1=sin((2:n)*2*pi/52),\n",
    "                 cos1=cos((2:n)*2*pi/52),\n",
    "                 season=sanjuan$season[2:n],\n",
    "                 w=sanjuan$season_week[2:n],\n",
    "                 lpop.m1=log(sanjuan$adjpop+1)[1:(n-1)],\n",
    "                 lp.m1=log(sanjuan$prec+1)[1:(n-1)],\n",
    "                 tavg.m1=sanjuan$tavg[1:(n-1)],\n",
    "                 ndvi45.m1=sanjuan$NDVI.18.45.66.14.[1:(n-1)],\n",
    "                 ndvi50.m1=sanjuan$NDVI.18.50..66.14.[1:(n-1)],\n",
    "                 nino12.m1=sanjuan$nino12[1:(n-1)],\n",
    "                 soi.m1=sanjuan$soi[1:(n-1)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Guidelines\n",
    "\n",
    "We suggest the following steps for your analysis. \n",
    "\n",
    "**(1) Hypotheses**\n",
    "\n",
    "Before you start, think about which things you expect to be good predictors of dengue transmission. Think of 2 or 3 hypotheses and write down a (linear) model to represent the mathematical form of the hypothesis.\n",
    "\n",
    "**(2) Fitting and analyzing a first model**\n",
    "\n",
    "Fit a linear model to the square-root response with the trend, and sine/cosine components, ONLY. Then you'll evaluate the model. Following the examples in the lecture, plot the residuals over time and the ACF of the residuals. Also plot the data together with the predicted values (e.g., the _fitted_ values from your model). Examine your summary -- are all of the coefficiants significantly different from zero; what is your R$^2$ value? Based on the combination of residual diagnositcs and summaries, are you satisfied with this model?\n",
    "\n",
    "**(3) Building a comparison model**\n",
    "\n",
    "Build a second model by adding in the AR-1 component. Again examine your summaries, residual diagnostics, and predictions. How do you think this model compares to the first one? You may also want to try building boxplots of residuals by week in the season and see if there are any patterns, similarly to the airline example.\n",
    "\n",
    "**(4) Including environmental components**\n",
    "\n",
    "By trial and error (or if you know another way, such as the step function) try to build a better model that includes at least one environmental covariate while staying parsimonious. Again check your diagnostics, etc.\n",
    "\n",
    "**(5) Comparing models**\n",
    "\n",
    "Now compare your 3 models via BIC (optional: calculate the relative model probabilities). Which comes out on top? Is this what you expected? What biological insights have you gained?\n",
    "\n",
    "\n",
    "**_Extra challenge_**\n",
    "\n",
    "For convenience we simply chose a lag of 1 week when we built the data set. However, the lag time between an infected human, and another human getting  infected is likely to be multiple weeksbecause of the various incubation and development times in the human and the mosquito. To examine the lags at which the covariates are most related to the response, we can use the cross-correlation function (ccf). For instance:b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LErKCgYMWKEEGLPnj2O30tRlJ9//rmmpsbOmIMHDzY2HAAAwI0nT7Grrq7Oysq6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IaGjhw50mKxZGZmTp48+fbt2zt37vT09FyxYsX27duj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\nOwAAAEX8D2ho2zl7F/KhAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “sanjuan$tavg & sanjuan$total_cases”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ccf(sanjuan$tavg, sanjuan$total_cases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This indicates that the temperature about 10 weeks back is more correlated with the incidence than the temperature 1 week ago. \n",
    "\n",
    "Plot a few other ccfs, choose some alternative lags, and build a NEW dataset with these lagged variables. Then build a few models (perhaps starting again from the simple versions without environmental covariates), and compare them. Does including the extra information about lags seem to improve fit?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Open Challenge\n",
    "\n",
    "Finally, in groups you will develop and analyze data from VecTraits or VecDyn using one or more of the methods you have learned till now. \n"
   ]
  }
 ],
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   "display_name": "R",
   "language": "R",
   "name": "ir"
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   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.4"
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  "latex_envs": {
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   "cite_by": "apalike",
   "current_citInitial": 1,
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   "hotkeys": {
    "equation": "Ctrl-E",
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