first part of GLM-chapter drafted

TobiasRoth · Sep 29, 2024 · 757083b · 757083b
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diff --git a/1.3-distributions.Rmd b/1.3-distributions.Rmd
@@ -32,9 +32,9 @@ The expected value is $E(x) = np$ and the variance is $Var(x) = np(1-p)$.
 
 ```{r, echo=FALSE, fig.cap="Two examples of a binomial distribution. size: number of trials (the argument in the corresponding R function, for example in rbinom, is called size). p: success probability."}
 randombinom <- rbinom(100000, size=10, prob=0.3)
-histrandombin <- hist(randombinom, breaks=seq(-0.5, size+0.5,by=1), plot=FALSE)
+histrandombin <- hist(randombinom, breaks=seq(-0.5, 10.5,by=1), plot=FALSE)
 par(mfrow=c(1,2), oma=c(0, 2, 0,0))
-plot(histrandombin$mids, histrandombin$density, type="h",  lwd=5,col="blue", las=1, xlim=c(0, size), cex.lab=1.2, cex.axis=1,
+plot(histrandombin$mids, histrandombin$density, type="h",  lwd=5,col="blue", las=1, xlim=c(0, 10), cex.lab=1.2, cex.axis=1,
   xlab="size=10, p=0.3", lend="butt", ylab="")
 
 randombinom <- rbinom(100000, size=100, prob=0.2)

diff --git a/2.06-glm.Rmd b/2.06-glm.Rmd
diff --git a/docs/1.3-distributions.md b/docs/1.3-distributions.md
@@ -9,7 +9,7 @@ Probability distributions are grouped into discrete and continuous distributions
 
 ## Discrete distributions
 
-### Bernoulli distribution
+### Bernoulli distribution {#bernoulli-dist}
 
 Bernoulli distributed data take on the exact values 0 or 1. The value 1 occurs with probability $p$.    
 
@@ -20,7 +20,7 @@ The expected value is $E(x) = p$ and the variance is $Var(x) = p(1-p)$.
 
 The flipping experiment of a fair coin produces Bernoulli distributed data with $p=0.5$ if head is taken as one and tail is taken as zero. The Bernoulli distribution is usually used as a data model for binary data such as whether a nest box is used or not, whether a seed germinated or not, whether a species occurs or not in a plot etc. 
 
-### Binomial distribution
+### Binomial distribution {#binomial-dist}
 
 The binomial distribution describes the number of ones among a predefined number of Bernoulli trials. For example, the number of heads among 20 coin flips, the number of used nest boxes among the 50 nest boxes of the study area, or the number of seed that germinated among the 10 seeds in the pot. Binomially distributed data are counts with an upper limit ($n$).
 
@@ -30,6 +30,12 @@ The probability function is $p(x) = {n\choose x} p^x(1-p)^{(n-x)}$.
 The expected value is $E(x) = np$ and the variance is $Var(x) = np(1-p)$.
 
 
+<div class="figure">
+<img src="1.3-distributions_files/figure-html/unnamed-chunk-1-1.png" alt="Two examples of a binomial distribution. size: number of trials (the argument in the corresponding R function, for example in rbinom, is called size). p: success probability." width="672" />
+<p class="caption">(\#fig:unnamed-chunk-1)Two examples of a binomial distribution. size: number of trials (the argument in the corresponding R function, for example in rbinom, is called size). p: success probability.</p>
+</div>
+
+
 ### Poisson distribution
 
 The Poisson distribution describes the distribution of counts without upper boundary, i.e., when we know how many times something happened but we do not know how many times it did not happen. A typical Poisson distributed variable is the number of raindrops in equally-sized grid cells on the floor, if we can assume that every rain drop falls down completely independent of the other raindrops and at a completely random point. 
@@ -154,8 +160,8 @@ The F-distribution is not important in Bayesian statistics.
 Ratios of sample variances drawn from populations with equal variances follow an F-distribution. The density function of the F-distribution is even more complicated than the one of the t-distribution! We do not copy it here. Further, we have not yet met any Bayesian example where the F-distribution is used (that does not mean that there is no). It is used in frequentist analyses in order to compare variances, e.g. within ANOVAs. If two variances only differ because of natural variance in the data (nullhypothesis) then $\frac{Var(X_1)}{Var(X_2)}\sim F_{df_1,df_2}$.
