ivDiag

https://yiqingxu.org/packages/ivDiag/
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ivDiag is an R toolkit for estimation and diagnostics with instrumental variable (IV) designs that...
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### Install ivDiag Development Version from GitHub

Source: https://yiqingxu.org/packages/ivDiag/index.html

Install the latest development version of the ivDiag package directly from GitHub using the remotes package.

```r
library(remotes)
install_github("apoorvalal/ivDiag")
```

--------------------------------

### Install Required Packages for ivDiag

Source: https://yiqingxu.org/packages/ivDiag/index.html

This function checks for and installs all necessary packages for the ivDiag package if they are not already installed. It ensures all dependencies are met before using the package.

```r
install_all <- function(packages) {
  installed_pkgs <- installed.packages()[, "Package"]
  for (pkg in packages) {
    if (!pkg %in% installed_pkgs) {
      install.packages(pkg)
    }
  }
}

packages <- c("foreach", "future", "doParallel", "lfe", "fixest", "ggplot2", 
              "ggfortify", "wCorr", "haven", "glue", "patchwork", "testthat")
install_all(packages)
```

--------------------------------

### Perform ZFS Test with lm_robust

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Conducts a ZFS (reduced-form) test using `lm_robust` on a subsample. This regression of the outcome on the instrument helps in setting up prior distributions for LTZ adjustments. Ensure `estimatr` library is installed.

```r
library(estimatr)
zfs <- lm_robust(totassoc_p ~ bishopcity + altitudine + escursione 
                 + costal + nearsea + population + pop2 + gini_land + 
                   gini_income + capoluogo, data = gsz_south, 
                 weights = gsz_south$population, se_type = "HC1")

summary(zfs)$coefficients["bishopcity", 1:2]
```

--------------------------------

### Install ivDiag from CRAN

Source: https://yiqingxu.org/packages/ivDiag/index.html

Use this command to install the stable version of the ivDiag package from CRAN.

```r
install.packages("ivDiag", repos='http://cran.us.r-project.org')
```

--------------------------------

### Check tF Output with testthat

Source: https://yiqingxu.org/packages/ivDiag/reference/tF.html

This snippet demonstrates how to use the 'testthat' package to verify the output of the `tF` function. It checks if the calculated t-ratio matches the expected value.

```r
library(testthat)
test_that("Check tF cF", {
  expect_equal(as.numeric(tf.out[2]), 1.96)
})
```

--------------------------------

### Visualize First Stage (Raw Data)

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Plots the raw data for the first stage of an IV analysis, showing the relationship between the instrument and the endogenous treatment. Requires setting up outcome, treatment, instrument, covariates, and cluster variables.

```R
Y <- "e_vote_buying" # Y: outcome of interest
D <-"lm_pob_mesa" # D: endogenous treatment
Z <- "lz_pob_mesa_f" # Z: instrumental variable
controls <- c("lpopulation", "lpotencial") # covariates of control variables
cl <- "muni_code" # clusters

# first stage (raw)
par(mar = c(4, 4, 2, 2))
plot(rueda$lz_pob_mesa_f, rueda$lm_pob_mesa, col = "#777777", cex = 0.5, 
     main = "Raw Data", xlab = "Instrument", ylab = "Treatment")
abline(lm(lm_pob_mesa ~ lz_pob_mesa_f, data = rueda), 
       col = 2, lwd = 2, lty = 2)
```

--------------------------------

### Load ivDiag and datasets

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Loads the ivDiag package and its associated datasets. Use ls() to view available datasets.

```R
library(ivDiag)
data(ivDiag)
ls()
#> [1] "gsz"       "gsz_south" "rueda"
```

--------------------------------

### tF()

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Implements the Valid t-Ratio Procedure.

```APIDOC
## tF()

### Description
Valid t-Ratio Procedure.

### Method
Not applicable (R function)

### Endpoint
Not applicable (R function)

### Parameters
Not specified in source.

### Request Example
Not applicable (R function)

### Response
Not specified in source.
```

