tweaks

Author: chrismainey

to_explain_or_predict.Rmd

@@ -299,18 +299,30 @@ $$\large{y= \alpha + \beta_{i} x_{i} + \epsilon}$$
 
 
 ---
-# The Generalized Linear Model (GLM):
+## How can we use regression on other distributions / data types?
 
-For distributions in the exponential family, GLM allows the linear model to relate to response through a function:
+We can 'zoom out' to a more the 'Generalized Linear Model (GLM):
+
+_For distributions in the exponential family, GLM allows the linear model to relate to response through a function:_
 
 $$\large{g(\mu)= \alpha + \beta_{i} x_{i}}$$
 <br>
 + Where $\mu$ is the _expectation_ of $Y$, 
 + $g$ is the link function - related to each
 
 --
+<br>
+
+###So, for logistic regression, the link function is 'logit' or the log odds of the event.
+
+???
+
+As the name suggest, a more general form allows us to use different distributions, but understand them as a linear model on a given scale.  E.g. for count data, $\mu$ would be the expected count, and $g$ would be the natural logarithm, and the model is using the Poisson distribution.  
 
-So, for logistic regression, the link function is 'logit' or the log odds of the event.
+In our case, for binary, we are modelling the 'odds' of the outcome (death) on the log scale, with a binomial distribution.
+This is the log-odd, or 'logit' link fiction:  hence logistic regression.
+
+__Importantly, I can use it to examine the explanatory relationships, or to predict new data__
 
 ---
 
@@ -607,10 +619,9 @@ You might be happy with a 'wrong' model for in prediction, if it gives better pr
 ]
 
 .pull-right[
-<center>
-<div class="tenor-gif-embed" data-postid="1688826665026359193" data-share-method="host" data-aspect-ratio="1.25758" data-width="75%"><a href="https://tenor.com/view/miles-morales-miles-across-the-spider-verse-i-made-another-mistake-i-made-a-mistake-gif-1688826665026359193">Miles Morales Across The Spider Verse GIF</a>from <a href="https://tenor.com/search/miles+morales-gifs">Miles Morales GIFs</a></div> <script type="text/javascript" async src="https://tenor.com/embed.js"></script></center>
-<br>
-> "With great power comes greate responsibility"
+
+
+> "With great power comes great responsibility"
 - Stan Lee (via Spiderman's Uncle Ben)
 
 ]

to_explain_or_predict.html

@@ -4,7 +4,7 @@
     <title>To Explain or Predict: how different modelling objectives change how you use the same tools</title>
     <meta charset="utf-8" />
     <meta name="author" content="Chris Mainey" />
-    <meta name="date" content="2024-11-18" />
+    <meta name="date" content="2024-11-19" />
     <script src="libs/header-attrs/header-attrs.js"></script>
     <link rel="stylesheet" href="xaringan-themer.css" type="text/css" />
   </head>
@@ -223,18 +223,30 @@
 
 
 ---
-# The Generalized Linear Model (GLM):
+## How can we use regression on other distributions / data types?
 
-For distributions in the exponential family, GLM allows the linear model to relate to response through a function:
+We can 'zoom out' to a more the 'Generalized Linear Model (GLM):
+
+_For distributions in the exponential family, GLM allows the linear model to relate to response through a function:_
 
 `$$\large{g(\mu)= \alpha + \beta_{i} x_{i}}$$`
 &lt;br&gt;
 + Where `\(\mu\)` is the _expectation_ of `\(Y\)`, 
 + `\(g\)` is the link function - related to each
 
 --
+&lt;br&gt;
+
+###So, for logistic regression, the link function is 'logit' or the log odds of the event.
+
+???
+
+As the name suggest, a more general form allows us to use different distributions, but understand them as a linear model on a given scale.  E.g. for count data, `\(\mu\)` would be the expected count, and `\(g\)` would be the natural logarithm, and the model is using the Poisson distribution.  
 
-So, for logistic regression, the link function is 'logit' or the log odds of the event.
+In our case, for binary, we are modelling the 'odds' of the outcome (death) on the log scale, with a binomial distribution.
+This is the log-odd, or 'logit' link fiction:  hence logistic regression.
+
+__Importantly, I can use it to examine the explanatory relationships, or to predict new data__
 
 ---
 
@@ -298,8 +310,8 @@
 ## Dep. Variable:            DEATH_EVENT   No. Observations:                  299
 ## Model:                          Logit   Df Residuals:                      296
 ## Method:                           MLE   Df Model:                            2
-## Date:                Mon, 18 Nov 2024   Pseudo R-squ.:                  0.1359
-## Time:                        15:02:46   Log-Likelihood:                -162.16
+## Date:                Tue, 19 Nov 2024   Pseudo R-squ.:                  0.1359
+## Time:                        17:16:16   Log-Likelihood:                -162.16
 ## converged:                       True   LL-Null:                       -187.67
 ## Covariance Type:            nonrobust   LLR p-value:                 8.308e-12
 ## =====================================================================================
@@ -430,7 +442,7 @@
 ```
 
 ```
-## 0.69
+## 0.7713068181818182
 ```
 
 ---
@@ -571,10 +583,9 @@
 ]
 
 .pull-right[
-&lt;center&gt;
-&lt;div class="tenor-gif-embed" data-postid="1688826665026359193" data-share-method="host" data-aspect-ratio="1.25758" data-width="75%"&gt;&lt;a href="https://tenor.com/view/miles-morales-miles-across-the-spider-verse-i-made-another-mistake-i-made-a-mistake-gif-1688826665026359193"&gt;Miles Morales Across The Spider Verse GIF&lt;/a&gt;from &lt;a href="https://tenor.com/search/miles+morales-gifs"&gt;Miles Morales GIFs&lt;/a&gt;&lt;/div&gt; &lt;script type="text/javascript" async src="https://tenor.com/embed.js"&gt;&lt;/script&gt;&lt;/center&gt;
-&lt;br&gt;
-&gt; "With great power comes greate responsibility"
+
+
+&gt; "With great power comes great responsibility"
 - Stan Lee (via Spiderman's Uncle Ben)
 
 ]

working_r.R

@@ -77,3 +77,29 @@ predictions <- predict(ridge1, newx=x.test, type="response") |> as.vector()
 
 ModelMetrics::auc(Test$DEATH_EVENT, predictions)
 
+
+
+
+
+# logarithmic relationship tested
+
+library(readr)
+heart_failure_dt <- read_csv("data/heart_failure_clinical_records_dataset.csv")
+
+r_model_exp2 <- glm(DEATH_EVENT ~ serum_creatinine + ejection_fraction
+                   , data=heart_failure_dt
+                   , family = "binomial")
+
+
+r_model_exp3 <- glm(DEATH_EVENT ~ serum_creatinine + ejection_fraction
+                    , data=heart_failure_dt
+                    , family = binomial(link = "cloglog"))
+
+
+summary(r_model_exp2)
+summary(r_model_exp3)
+
+
+library(ModelMetrics)
+
+auc(r_model_exp2)

xaringan-themer.css

@@ -123,6 +123,7 @@ a, a > code {
   color: var(--link-color);
   text-decoration: none;
 }
+
 .mjx-chtml{ font-size: 130% !important; }
 
 .footnote {