adding rerendered website

docs/Stats_review.html

@@ -340,7 +340,7 @@ <h1>Random Variables (RVs)</h1>
 <li>discrete (numbers of items or successes)</li>
 <li>continuous (heights, times, weights)</li>
 </ul>
-<p>We usually use capital letters – e.g.&nbsp;<span class="math inline">X</span>, <span class="math inline">Y</span>, sometimes with bold or with subscripts – to denote the RVs. In contrast we use lower case letters, e.g.&nbsp;<span class="math inline">x</span>, <span class="math inline">y</span>, <span class="math inline">k</span>, to denote the values that the RV takes. For instance, lets say that the heights of the woman at Virginia Tech are the RV, <span class="math inline">X</span>, and <span class="math inline">X</span> has a normal distribution with mean 62 inches and variance 6<span class="math inline">^2</span>, i.e., <span class="math inline">X \sim \mathrm{N}(62,6^2)</span> distribution. Say we then observe the heights of 3 individuals drawn from this distribution – we would write this as: <span class="math inline">x=(</span> 58.8, 62.1, 64.2 <span class="math inline">)</span>.</p>
+<p>We usually use capital letters – e.g.&nbsp;<span class="math inline">X</span>, <span class="math inline">Y</span>, sometimes with bold or with subscripts – to denote the RVs. In contrast we use lower case letters, e.g.&nbsp;<span class="math inline">x</span>, <span class="math inline">y</span>, <span class="math inline">k</span>, to denote the values that the RV takes. For instance, lets say that the heights of the woman at Virginia Tech are the RV, <span class="math inline">X</span>, and <span class="math inline">X</span> has a normal distribution with mean 62 inches and variance 6<span class="math inline">^2</span>, i.e., <span class="math inline">X \sim \mathrm{N}(62,6^2)</span> distribution. Say we then observe the heights of 3 individuals drawn from this distribution – we would write this as: <span class="math inline">x=(</span> 56.2, 58.4, 60.8 <span class="math inline">)</span>.</p>
 <p><br> <br> </p>
 </section>
 <section id="probability-distributions" class="level1">
@@ -564,7 +564,7 @@ <h1>Probability Distributions in <code>R</code></h1>
 <div class="cell">
 <div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">rnorm</span>(<span class="dv">3</span>, <span class="at">mean=</span><span class="dv">0</span>, <span class="at">sd=</span><span class="dv">1</span>) <span class="do">## random draws</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>[1] 0.02318727 0.28406256 0.56712882</code></pre>
+<pre><code>[1]  0.5637509 -0.7347765 -0.4281301</code></pre>
 </div>
 </div>
 <div class="cell">

docs/data/Culex_erraticus_walton_covariates_aggregated.csv

@@ -0,0 +1,37 @@
+"Month_Yr","sample_value","MaxTemp","Precip"
+"2015-01",0,17.7460156583238,3.30399188776126
+"2015-02",0.0181818181818182,17.8726865768433,16.5442658017982
+"2015-03",0.468085106382979,23.8176727092012,2.40565121451274