--------------------------------

### ltz()

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Performs the Local-to-Zero Test.

```APIDOC
## ltz()

### Description
Local-to-Zero Test.

### Method
Not applicable (R function)

### Endpoint
Not applicable (R function)

### Parameters
Not specified in source.

### Request Example
Not applicable (R function)

### Response
Not specified in source.
```

--------------------------------

### Visualize First Stage (Partialled Out)

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Plots the first stage of an IV analysis after partialling out covariates. This visualization helps to see the relationship between the residualized instrument and the residualized treatment.

```R
# first stage (partial out)
z_res <- lm(lz_pob_mesa_f ~ lpopulation + lpotencial, data = rueda)$residuals
d_res <- lm(lm_pob_mesa ~ lpopulation + lpotencial, data = rueda)$residuals
plot(z_res, d_res, col = "#777777", cex = 0.5, 
     main = "Covariates Partialled Out", 
     xlab = "Residualized Instrument", 
     ylab = "Residualized Treatment")
abline(lm(d_res ~ z_res), col = 2, lwd = 2, lty = 2)
```

--------------------------------

### First-Stage Regression Results

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Presents the results of the first-stage regression, including coefficients, standard errors (analytic and bootstrap), and p-values. Confidence intervals are based on the bootstrap percentile method.

```R
g$est_fs
#>                 Coef     SE p.value   SE.b CI.b2.5% CI.b97.5% p.value.b
#> lz_pob_mesa_f 0.7957 0.0086       0 0.0087   0.7804    0.8145         0
```

--------------------------------

### Test ivDiag Output

Source: https://yiqingxu.org/packages/ivDiag/reference/ivDiag.html

This snippet demonstrates how to use the testthat package to assert specific values in the output of the ivDiag function, ensuring the estimation results are as expected.

```R
library(testthat)    
test_that("Check ivDiag output", {
  expect_equal(as.numeric(g$est_2sls[1,1]), -0.9835)
})
```

--------------------------------

### First-Stage F-Statistics

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Reports various first-stage partial F-statistics to assess instrument strength, including standard, robust, cluster-robust, bootstrapped, and effective F statistics.

```R
g$F_stat
#>  F.standard    F.robust   F.cluster F.bootstrap F.effective 
#>    3106.387    3108.591    8598.326    8408.152    8598.326
```

--------------------------------

### plot_ltz()

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Visualizes Local-to-Zero Adjustment.

```APIDOC
## plot_ltz()

### Description
Visualizing Local-to-Zero Adjustment.

### Method
Not applicable (R function)

### Endpoint
Not applicable (R function)

### Parameters
Not specified in source.

### Request Example
Not applicable (R function)

### Response
Not specified in source.
```

--------------------------------

### Tabulate Instrument and Treatment Variables in R

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

These R commands tabulate the counts for the instrument ('bishopcity') and the treatment ('libero_comune_allord') variables, providing a basic understanding of their distribution.

```r
# table instrument and treatment
table(gsz$bishopcity)
#> 
#>    0    1 
#> 5178  179
table(gsz$libero_comune_allord)
#> 
#>    0    1 
#> 5293   64
```

--------------------------------

### 2SLS Estimation and Inferential Results

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Presents Two-Stage Least Squares (2SLS) estimation results using the `felm` package, including analytic and bootstrapped standard errors and confidence intervals.

```R
g$est_2sls
#>             Coef     SE       t CI 2.5% CI 97.5% p.value
#> Analytic -0.9835 0.1424 -6.9071 -1.2626  -0.7044       0
#> Boot.c   -0.9835 0.1410 -6.9758 -1.2647  -0.7244       0
#> Boot.t   -0.9835 0.1424 -6.9071 -1.2248  -0.7423       0
```

--------------------------------

### Check Local-to-Zero Adjustment Accuracy

Source: https://yiqingxu.org/packages/ivDiag/reference/ltz.html

This test verifies the accuracy of the Local-to-Zero adjustment by comparing the calculated coefficient to an expected value. It requires the `testthat` package and the output from the `ltz` function.

```R
library(testthat)
test_that("Check local-to-zero adjustment", {
  expect_equal(as.numeric(ltz_out$ltz[1]), 3.6088)
})
```