 
 <div class="figure">
-<img src="1.3-distributions_files/figure-html/unnamed-chunk-1-1.png" alt="Different density functions of the F statistics" width="672" />
-<p class="caption">(\#fig:unnamed-chunk-1)Different density functions of the F statistics</p>
+<img src="1.3-distributions_files/figure-html/unnamed-chunk-2-1.png" alt="Different density functions of the F statistics" width="672" />
+<p class="caption">(\#fig:unnamed-chunk-2)Different density functions of the F statistics</p>
 </div>
 
 
diff --git a/docs/1.3-distributions_files/figure-html/unnamed-chunk-1-1.png b/docs/1.3-distributions_files/figure-html/unnamed-chunk-1-1.png
diff --git a/docs/1.3-distributions_files/figure-html/unnamed-chunk-2-1.png b/docs/1.3-distributions_files/figure-html/unnamed-chunk-2-1.png
diff --git a/docs/2.06-glm.md b/docs/2.06-glm.md
diff --git a/docs/2.06-glm_files/figure-html/illlink-1.png b/docs/2.06-glm_files/figure-html/illlink-1.png
diff --git a/docs/2.06-glm_files/figure-html/lrgof-1.png b/docs/2.06-glm_files/figure-html/lrgof-1.png
diff --git a/docs/2.06-glm_files/figure-html/unnamed-chunk-4-1.png b/docs/2.06-glm_files/figure-html/unnamed-chunk-4-1.png
diff --git a/docs/2.07-glmm.md b/docs/2.07-glmm.md
@@ -2,7 +2,6 @@
 # Generalized linear mixed models {#glmm}
 
 ## Introduction
-THIS CHAPTER IS UNDER CONSTRUCTION!!!   
 <!-- Steffis draft version, started 17.11.2021, fk worked on it 15.11.2022, svf revised it 22.11.2022-->
 
 In chapter \@ref(lmer) on linear mixed effect models we have introduced how to analyze metric outcome variables for which a normal error distribution can be assumed (potentially after transformation), when the data have a hierarchical structure and, as a consequence, observations are not independent.

diff --git a/docs/2.07-glmm_files/figure-html/ppbinomial-1.png b/docs/2.07-glmm_files/figure-html/ppbinomial-1.png
diff --git a/docs/404.html b/docs/404.html
@@ -23,7 +23,7 @@
 <meta name="author" content="Fränzi Korner-Nievergelt, Tobias Roth, Stefanie von Felten, Jerôme Guélat, Bettina Almasi, Pius Korner-Nievergelt" />
 
 
-<meta name="date" content="2024-07-12" />
+<meta name="date" content="2024-09-29" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1" />
   <meta name="apple-mobile-web-app-capable" content="yes" />
@@ -221,8 +221,8 @@
 <li class="chapter" data-level="4.1" data-path="distributions.html"><a href="distributions.html#introduction"><i class="fa fa-check"></i><b>4.1</b> Introduction</a></li>
 <li class="chapter" data-level="4.2" data-path="distributions.html"><a href="distributions.html#discrete-distributions"><i class="fa fa-check"></i><b>4.2</b> Discrete distributions</a>
 <ul>
-<li class="chapter" data-level="4.2.1" data-path="distributions.html"><a href="distributions.html#bernoulli-distribution"><i class="fa fa-check"></i><b>4.2.1</b> Bernoulli distribution</a></li>
-<li class="chapter" data-level="4.2.2" data-path="distributions.html"><a href="distributions.html#binomial-distribution"><i class="fa fa-check"></i><b>4.2.2</b> Binomial distribution</a></li>
+<li class="chapter" data-level="4.2.1" data-path="distributions.html"><a href="distributions.html#bernoulli-dist"><i class="fa fa-check"></i><b>4.2.1</b> Bernoulli distribution</a></li>
+<li class="chapter" data-level="4.2.2" data-path="distributions.html"><a href="distributions.html#binomial-dist"><i class="fa fa-check"></i><b>4.2.2</b> Binomial distribution</a></li>
 <li class="chapter" data-level="4.2.3" data-path="distributions.html"><a href="distributions.html#poisson-distribution"><i class="fa fa-check"></i><b>4.2.3</b> Poisson distribution</a></li>
 <li class="chapter" data-level="4.2.4" data-path="distributions.html"><a href="distributions.html#negative-binomial-distribution"><i class="fa fa-check"></i><b>4.2.4</b> Negative-binomial distribution</a></li>
 </ul></li>
@@ -312,29 +312,44 @@