+"2015-04",1.61904761904762,26.0355911254883,8.97440616825901
+"2015-05",0.821428571428571,30.0160168011983,0.567960943028863
+"2015-06",3.00595238095238,31.1209421157837,4.84134272920589
+"2015-07",2.38095238095238,32.8113037109375,3.84901035286131
+"2015-08",1.82634730538922,32.5624453493221,5.56284532361401
+"2015-09",0.648809523809524,30.5515534877777,10.4097246267345
+"2015-10",0.988023952095808,27.226053329285,0.337750268821231
+"2015-11",0.73780487804878,24.8676840851947,18.3067496796934
+"2015-12",0.142857142857143,22.4658838510513,5.62147537689834
+"2016-01",0,16.0240589777629,3.55062202910301
+"2016-02",0.0202020202020202,19.420570479499,11.2546808033655
+"2016-03",0.0151515151515152,23.1360999213325,4.78566472774202
+"2016-04",0.0261437908496732,24.9808234420477,4.58042451914619
+"2016-05",0.0252525252525253,28.7288377549913,0.0530576339424258
+"2016-06",0.833333333333333,30.9698980119493,6.15541747283905
+"2016-07",1.26136363636364,33.3050937652588,4.49636819271836
+"2016-08",1.68527918781726,32.0963299746441,11.3387491821789
+"2016-09",2.61714285714286,31.605746710641,2.86828845062426
+"2016-10",1.21212121212121,29.142751481798,0
+"2016-11",1.53977272727273,24.4848198890686,0.00546268122905696
+"2016-12",0.771573604060914,20.4605378088007,11.6155217247566
+"2017-01",0.0454545454545455,18.3547306060791,0
+"2017-02",0.0363636363636364,23.6558444976807,3.15071005333554
+"2017-03",0.194285714285714,22.5357287979126,1.43009495224271
+"2017-04",0.436548223350254,26.1529895859927,0.499381616484695
+"2017-05",1.2020202020202,28.0017344156901,6.58056266321753
+"2017-06",0.83419689119171,29.4895135158084,13.3339398578195
+"2017-07",1.76536312849162,32.2513512552783,7.49392703533506
+"2017-08",0.744791666666667,31.8647617797057,6.08211343444419
+"2017-09",0.722222222222222,30.6056567298041,4.63103739480779
+"2017-10",0.142131979695431,27.7345255449944,11.5671122144095
+"2017-11",0.289772727272727,23.2313950061798,1.19576047259298
+"2017-12",0.00917431192660551,18.9360333013972,4.01825444195248

docs/search.json

@@ -349,6 +349,34 @@
     "section": "",
     "text": "Main materials\n\nPre-workshop\nInformation about pre-workshop preparation – including software installation, expectations for what you should already be familiar with, and review materials – is available in the pre-work portion of the materials page.\n  \n\n\n22 July 2024\n\n\n\nTime\nActivity\nMaterials\n\n\n\n\n\nArrival\n\n\n\n\n  \n\n\n23 July 2024 (08:30 - 17:00)\n\n\n\n\n\n\n\n\nTime\nActivity\nMaterials\n\n\n\n\n\nComing Soon!\n\n\n\n12:00\nLunch\n\n\n\n\n  \n\n\n24 July 2024 (08:30 - 17:00)\n\n\n\n\n\n\n\n\nTime\nActivity\nMaterials\n\n\n\n\n\nComing Soon!\n\n\n\n\n\n\n\n\n12:00\nLunch\n\n\n\n\n\n\n\n\n\n\n\n25 July 2024 (08:30 - 17:00)\n\n\n\nTime\nActivity\nMaterials\n\n\n\n\n\nComing Soon!\n\n\n\n\n\n\n26 July 2024\n\n\n\nTime\nActivity\nMaterials\n\n\n\n\n\nTravel\n\n\n\n\n\n\nPost-workshop\nEnjoy using these new techniques and databases!"