--------------------------------

### Run IV Estimation and Diagnostics with ivDiag

Source: https://yiqingxu.org/packages/ivDiag/reference/ivDiag.html

Use this function to perform IV estimation and diagnostics. It requires a dataframe and variable names for the outcome, treatment, and instruments. Options for controls, fixed effects, clustering, and bootstrapping are available.

```R
data(ivDiag)
g <- ivDiag(data = rueda, Y = "e_vote_buying", D = "lm_pob_mesa", 
    Z = "lz_pob_mesa_f", controls = c("lpopulation", "lpotencial"), 
    cl = "muni_code", bootstrap = FALSE, run.AR = FALSE)
plot_coef(g)
```

--------------------------------

### Visualize LTZ Adjustment with Separate Inputs

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Provides an alternative way to visualize LTZ adjustment results using `plot_ltz` by passing IV estimates, LTZ estimates, and prior information as separate two-element vectors.

```r
plot_ltz(iv_est = ltz_out$iv[1:2], ltz_est = ltz_out$ltz[1:2], 
         prior = ltz_out$prior)
```

--------------------------------

### Disable Bootstrapping in ivDiag

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Demonstrates how to disable the bootstrap option in the `ivDiag` function by setting `bootstrap = FALSE` for estimations that do not require bootstrapped standard errors.

```R
ivDiag(data = rueda, Y=Y, D = D, Z = Z, controls = controls, 
            cl = cl, bootstrap = FALSE)
```

--------------------------------

### gsz

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Dataset from GSZ (2016).

```APIDOC
## gsz

### Description
Data from GSZ (2016).

### Method
Not applicable (Dataset)

### Endpoint
Not applicable (Dataset)

### Parameters
Not specified in source.

### Request Example
Not applicable (Dataset)

### Response
Not specified in source.
```

--------------------------------

### AR_test()

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Performs the Anderson Rubin Test.

```APIDOC
## AR_test()

### Description
Anderson Rubin Test.

### Method
Not applicable (R function)

### Endpoint
Not applicable (R function)

### Parameters
Not specified in source.

### Request Example
Not applicable (R function)

### Response
Not specified in source.
```

--------------------------------

### Check Anderson Rubin Test Results

Source: https://yiqingxu.org/packages/ivDiag/reference/AR_test.html

Verify the results of the Anderson Rubin test using expect_equal from the testthat package. This is useful for automated testing and ensuring reproducibility.

```R
library(testthat)    
test_that("Check AR results", {
  expect_equal(as.numeric(AR.out$Fstat[1]), 50.5097)
})
```

--------------------------------

### Run Omnibus Function in ivDiag

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Initiates the `ivDiag` function for OLS and 2SLS estimation with multiple inferential methods. It outputs various diagnostic statistics and results.

```R
library(ivDiag)
g <- ivDiag(data = rueda, Y=Y, D = D, Z = Z, controls = controls, cl = cl)
names(g)
#>  [1] "est_ols"  "est_2sls" "AR"       "F_stat"   "rho"      "tF"      
#>  [7] "est_rf"   "est_fs"   "p_iv"     "N"        "N_cl"     "df"      
#> [13] "nvalues"
```

--------------------------------

### OLS Estimation and Inferential Results

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Displays Ordinary Least Squares (OLS) estimation results, including analytic standard errors and bootstrap-based confidence intervals (coefficient and t-ratio methods).

```R
g$est_ols
#>            Coef     SE       t CI 2.5% CI 97.5% p.value
#> Analytic -0.675 0.1011 -6.6803 -0.8731  -0.4770       0
#> Boot.c   -0.675 0.1030 -6.5548 -0.8923  -0.4891       0
#> Boot.t   -0.675 0.1011 -6.6803 -0.8400  -0.5101       0
```

--------------------------------

### rueda

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Dataset from Rueda (2017).

```APIDOC
## rueda

### Description
Data from Rueda (2017).

### Method
Not applicable (Dataset)

### Endpoint
Not applicable (Dataset)

### Parameters
Not specified in source.

### Request Example
Not applicable (Dataset)

### Response
Not specified in source.
```

