miscnotes.Rmd

JUNK BELOW

### Estimation

If you want to estimate an average treatment effect (ATE) and the

but you have unequal
block sizes, how should you *define* the weighted version of the ATE that you
want? There are two options (1) weighting only by the size of the block or (2)
weighting by both the size of the block and the proportion treated-vs-control
in each block. This last weighting is called "harmonic mean weighting" and it
is the default when you use OLS with fixed effects for blocks (or when you
block-align or block-mean-center the outcome and the treatment assignment).


```{r eval=FALSE}
data(nuclearplants)
xb<-xBalance(pr~t1+strata(ptF),data=nuclearplants,report="all")
xb$results[,"adj.diff",]

unadj<-with(nuclearplants,mean(t1[pr==1])-mean(t1[pr==0]))

res_b<-with(nuclearplants,mapply(function(y,z){
				   c( T=mean(y[z==1]), C=mean(y[z==0]) )
}, y=split(t1,ptF), z=split(pr,ptF)))

trtavg<-mean(nuclearplants$t1[nuclearplants$pr==1])
ctlavg<-mean(nuclearplants$t1[nuclearplants$pr==0])


nb<-table(nuclearplants$pt)
ntrtb<-with(nuclearplants,sapply(split(pr,pt),function(x){ sum(x) }))

sum(res_b*(ntrtb/nb))

sum(res_b*(ntrtb/sum(ntrtb)))


```

```{r}

res_b<-with(dat,mapply(function(y,z){ mean(y[z==1])-mean(y[z==0]) }, y=split(Y,femaleF), z=split(Z,femaleF)))
nb<-table(femaleF)
weighted.mean(res_b,weights=nb)

## A simple estimate of the average treatment effect using a harmonic weighting scheme for unequal block sizes
ate<-lm(Y~Z+femaleF,data=dat)

## A version that does not rely on large-sample assumptions
nullp<-RItest(y=Y,z=Z,test.stat=mean.difference,sample=treatmentAssigner,samples=5000)

## A version that approximates the previous version with a Normal approximation
xb1<-xBalance(Z~Y+strata(femaleF),report="all",data=dat)
nullp2<-xb1$results[,"p",]
ate2<-xb1$results[,"adj.diff",]
xb1$results[,"adj.diff","femaleF"]


```

## Assess Validity of the Tests or Unbiasedness of the Estimation



## Assess Power (given Effect Size)/Minimum Detectable Effect Size (given Power)

If we test the "truth" then we can assess the validity of the tests and/or unbiasedness of the estimation method.

```{r}

newY<-y0 ## make truth zero
Zs<-treatmentAssigner(1000)
ALTS<-sort(unique(c(0,seq(-3,3,length=100))))



```


## What to do if you want to block on many covariates? Or if you want to create pairs based on one covariate?

Try the `blockTools` package in R, especially the non-bipartite matching option.