 <li class="chapter" data-level="14" data-path="glm.html"><a href="glm.html"><i class="fa fa-check"></i><b>14</b> Generalized linear models</a>
 <ul>
 <li class="chapter" data-level="14.1" data-path="glm.html"><a href="glm.html#introduction-3"><i class="fa fa-check"></i><b>14.1</b> Introduction</a></li>
-<li class="chapter" data-level="14.2" data-path="glm.html"><a href="glm.html#summary-4"><i class="fa fa-check"></i><b>14.2</b> Summary</a></li>
+<li class="chapter" data-level="14.2" data-path="glm.html"><a href="glm.html#bernoulli-model"><i class="fa fa-check"></i><b>14.2</b> Bernoulli model</a>
+<ul>
+<li class="chapter" data-level="14.2.1" data-path="glm.html"><a href="glm.html#background-2"><i class="fa fa-check"></i><b>14.2.1</b> Background</a></li>
+<li class="chapter" data-level="14.2.2" data-path="glm.html"><a href="glm.html#fitting-a-bernoulli-model-in-r"><i class="fa fa-check"></i><b>14.2.2</b> Fitting a Bernoulli model in R</a></li>
+<li class="chapter" data-level="14.2.3" data-path="glm.html"><a href="glm.html#assessing-model-assumptions-in-a-bernoulli-model"><i class="fa fa-check"></i><b>14.2.3</b> Assessing model assumptions in a Bernoulli model</a></li>
+<li class="chapter" data-level="14.2.4" data-path="glm.html"><a href="glm.html#visualising-the-results"><i class="fa fa-check"></i><b>14.2.4</b> Visualising the results</a></li>
+<li class="chapter" data-level="14.2.5" data-path="glm.html"><a href="glm.html#some-remarks"><i class="fa fa-check"></i><b>14.2.5</b> Some remarks</a></li>
+</ul></li>
+<li class="chapter" data-level="14.3" data-path="glm.html"><a href="glm.html#binomial-model"><i class="fa fa-check"></i><b>14.3</b> Binomial model</a>
+<ul>
+<li class="chapter" data-level="14.3.1" data-path="glm.html"><a href="glm.html#background-3"><i class="fa fa-check"></i><b>14.3.1</b> Background</a></li>
+<li class="chapter" data-level="14.3.2" data-path="glm.html"><a href="glm.html#fitting-a-binomial-model-in-r"><i class="fa fa-check"></i><b>14.3.2</b> Fitting a binomial model in R</a></li>
+<li class="chapter" data-level="14.3.3" data-path="glm.html"><a href="glm.html#assessing-assumptions-of-a-binomial-model"><i class="fa fa-check"></i><b>14.3.3</b> Assessing assumptions of a binomial model</a></li>
+<li class="chapter" data-level="14.3.4" data-path="glm.html"><a href="glm.html#visualising-results"><i class="fa fa-check"></i><b>14.3.4</b> Visualising results</a></li>
+</ul></li>
+<li class="chapter" data-level="14.4" data-path="glm.html"><a href="glm.html#poisson-model"><i class="fa fa-check"></i><b>14.4</b> Poisson model</a></li>
 </ul></li>
 <li class="chapter" data-level="15" data-path="glmm.html"><a href="glmm.html"><i class="fa fa-check"></i><b>15</b> Generalized linear mixed models</a>
 <ul>
 <li class="chapter" data-level="15.1" data-path="glmm.html"><a href="glmm.html#introduction-4"><i class="fa fa-check"></i><b>15.1</b> Introduction</a>
 <ul>
 <li class="chapter" data-level="15.1.1" data-path="glmm.html"><a href="glmm.html#binomial-mixed-model"><i class="fa fa-check"></i><b>15.1.1</b> Binomial Mixed Model</a></li>
 </ul></li>
-<li class="chapter" data-level="15.2" data-path="glmm.html"><a href="glmm.html#summary-5"><i class="fa fa-check"></i><b>15.2</b> Summary</a></li>
+<li class="chapter" data-level="15.2" data-path="glmm.html"><a href="glmm.html#summary-4"><i class="fa fa-check"></i><b>15.2</b> Summary</a></li>
 </ul></li>
 <li class="chapter" data-level="16" data-path="modelchecking.html"><a href="modelchecking.html"><i class="fa fa-check"></i><b>16</b> Posterior predictive model checking</a>
 <ul>
 <li class="chapter" data-level="16.1" data-path="modelchecking.html"><a href="modelchecking.html#introduction-5"><i class="fa fa-check"></i><b>16.1</b> Introduction</a></li>
-<li class="chapter" data-level="16.2" data-path="modelchecking.html"><a href="modelchecking.html#summary-6"><i class="fa fa-check"></i><b>16.2</b> Summary</a></li>