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+    "section": "Exploring the Data",
+    "text": "Exploring the Data\nAs always, we first want to take a look at the data, to make sure we understand it, and that we don’t have missing or weird values.\n\nmozData<-read.csv(\"data/Culex_erraticus_walton_covariates_aggregated.csv\")\nsummary(mozData)\n\n   Month_Yr          sample_value        MaxTemp          Precip      \n Length:36          Min.   :0.00000   Min.   :16.02   Min.   : 0.000  \n Class :character   1st Qu.:0.04318   1st Qu.:22.99   1st Qu.: 2.162  \n Mode  :character   Median :0.73001   Median :26.69   Median : 4.606  \n                    Mean   :0.80798   Mean   :26.23   Mean   : 5.595  \n                    3rd Qu.:1.22443   3rd Qu.:30.70   3rd Qu.: 7.864  \n                    Max.   :3.00595   Max.   :33.31   Max.   :18.307  \n\n\nWe can see that the minimum observed average number of mosquitoes it zero, and max is only 3 (there are likely many zeros averaged over many days in the month). There don’t appear to be any NAs in the data. In this case the dataset itself is small enough that we can print the whole thing to ensure it’s complete:\n\nmozData\n\n   Month_Yr sample_value  MaxTemp       Precip\n1   2015-01  0.000000000 17.74602  3.303991888\n2   2015-02  0.018181818 17.87269 16.544265802\n3   2015-03  0.468085106 23.81767  2.405651215\n4   2015-04  1.619047619 26.03559  8.974406168\n5   2015-05  0.821428571 30.01602  0.567960943\n6   2015-06  3.005952381 31.12094  4.841342729\n7   2015-07  2.380952381 32.81130  3.849010353\n8   2015-08  1.826347305 32.56245  5.562845324\n9   2015-09  0.648809524 30.55155 10.409724627\n10  2015-10  0.988023952 27.22605  0.337750269\n11  2015-11  0.737804878 24.86768 18.306749680\n12  2015-12  0.142857143 22.46588  5.621475377\n13  2016-01  0.000000000 16.02406  3.550622029\n14  2016-02  0.020202020 19.42057 11.254680803\n15  2016-03  0.015151515 23.13610  4.785664728\n16  2016-04  0.026143791 24.98082  4.580424519\n17  2016-05  0.025252525 28.72884  0.053057634\n18  2016-06  0.833333333 30.96990  6.155417473\n19  2016-07  1.261363636 33.30509  4.496368193\n20  2016-08  1.685279188 32.09633 11.338749182\n21  2016-09  2.617142857 31.60575  2.868288451\n22  2016-10  1.212121212 29.14275  0.000000000\n23  2016-11  1.539772727 24.48482  0.005462681\n24  2016-12  0.771573604 20.46054 11.615521725\n25  2017-01  0.045454545 18.35473  0.000000000\n26  2017-02  0.036363636 23.65584  3.150710053\n27  2017-03  0.194285714 22.53573  1.430094952\n28  2017-04  0.436548223 26.15299  0.499381616\n29  2017-05  1.202020202 28.00173  6.580562663\n30  2017-06  0.834196891 29.48951 13.333939858\n31  2017-07  1.765363128 32.25135  7.493927035\n32  2017-08  0.744791667 31.86476  6.082113434\n33  2017-09  0.722222222 30.60566  4.631037395\n34  2017-10  0.142131980 27.73453 11.567112214\n35  2017-11  0.289772727 23.23140  1.195760473\n36  2017-12  0.009174312 18.93603  4.018254442"
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+    "title": "VectorByte Methods Training",
+    "section": "Plotting the data",
+    "text": "Plotting the data\nFirst we’ll examine the data itself, including the predictors:\n\nmonths<-dim(mozData)[1]\nt<-1:months ## counter for months in the data set\npar(mfrow=c(3,1))\nplot(t, mozData$sample_value, type=\"l\", lwd=2, \n     main=\"Average Monthly Abundance\", \n     xlab =\"Time (months)\", \n     ylab = \"Average Count\")\nplot(t, mozData$MaxTemp, type=\"l\",\n     col = 2, lwd=2, \n     main=\"Average Maximum Temp\", \n     xlab =\"Time (months)\", \n     ylab = \"Temperature (C)\")\nplot(t, mozData$Precip, type=\"l\",\n     col=\"dodgerblue\", lwd=2,\n     main=\"Average Monthly Precip\", \n     xlab =\"Time (months)\", \n     ylab = \"Precipitation (in)\")\n\n\n\n\n\n\n\n\nVisually we noticed that there may be a bit of clumping in the values for abundance (this is subtle) – in particular, since we have a lot of very small/nearly zero counts, a transform, such as a square root, may spread things out for the abundances. It also looks like both the abundance and temperature data are more cyclical than the precipitation, and thus more likely to be related to each other. There’s also not visually a lot of indication of a trend, but it’s usually worthwhile to consider it anyway. Replotting the abundance data with a transformation:\n\nmonths<-dim(mozData)[1]\nt<-1:months ## counter for months in the data set\nplot(t, sqrt(mozData$sample_value), type=\"l\", lwd=2, \n     main=\"Sqrt Average Monthly Abundance\", \n     xlab =\"Time (months)\", \n     ylab = \"Average Count\")\n\n\n\n\n\n\n\n\nThat looks a little bit better. I suggest we go with this for our response."
