**nawtilus** provides a procedure for the navigated
weighting (NAWT) proposed by Katsumata (2020), which
estimates a pre-specified parameter of interest (e.g., the average
treatment effects or the average treatment effects on the treated) with
the inverse probability weighting where propensity scores are estimated
using estimating equations suitable for the parameter of interest. It
also provides several tools for summarizing and checking the estimation
results, including a covariate balance check and an inverse probability
weights plot.

Katsumata, Hiroto. 2020. “Navigated Weighting to Improve Inverse Probability Weighting for Missing Data Problems and Causal Inference.” Working Paper, arxiv:2005.10998.

Katsumata, Hiroto. 2020. nawtilus: Navigated Weighting for the Inverse Probability Weighting. R package version 0.1.4. https://CRAN.R-project.org/package=nawtilus.

You can install the released version of nawtilus from CRAN with:

`install.packages("nawtilus")`

And the development version from GitHub with:

```
# install.packages("devtools")
::install_github("hirotokatsumata/nawtilus") devtools
```

This example shows how to use **nawtilus** for
estimation of parameter of interest.

First, load the package and make toy data.

```
# Load the package
library(nawtilus)
# Make toy data
# ATT estimation
# True ATT is 10
<- 10
tau set.seed(12345)
<- 1000
n <- matrix(rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 4)
X <- 1 / (1 + exp(X[, 1] - 0.5 * X[, 2] + 0.25 * X[, 3] + 0.1 * X[, 4]))
prop <- rbinom(n, 1, prop)
treat <- 210 + 27.4 * X[, 1] + 13.7 * X[, 2] + 13.7 * X[, 3] + 13.7 * X[, 4] +
y * treat + rnorm(n)
tau
# Data frame
<- data.frame(X, treat, y)
df colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y")
```

Then, specify a model for propensity score estimation.

`<- as.formula(treat ~ x1 + x2 + x3 + x4) formula_c `

Fit the model for the average treatment effects on the treated (ATT)
estimation using `nawt()`

with the default setting (a power
weighting function with α = 2).

```
# Power weighting function with alpha = 2
<- nawt(formula = formula_c, outcome = "y", estimand = "ATT",
fit method = "score", data = df, alpha = 2)
#> [1] "Estimate weights for the ATT estimation by (weighted) score conditions"
```

You can summarize the results easily with `summary()`

.

```
summary(fit)
#>
#> Call:
#> nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score",
#> data = df, alpha = 2)
#>
#> ATT estimates: 10.54
#>
#> Coefficients:
#> Estimate Std..Error z.value Pr...z..
#> est 10.54356 1.19535 8.8205 0.000e+00 ***
#> (Intercept) 0.01142 0.07642 0.1494 8.812e-01
#> x1 -1.05398 0.12718 -8.2871 2.220e-16 ***
#> x2 0.43165 0.09211 4.6860 2.786e-06 ***
#> x3 -0.21745 0.08829 -2.4629 1.378e-02 *
#> x4 0.12933 0.09039 1.4308 1.525e-01
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Effective N for the propensity score estimation: 610.16
#> Effective N for the ATT estimation:
#> treatment: 475
#> control: 156.68
```

Note that the estimated coefficients except for `est`

are
for the propensity score estimation.

Check covariate balance between the treatment and control groups
before and after the NAWT with `cbcheck()`

.

```
<- par(no.readonly = TRUE) # Just for adjusting plot margins
oldpar par(mar = c(5.1, 5.1, 4.1, 2.1)) # Just for adjusting plot margins
cbcheck(fit)
```

`<- oldpar # Just for adjusting plot margins par `

Let’s compare the inverse probability weights estimated by the nawt
with those estimated by the standard logistic regression with
`plot()`

.

`plot(fit)`

Finally, check the weights used in propensity score estimation and
distribution of the estimated propensity scores in the NAWT with
`plot_omega()`

.

`plot_omega(fit)`