added LOESS example and outline for the normalization section

graphics_bioinf.R

@@ -36,6 +36,9 @@ library("limma")
 library("Single.mTEC.Transcriptomes")
 library("DESeq2")
 library("tibble")
+library("broom")
+library("scran")
+library("locfit")
 
 theme_set(theme_gray(base_size = 18))
 
@@ -138,6 +141,36 @@ scatter_tra +
 lm_tra <- lm(tra ~ total_detected, data = tra_detected)
 lm_tra
 
+## ----loessExampleLinFit, dependson="fit_model"---------------------------
+
+# create_data
+y <- seq(from=1, to=10, length.out=100)
+a <- y^3 +y^2  + rnorm(100,mean=0, sd=30)
+dataL <- data.frame(a=a, y=y)
+qplot(y, a, data = dataL)
+
+# linear fit
+linreg <- lm(a~y, data = dataL)
+
+
+(qplot(y, a, data = dataL) +
+  geom_abline(slope = tidy(linreg, quick = TRUE)[2,2], 
+              intercept = tidy(linreg, quick = TRUE)[1,2]))
+tidy(linreg)
+
+dataL$LinReg <- predict(linreg)
+
+## ----loessExampleFit, dependson="loessExampleLinFit"---------------------
+
+dataL$locFit  <- predict(locfit(y~lp(a, nn=0.5, deg=1), data=dataL),
+                         newdata = dataL$a)
+
+
+ (qplot(a, y, data = dataL, main = "Linear vs. local regression")
+ +  geom_line(aes(x = a, y = locFit), color = "dodgerblue3")
+ +  geom_line(aes(x = a, y = LinReg), color = "coral3"))
+
+
 ## ----session_info, cache = FALSE-----------------------------------------
 sessionInfo()
 

graphics_bioinf.Rmd

@@ -64,6 +64,9 @@ library("limma")
 library("Single.mTEC.Transcriptomes")
 library("DESeq2")
 library("tibble")
+library("broom")
+library("scran")
+library("locfit")
 
 theme_set(theme_gray(base_size = 18))
 
@@ -311,13 +314,89 @@ We can of course always add more predictors to the linear function. The coeffici
 \(b\) is called the __slope__ and \(a\) is called the __intercept__ .
 
 We can fit a linear regression via a call to the function `lm()`. The regression
-model is specified using R's formula notation.
+model is specified using R's formula notation. 
 
 ```{r regresssion_tra}
 lm_tra <- lm(tra ~ total_detected, data = tra_detected)
 lm_tra
 ```
 
+As we can see, the estimated 
+slope is ~ `r tidy(lm_tra, quick = TRUE)[2, "estimate"]`, indicating 
+that we have a proportion of `r tidy(lm_tra, quick = TRUE)[2, "estimate"]` 
+tra expressing genes on average per cell for the highly variable genes. 
+This is in line with the supplementary figure 1 of the original publication,
+which uses the full set of expressed genes, not just the highly variable 
+ones.
+
+# Local regression  (LOESS)
+
+
+
+Local regression is a commonly used approach for fitting flexible non--linear
+functions, which involves computing many local linear regression fits and combining
+them. Local regression is a very useful technique both for  data visualization and
+trend fitting. Fitting many local models requires quite some computational power,
+but it usually feasible with today's hardware. We illustrate the local regression
+using the `r CRANpkg("locfit") ` package on simulated data.
+
+We first fit a linear regression line to simulated
+data that follows a polynomial trend and see that it does not really
+fit well.
+
+```{r loessExampleLinFit, dependson="fit_model"}
+
+# create_data
+y <- seq(from=1, to=10, length.out=100)
+a <- y^3 +y^2  + rnorm(100,mean=0, sd=30)
+dataL <- data.frame(a=a, y=y)
+qplot(y, a, data = dataL)
+
+# linear fit
+linreg <- lm(a~y, data = dataL)
+
+
+(qplot(y, a, data = dataL) +
+  geom_abline(slope = tidy(linreg, quick = TRUE)[2,2], 
+              intercept = tidy(linreg, quick = TRUE)[1,2]))
+tidy(linreg)
+
+dataL$LinReg <- predict(linreg)
+```
+
+We now use the function `locfit` to perform a local regression on the
+data. It takes the predictors wrapped in a call to `lp()`. Within this
+function we can also set tunning parameters. An important one is the  `nn`
+one, which set the proportion of nearest--neighbors to be used for the local fits.
+
+The lower this percentage, the more closely the line will follow the data points.
+
+```{r loessExampleFit, dependson="loessExampleLinFit"}
+
+dataL$locFit  <- predict(locfit(y~lp(a, nn=0.5, deg=1), data=dataL),
+                         newdata = dataL$a)
+
+
+ (qplot(a, y, data = dataL, main = "Linear vs. local regression")
+ +  geom_line(aes(x = a, y = locFit), color = "dodgerblue3")
+ +  geom_line(aes(x = a, y = LinReg), color = "coral3"))
+
+```
+
+
+
+# Normalization and confounding factors.
+
+
+## Normalization of single cell data
+
+* use scran size factors
+
+## Confounding factors
+
+* ZINBA Wave
+
+
 
 # Session Info