Add FAQ section header

rdpeng · Sep 4, 2020 · eb7c315 · eb7c315
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diff --git a/manuscript/images/inferencepred-unnamed-chunk-10-1.png b/manuscript/images/inferencepred-unnamed-chunk-10-1.png
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diff --git a/manuscript/inferencepred.Rmd b/manuscript/inferencepred.Rmd
@@ -1,3 +1,8 @@
+---
+output: 
+  html_document: 
+    keep_md: yes
+---
 # Inference vs. Prediction: Implications for Modeling Strategy
 
 ```{r,include=FALSE}
@@ -143,6 +148,8 @@ Notice that the variable `pm10tmean` comes near the bottom of the list in terms
 
 However, just because PM10 is not a strong predictor of mortality doesn't mean that it does not have a relevant association with mortality. Given the tradeoffs that have to be made when developing a prediction model, PM10 is not high on the list of predictors that we would include--we simply cannot include every predictor.
 
+## Frequently Asked Questions
+
 
 ## Summary
 

diff --git a/manuscript/inferencepred.md b/manuscript/inferencepred.md
@@ -1,3 +1,8 @@
+---
+output: 
+  html_document: 
+    keep_md: yes
+---
 # Inference vs. Prediction: Implications for Modeling Strategy
 
 
@@ -39,11 +44,10 @@ Let's take a look at the bivariate association between PM10 and mortality. Here
 There doesn't appear to be much going on there, and a simple linear regression model of the log of daily mortality and PM10 seems to confirm that.
 
 
-```
-                 Estimate   Std. Error      t value  Pr(>|t|)
-(Intercept) 5.08884308354 0.0069353779 733.75138151 0.0000000
-pm10tmean   0.00004033446 0.0006913941   0.05833786 0.9535247
-```
+|            | Estimate| Std. Error|    t value| Pr(>&#124;t&#124;)|
+|:-----------|--------:|----------:|----------:|------------------:|
+|(Intercept) | 5.088843|   0.006935| 733.751382|           0.000000|
+|pm10tmean   | 0.000040|   0.000691|   0.058338|           0.953525|
 
 In the table of coefficients above, the coefficient for `pm10tmean` is quite small and its standard error is relatively large. Effectively, this estimate of the association is zero.
 
@@ -53,14 +57,13 @@ Here are the results for a second model, which includes both PM10 and season. Se
 
 
 
-```
-                Estimate   Std. Error    t value     Pr(>|t|)
-(Intercept)  5.166484285 0.0112629532 458.714886 0.000000e+00
-seasonQ2    -0.109271301 0.0166902948  -6.546996 3.209291e-10
-seasonQ3    -0.155503242 0.0169729148  -9.161847 1.736346e-17
-seasonQ4    -0.060317619 0.0167189714  -3.607735 3.716291e-04
-pm10tmean    0.001499111 0.0006156902   2.434847 1.558453e-02
-```
+|            | Estimate| Std. Error|  t value| Pr(>&#124;t&#124;)|
+|:-----------|--------:|----------:|--------:|------------------:|
+|(Intercept) |   5.1665|     0.0113| 458.7149|             0.0000|
+|seasonQ2    |  -0.1093|     0.0167|  -6.5470|             0.0000|
+|seasonQ3    |  -0.1555|     0.0170|  -9.1618|             0.0000|
+|seasonQ4    |  -0.0603|     0.0167|  -3.6077|             0.0004|
+|pm10tmean   |   0.0015|     0.0006|   2.4348|             0.0156|
 
 Notice now that the `pm10tmean` coefficient is quite a bit larger than before and its `t value` is large, suggesting a strong association. How is this possible?
