AsyVar {CBPS} | R Documentation |

## Asymptotic Variance and Confidence Interval Estimation of the ATE

### Description

`AsyVar`

estimates the asymptotic variance of the ATE obtained with the CBPS or oCBPS method. It also returns the finite variance estimate, the finite standard error, and a CI for the ATE.

### Usage

```
AsyVar(
Y,
Y_1_hat = NULL,
Y_0_hat = NULL,
CBPS_obj,
method = "CBPS",
X = NULL,
TL = NULL,
pi = NULL,
mu = NULL,
CI = 0.95
)
```

### Arguments

`Y` |
The vector of actual outcome values (observations). |

`Y_1_hat` |
The vector of estimated outcomes according to the treatment model. (AsyVar automatically sets the treatment model as a linear regression model and it is fitted within the function.) If |

`Y_0_hat` |
The vector of estimated outcomes according to the control model. (AsyVar automatically sets the control model as a linear regression model and it is fitted within the function.) If |

`CBPS_obj` |
An object obtained with the CBPS function. If this object is not sepecified, then |

`method` |
The specific method to be considered. Either |

`X` |
The matrix of covariates with the rows corresponding to the observations and the columns corresponding to the variables. The left most column must be a column of 1's for the intercept. ( |

`TL` |
The vector of treatment labels. More specifically, the label is 1 if it is in the treatment group and 0 if it is in the control group. ( |

`pi` |
The vector of estimated propensity scores. ( |

`mu` |
The estimated average treatment effect obtained with either the CBPS or oCBPS method. ( |

`CI` |
The specified confidence level (between 0 and 1) for calculating the confidence interval for the average treatment effect. Default value is 0.95. |

### Value

`mu.hat` |
The estimated average treatment effect, |

`asy.var` |
The estimated asymptotic variance of |

`var` |
The estimated variance of |

`std.err` |
The standard error of |

`CI.mu.hat` |
The confidence interval of |

### Author(s)

Inbeom Lee

### References

Fan, Jianqing and Imai, Kosuke and Lee, Inbeom and Liu, Han and Ning, Yang and Yang, Xiaolin. 2021. “Optimal Covariate Balancing Conditions in Propensity Score Estimation.” Journal of Business & Economic Statistics. https://imai.fas.harvard.edu/research/CBPStheory.html

### Examples

```
#GENERATING THE DATA
n=300
#Initialize the X matrix.
X_v1 <- rnorm(n,3,sqrt(2))
X_v2 <- rnorm(n,0,1)
X_v3 <- rnorm(n,0,1)
X_v4 <- rnorm(n,0,1)
X_mat <- as.matrix(cbind(rep(1,n), X_v1, X_v2, X_v3, X_v4))
#Initialize the Y_1 and Y_0 vector using the treatment model and the control model.
Y_1 <- X_mat %*% matrix(c(200, 27.4, 13.7, 13.7, 13.7), 5, 1) + rnorm(n)
Y_0 <- X_mat %*% matrix(c(200, 0 , 13.7, 13.7, 13.7), 5, 1) + rnorm(n)
#True Propensity Score calculation.
pre_prop <- X_mat[,2:5] %*% matrix(c(0, 0.5, -0.25, -0.1), 4, 1)
propensity_true <- (exp(pre_prop))/(1+(exp(pre_prop)))
#Generate T_vec, the treatment vector, with the true propensity scores.
T_vec <- rbinom(n, size=1, prob=propensity_true)
#Now generate the actual outcome Y_outcome (accounting for treatment/control groups).
Y_outcome <- Y_1*T_vec + Y_0*(1-T_vec)
#Use oCBPS.
ocbps.fit <- CBPS(T_vec ~ X_mat, ATT=0, baseline.formula = ~X_mat[,c(1,3:5)],
diff.formula = ~X_mat[,2])
#Use the AsyVar function to get the asymptotic variance of the
#estimated average treatment effect and its confidence interval when using oCBPS.
AsyVar(Y=Y_outcome, CBPS_obj=ocbps.fit, method="oCBPS", CI=0.95)
#Use CBPS.
cbps.fit <- CBPS(T_vec ~ X_mat, ATT=0)
#Use the AsyVar function to get the asymptotic variance of the
#estimated average treatment effect and its confidence interval when using CBPS.
AsyVar(Y=Y_outcome, CBPS_obj=cbps.fit, method="CBPS", CI=0.95)
```

*CBPS*version 0.23 Index]