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+    "href": "VB_IntroTimeDepData_practical.html#building-a-data-frame",
+    "title": "VectorByte Methods Training",
+    "section": "Building a data frame",
+    "text": "Building a data frame\nBefore we get into model building, we always want to build a data frame to contain all of the predictors that we want to consider, at the potential lags that we’re interested in. In the lecture we saw building the AR, sine/cosine, and trend predictors:\n\nt <- 2:months ## to make building the AR1 predictors easier\n\nmozTS <- data.frame(\n  Y=sqrt(mozData$sample_value[t]), # transformed response\n  Yl1=sqrt(mozData$sample_value[t-1]), # AR1 predictor\n  t=t, # trend predictor\n  sin12=sin(2*pi*t/12), \n  cos12=cos(2*pi*t/12) # periodic predictors\n  )\n\nWe will also put in the temperature and precipitation predictors. But we need to think about what might be an appropriate lag. If this were daily or weekly data, we’d probably want to have a fairly sizable lag – mosquitoes take a while to develop, so the number we see today is not likely related to the temperature today. However, since these data are agregated across a whole month, as is the temperature/precipitaion, the current month values are likely to be useful. However, it’s even possible that last month’s values may be so we’ll add those in as well:\n\nmozTS$MaxTemp<-mozData$MaxTemp[t] ## current temps\nmozTS$MaxTempl1<-mozData$MaxTemp[t-1] ## previous temps\nmozTS$Precip<-mozData$Precip[t] ## current precip\nmozTS$Precipl1<-mozData$Precip[t-1] ## previous precip\n\nThus our full dataframe:\n\nsummary(mozTS)\n\n       Y               Yl1               t            sin12         \n Min.   :0.0000   Min.   :0.0000   Min.   : 2.0   Min.   :-1.00000  \n 1st Qu.:0.2951   1st Qu.:0.2951   1st Qu.:10.5   1st Qu.:-0.68301  \n Median :0.8590   Median :0.8590   Median :19.0   Median : 0.00000  \n Mean   :0.7711   Mean   :0.7684   Mean   :19.0   Mean   :-0.01429  \n 3rd Qu.:1.1120   3rd Qu.:1.1120   3rd Qu.:27.5   3rd Qu.: 0.68301  \n Max.   :1.7338   Max.   :1.7338   Max.   :36.0   Max.   : 1.00000  \n     cos12             MaxTemp        MaxTempl1         Precip      \n Min.   :-1.00000   Min.   :16.02   Min.   :16.02   Min.   : 0.000  \n 1st Qu.:-0.68301   1st Qu.:23.18   1st Qu.:23.18   1st Qu.: 1.918  \n Median : 0.00000   Median :27.23   Median :27.23   Median : 4.631  \n Mean   :-0.02474   Mean   :26.47   Mean   :26.44   Mean   : 5.660  \n 3rd Qu.: 0.50000   3rd Qu.:30.79   3rd Qu.:30.79   3rd Qu.: 8.234  \n Max.   : 1.00000   Max.   :33.31   Max.   :33.31   Max.   :18.307  \n    Precipl1     \n Min.   : 0.000  \n 1st Qu.: 1.918  \n Median : 4.631  \n Mean   : 5.640  \n 3rd Qu.: 8.234  \n Max.   :18.307  \n\n\n\nhead(mozTS)\n\n          Y       Yl1 t         sin12         cos12  MaxTemp MaxTempl1\n1 0.1348400 0.0000000 2  8.660254e-01  5.000000e-01 17.87269  17.74602\n2 0.6841675 0.1348400 3  1.000000e+00  6.123234e-17 23.81767  17.87269\n3 1.2724180 0.6841675 4  8.660254e-01 -5.000000e-01 26.03559  23.81767\n4 0.9063270 1.2724180 5  5.000000e-01 -8.660254e-01 30.01602  26.03559\n5 1.7337683 0.9063270 6  1.224647e-16 -1.000000e+00 31.12094  30.01602\n6 1.5430335 1.7337683 7 -5.000000e-01 -8.660254e-01 32.81130  31.12094\n      Precip   Precipl1\n1 16.5442658  3.3039919\n2  2.4056512 16.5442658\n3  8.9744062  2.4056512\n4  0.5679609  8.9744062\n5  4.8413427  0.5679609\n6  3.8490104  4.8413427"
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+    "title": "VectorByte Methods Training",
+    "section": "Building a first model",
+    "text": "Building a first model\nWe will first build a very simple model – just a trend – to practice building the model, checking diagnostics, and plotting predictions.\n\nmod1<-lm(Y ~ t, data=mozTS)\nsummary(mod1)\n\n\nCall:\nlm(formula = Y ~ t, data = mozTS)\n\nResiduals:\n     Min       1Q   Median       3Q      Max \n-0.81332 -0.47902  0.03671  0.37384  0.87119 \n\nCoefficients:\n             Estimate Std. Error t value Pr(>|t|)    \n(Intercept)  0.904809   0.178421   5.071  1.5e-05 ***\nt           -0.007038   0.008292  -0.849    0.402    \n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.4954 on 33 degrees of freedom\nMultiple R-squared:  0.02136,   Adjusted R-squared:  -0.008291 \nF-statistic: 0.7204 on 1 and 33 DF,  p-value: 0.4021\n\n\nThe model output indicates that this model is not useful – the trend is not significant and it only explains about 2% of the variability. Let’s plot the predictions:\n\n## plot points and fitted lines\nplot(Y~t, data=mozTS, col=1, type=\"l\")\nlines(t, mod1$fitted, col=\"dodgerblue\", lwd=2)\n\n\n\n\n\n\n\n\nNot good – we’ll definitely need to try something else! Remember that since we’re using a linear model for this, that we should check our residual plots as usual, and then also plot the acf of the residuals:\n\npar(mfrow=c(1,3), mar=c(4,4,2,0.5))   \n\n## studentized residuals vs fitted\nplot(mod1$fitted, rstudent(mod1), col=1,\n     xlab=\"Fitted Values\", \n     ylab=\"Studentized Residuals\", \n     pch=20, main=\"AR 1 only model\")\n\n## qq plot of studentized residuals\nqqnorm(rstudent(mod1), pch=20, col=1, main=\"\" )\nabline(a=0,b=1,lty=2, col=2)\n\n## histogram of studentized residuals\nhist(rstudent(mod1), col=1, \n     xlab=\"Studentized Residuals\", \n     main=\"\", border=8)\n\n\n\n\n\n\n\n\nThis doesn’t look really bad, although the histogram might be a bit weird. Finally the acf\n\nacf(mod1$residuals)\n\n\n\n\n\n\n\n\nThis is where we can see that we definitely aren’t able to capture the pattern. There’s substantial autocorrelation left at a 1 month lag, and around 6 months.\nFinally, for moving forward, we can extract the BIC for this model so that we can compare with other models that you’ll build next.\n\nn<-length(t)\nextractAIC(mod1, k=log(n))[2]\n\n[1] -44.11057"
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