 
@@ -72,35 +75,33 @@ In the following model we include temperature (`tmpd`) and dew point temperature
 
 
 
-```
-                  Estimate    Std. Error    t value     Pr(>|t|)
-(Intercept)  5.62066568788 0.16471183741 34.1242365 1.851690e-96
-date        -0.00002984198 0.00001315212 -2.2689856 2.411521e-02
-seasonQ2    -0.05805970053 0.02299356287 -2.5250415 1.218288e-02
-seasonQ3    -0.07655519887 0.02904104658 -2.6361033 8.906912e-03
-seasonQ4    -0.03154694305 0.01832712585 -1.7213252 8.641910e-02
-tmpd        -0.00295931276 0.00128835065 -2.2969777 2.244054e-02
-dptp         0.00068342228 0.00103489541  0.6603781 5.096144e-01
-pm10tmean    0.00237049992 0.00065856022  3.5995189 3.837886e-04
-```
+|            | Estimate| Std. Error| t value| Pr(>&#124;t&#124;)|
+|:-----------|--------:|----------:|-------:|------------------:|
+|(Intercept) |   5.6207|     0.1647| 34.1242|             0.0000|
+|date        |   0.0000|     0.0000| -2.2690|             0.0241|
+|seasonQ2    |  -0.0581|     0.0230| -2.5250|             0.0122|
+|seasonQ3    |  -0.0766|     0.0290| -2.6361|             0.0089|
+|seasonQ4    |  -0.0315|     0.0183| -1.7213|             0.0864|
+|tmpd        |  -0.0030|     0.0013| -2.2970|             0.0224|
+|dptp        |   0.0007|     0.0010|  0.6604|             0.5096|
+|pm10tmean   |   0.0024|     0.0007|  3.5995|             0.0004|
 
 Notice that the `pm10tmean` coefficient is even bigger than it was in the previous model. There appears to still be an association between PM10 and mortality. The effect size is small, but we will discuss that later.
 
 Finally, another class of potential confounders includes other pollutants. Before we place blame on PM10 as a harmful pollutant, it's important that we examine whether there might be another pollutant that can explain what we're observing. NO2 is a good candidate because it shares some of the same sources as PM10 and is known to be related to mortality. Let's see what happens when we include that in the model.
 
 
-```
-                  Estimate    Std. Error    t value     Pr(>|t|)
-(Intercept)  5.61378604085 0.16440280471 34.1465345 2.548704e-96
-date        -0.00002973484 0.00001312231 -2.2659756 2.430503e-02
-seasonQ2    -0.05143935218 0.02338034983 -2.2001105 2.871069e-02
-seasonQ3    -0.06569205605 0.02990520457 -2.1966764 2.895825e-02
-seasonQ4    -0.02750381423 0.01849165119 -1.4873639 1.381739e-01
-tmpd        -0.00296833498 0.00128542535 -2.3092239 2.174371e-02
-dptp         0.00070306996 0.00103262057  0.6808599 4.965877e-01
-no2tmean     0.00126556418 0.00086229169  1.4676753 1.434444e-01
-pm10tmean    0.00174189857 0.00078432327  2.2208937 2.725117e-02
-```
+|            | Estimate| Std. Error| t value| Pr(>&#124;t&#124;)|
+|:-----------|--------:|----------:|-------:|------------------:|
+|(Intercept) |   5.6138|     0.1644| 34.1465|             0.0000|
+|date        |   0.0000|     0.0000| -2.2660|             0.0243|
+|seasonQ2    |  -0.0514|     0.0234| -2.2001|             0.0287|
+|seasonQ3    |  -0.0657|     0.0299| -2.1967|             0.0290|
+|seasonQ4    |  -0.0275|     0.0185| -1.4874|             0.1382|
+|tmpd        |  -0.0030|     0.0013| -2.3092|             0.0217|
+|dptp        |   0.0007|     0.0010|  0.6809|             0.4966|
+|no2tmean    |   0.0013|     0.0009|  1.4677|             0.1434|
+|pm10tmean   |   0.0017|     0.0008|  2.2209|             0.0273|
 
 Notice in the table of coefficients that the `no2tmean` coefficient is similar in magnitude to the `pm10tmean` coefficient, although its `t value` is not as large. The `pm10tmean` coefficient appears to be statistically significant, but it is somewhat smaller in magnitude now.
 
@@ -123,7 +124,7 @@ Notice that the variable `pm10tmean` comes near the bottom of the list in terms
 
 However, just because PM10 is not a strong predictor of mortality doesn't mean that it does not have a relevant association with mortality. Given the tradeoffs that have to be made when developing a prediction model, PM10 is not high on the list of predictors that we would include--we simply cannot include every predictor.
 
-
+## Frequently Asked Questions
 
 
 ## Summary