small changes for readability and changing to log likelihood loss

Author: hantonita

4tmle.Rmd

@@ -20,10 +20,10 @@ Now that we have covered
 - outcome models (e.g., G-computation) and 
 - exposure models (e.g., propensity score models), 
 
-let us talk about Doubly robust (DR) estimators. DR has several important properties: 
+let us talk about doubly robust (DR) estimators. DR has several important properties: 
 
-* They use information from 
-  - both the exposure and 
+* They use information from both 
+  - the exposure and 
   - the outcome models. 
 * They provide a **consistent estimator** if either of the above mentioned models is correctly specified.
   - consistent estimator means as the sample size increases, distribution of the estimates gets concentrated near the true parameter
@@ -108,7 +108,7 @@ Y.fit.sl <- SuperLearner(Y=ObsData$Y.bounded,
                        SL.library=c("SL.glm", 
                                     "SL.glmnet", 
                                     "SL.xgboost"),
-                       method="method.NNLS",
+                       method="method.CC_nloglik",
                        family="gaussian")
 ```
 
@@ -139,15 +139,15 @@ summary(ObsData$Pred.Y1)
 
 -  $Q^0(A=0,L)$ predictions:
 
-### Get initial treatment effect estimate
-
 ```{r SL_out02, cache=TRUE}
 ObsData.noY$A <- 0
 ObsData$Pred.Y0 <- predict(Y.fit.sl, newdata = ObsData.noY,
                            type = "response")$pred
 summary(ObsData$Pred.Y0)
 ```
 
+### Get initial treatment effect estimate
+
 ```{r SL_out03, cache=cachex, echo = TRUE}
 ObsData$Pred.TE <- ObsData$Pred.Y1 - ObsData$Pred.Y0  
 ```
@@ -201,7 +201,7 @@ PS.fit.SL <- SuperLearner(Y=ObsData$A,
                        SL.library=c("SL.glm", 
                                     "SL.glmnet", 
                                     "SL.xgboost"),
-                       method="method.NNLS",
+                       method="method.CC_nloglik",
                        family="binomial")
 ```
 
@@ -269,11 +269,11 @@ Aggregated or individual clever covariate components show slight difference in t
   - a vector with 2 components $\hat\epsilon_0$ and $\hat\epsilon_1$. 
 - It  is estimated through MLE, using a model with an offset based on the initial estimate, and clever covariates as independent variables [@gruber2009targeted]:
 
-  $E(Y=1|A,L)(\epsilon) = \frac{1}{1+\exp(-\log\frac{\bar Q^0(A,L)}{(1-\bar Q^0(A,L))}-\epsilon \times H(A,L))}$ 
+  $E(Y|A,L)(\epsilon) = \frac{1}{1+\exp(-\log\frac{\bar Q^0(A,L)}{(1-\bar Q^0(A,L))}-\epsilon \times H(A,L))}$ 
 
 ### $\hat\epsilon$ = $\hat\epsilon_0$ and $\hat\epsilon_1$ 
 
-This is more close to how how `tmle` package has implement clever covariates
+This is closer to how `tmle` package has implement clever covariates
 
 ```{r eestimate, cache=TRUE, warning=FALSE}
 eps_mod <- glm(Y.bounded ~ -1 + H.A1L + H.A0L +  
@@ -285,7 +285,7 @@ epsilon["H.A1L"]
 epsilon["H.A0L"]
 ```
 
-Note that, if `init.Pred` includes -ve values, `NaNs` would be produced after applying `qlogis()`.
+Note that, if `init.Pred` includes negative values, `NaNs` would be produced after applying `qlogis()`.
 
 ### Only 1 $\hat\epsilon$
 
@@ -330,7 +330,7 @@ summary(ObsData$Pred.Y1.update1)
 summary(ObsData$Pred.Y0.update1)  
 ```
 
-Note that, if `Pred.Y1` and `Pred.Y0` include -ve values, `NaNs` would be produced after applying `qlogis()`.
+Note that, if `Pred.Y1` and `Pred.Y0` include negative values, `NaNs` would be produced after applying `qlogis()`.
 
 ```{r hestimate, cache=TRUE, warning=FALSE, include = FALSE}
 # # clever covariates

5software.Rmd

@@ -60,7 +60,7 @@ SL.library = c("SL.glm",
 ```
 
 
-```{r tmlepkg33, cache=cachex, results='hide', message=FALSE, warning=FALSE}
+```{r tmlepkg33, cache=cachex, message=FALSE, warning=FALSE}
 tmle.fit <- tmle::tmle(Y = ObsData$Y_transf, 
                    A = ObsData$A, 
                    W = ObsData.noYA, 
@@ -72,15 +72,17 @@ tmle.fit
 ```
 
 
-```{r tmlepkgtr2, cache=cachex, results='hide', message=FALSE, warning=FALSE}
+```{r tmlepkgtr2, cache=cachex, message=FALSE, warning=FALSE}
 summary(tmle.fit)
 ```
 
 
-```{r tmlepkgtr, cache=cachex, results='hide', message=FALSE, warning=FALSE}
+```{r tmlepkgtr, cache=cachex, message=FALSE, warning=FALSE}
 tmle_est_tr <- tmle.fit$estimates$ATE$psi
 # transform back the ATE estimate
 tmle_est <- (max.Y-min.Y)*tmle_est_tr
+
+tmle_est
 ```
 
 ```{r, cache=TRUE, echo = TRUE}
@@ -107,7 +109,6 @@ Notes about the _tmle_ package:
 * does not scale the outcome for you
 * can give some error messages when dealing with variable types it is not expecting
 * practically all steps are nicely packed up in one function, very easy to use but need to dig a little to truly understand what it does
-* at first was not straightforward to figure out how to use with a continuous outcome and log-likelihood loss function as the difference between several parameters relating to variable type and loss function was unclear
 
 Most helpful resources: 
 
@@ -188,7 +189,7 @@ sl_disc <- Lrnr_sl$new(
 
 The SuperLearner is then trained on the sl3 task we created at the start and then it can be used to make predictions.
 
-```{r sl305, cache=cachexy, results='hide', message=FALSE, warning=FALSE}
+```{r sl305, cache=cachexy, message=FALSE, warning=FALSE}
 set.seed(1444)
 
 # train SL
@@ -202,6 +203,8 @@ sl3_data$sl_preds <- sl_fit$predict()
 
 sl3_est <- mean(sl3_data$sl_preds[sl3_data$A == 1]) - 
   mean(sl3_data$sl_preds[sl3_data$A == 0])
+
+sl3_est
 ```
 
 ```{r, cache=TRUE, echo = TRUE}