+<li class="chapter" data-level="16.2" data-path="modelchecking.html"><a href="modelchecking.html#summary-5"><i class="fa fa-check"></i><b>16.2</b> Summary</a></li>
 </ul></li>
 <li class="chapter" data-level="17" data-path="model_comparison.html"><a href="model_comparison.html"><i class="fa fa-check"></i><b>17</b> Model comparison and multimodel inference</a>
 <ul>
 <li class="chapter" data-level="17.1" data-path="model_comparison.html"><a href="model_comparison.html#introduction-6"><i class="fa fa-check"></i><b>17.1</b> Introduction</a></li>
-<li class="chapter" data-level="17.2" data-path="model_comparison.html"><a href="model_comparison.html#summary-7"><i class="fa fa-check"></i><b>17.2</b> Summary</a></li>
+<li class="chapter" data-level="17.2" data-path="model_comparison.html"><a href="model_comparison.html#summary-6"><i class="fa fa-check"></i><b>17.2</b> Summary</a></li>
 </ul></li>
 <li class="chapter" data-level="18" data-path="stan.html"><a href="stan.html"><i class="fa fa-check"></i><b>18</b> MCMC using Stan</a>
 <ul>
-<li class="chapter" data-level="18.1" data-path="stan.html"><a href="stan.html#background-3"><i class="fa fa-check"></i><b>18.1</b> Background</a></li>
+<li class="chapter" data-level="18.1" data-path="stan.html"><a href="stan.html#background-5"><i class="fa fa-check"></i><b>18.1</b> Background</a></li>
 <li class="chapter" data-level="18.2" data-path="stan.html"><a href="stan.html#install-rstan"><i class="fa fa-check"></i><b>18.2</b> Install <code>rstan</code></a></li>
 <li class="chapter" data-level="18.3" data-path="stan.html"><a href="stan.html#firststanmod"><i class="fa fa-check"></i><b>18.3</b> Writing a Stan model</a></li>
 <li class="chapter" data-level="18.4" data-path="stan.html"><a href="stan.html#run-stan-from-r"><i class="fa fa-check"></i><b>18.4</b> Run Stan from R</a></li>
@@ -351,7 +366,7 @@
 <li class="chapter" data-level="21" data-path="spatial_glmm.html"><a href="spatial_glmm.html"><i class="fa fa-check"></i><b>21</b> Modeling spatial data using GLMM</a>
 <ul>
 <li class="chapter" data-level="21.1" data-path="spatial_glmm.html"><a href="spatial_glmm.html#introduction-9"><i class="fa fa-check"></i><b>21.1</b> Introduction</a></li>
-<li class="chapter" data-level="21.2" data-path="spatial_glmm.html"><a href="spatial_glmm.html#summary-8"><i class="fa fa-check"></i><b>21.2</b> Summary</a></li>
+<li class="chapter" data-level="21.2" data-path="spatial_glmm.html"><a href="spatial_glmm.html#summary-7"><i class="fa fa-check"></i><b>21.2</b> Summary</a></li>
 </ul></li>
 <li class="part"><span><b>III ECOLOGICAL MODELS</b></span></li>
 <li class="chapter" data-level="22" data-path="PART-III.html"><a href="PART-III.html"><i class="fa fa-check"></i><b>22</b> Introduction to PART III</a>
@@ -366,7 +381,7 @@
 </ul></li>
 <li class="chapter" data-level="24" data-path="dailynestsurv.html"><a href="dailynestsurv.html"><i class="fa fa-check"></i><b>24</b> Daily nest survival</a>
 <ul>
-<li class="chapter" data-level="24.1" data-path="dailynestsurv.html"><a href="dailynestsurv.html#background-4"><i class="fa fa-check"></i><b>24.1</b> Background</a></li>
+<li class="chapter" data-level="24.1" data-path="dailynestsurv.html"><a href="dailynestsurv.html#background-6"><i class="fa fa-check"></i><b>24.1</b> Background</a></li>
 <li class="chapter" data-level="24.2" data-path="dailynestsurv.html"><a href="dailynestsurv.html#models-for-estimating-daily-nest-survival"><i class="fa fa-check"></i><b>24.2</b> Models for estimating daily nest survival</a></li>
 <li class="chapter" data-level="24.3" data-path="dailynestsurv.html"><a href="dailynestsurv.html#known-fate-model"><i class="fa fa-check"></i><b>24.3</b> Known fate model</a></li>
 <li class="chapter" data-level="24.4" data-path="dailynestsurv.html"><a href="dailynestsurv.html#dailynestsurvstan"><i class="fa fa-check"></i><b>24.4</b> The Stan model</a></li>