--------------------------------

### Reduced Form Regression Results

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Displays results from the reduced form regression, similar to the first-stage regression output, including coefficients, standard errors, and confidence intervals.

```R
g$est_rf
#>                  Coef     SE p.value   SE.b CI.b2.5% CI.b97.5% p.value.b
#> lz_pob_mesa_f -0.7826 0.1124       0 0.1118  -1.0127   -0.5731         0
```

--------------------------------

### Plot OLS and IV Coefficients Function Usage

Source: https://yiqingxu.org/packages/ivDiag/reference/plot_coef.html

This is the usage signature for the `plot_coef` function. It outlines the parameters available for customizing the visualization of OLS and IV coefficient estimates.

```R
plot_coef(out, 
  ols.methods = c("analy","bootc","boott"),
  iv.methods = c("analy","bootc","boott","ar","tf"),
  main = NULL, ylab = "Coefficient", grid = TRUE,
  stats = TRUE, ylim = NULL)
```

--------------------------------

### tF Function

Source: https://yiqingxu.org/packages/ivDiag/reference/tF.html

Performs the valid t-ratio procedure. It takes the estimated coefficient, its standard error, and the first-stage F statistic as input to provide valid inference.

```APIDOC
## tF

Performs the valid t-ratio procedure.

### Usage
```R
tF(coef, se, Fstat, prec = 4)
```

### Arguments

*   **coef** (numeric): a 2SLS coefficient.
*   **se** (numeric): a standard error estimate for the estimated 2SLS coefficient.
*   **Fstat** (numeric): a first-stage partial F statistic.
*   **prec** (numeric): precision of results (4 by default).

### Value

Results from a valid t-ratio test given the first-stage F statistic.

### References

Lee, David S, Justin McCrary, Marcelo J Moreira, and Jack Porter. 2022. "Valid t-Ratio Inference for IV." American Economic Review 112 (10): 3260–90.

### Examples

```R
tf.out <- tF(coef = -0.9835, se = 0.1540, Fstat = 8598)
library(testthat)
test_that("Check tF cF", {
  expect_equal(as.numeric(tf.out[2]), 1.96)
})
```
```

--------------------------------

### gsz_south

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Dataset from GSZ (2016): Subsample.

```APIDOC
## gsz_south

### Description
Data from GSZ (2016): Subsample.

### Method
Not applicable (Dataset)

### Endpoint
Not applicable (Dataset)

### Parameters
Not specified in source.

### Request Example
Not applicable (Dataset)

### Response
Not specified in source.
```

--------------------------------

### IV Regression Summary Statistics

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Provides key summary statistics for the IV regression, including the number of instruments (`p_iv`), total observations (`N`), number of clusters (`N_cl`), degrees of freedom (`df`), and unique values for outcome, treatment, and instruments (`nvalues`).

```R
g$p_iv
#> [1] 1
```

```R
g$N
#> [1] 4352
```

```R
g$N_cl
#> [1] 1098
```

```R
g$df
#> [1] 4348
```

```R
g$nvalues
#>      e_vote_buying lm_pob_mesa lz_pob_mesa_f
#> [1,]            16        4118          3860
```

--------------------------------

### ivDiag()

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Omnibus Function for IV Estimation and Diagnostics.

```APIDOC
## ivDiag()

### Description
Omnibus Function for IV Estimation and Diagnostics.

### Method
Not applicable (R function)

### Endpoint
Not applicable (R function)

### Parameters
Not specified in source.

### Request Example
Not applicable (R function)

### Response
Not specified in source.
```

--------------------------------

### Visualize LTZ Adjustment Results

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Visualizes the sampling distribution of 2SLS estimates before and after LTZ adjustment, along with the prior distribution. The function `plot_ltz` takes the output from the `ltz` function.

```r
plot_ltz(ltz_out, xlim = c(-0.5, 7))
```

--------------------------------

### plot_coef()

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Plots OLS and IV Coefficients.

```APIDOC
## plot_coef()

### Description
Plot OLS and IV Coefficents.

### Method
Not applicable (R function)

### Endpoint
Not applicable (R function)

### Parameters
Not specified in source.

### Request Example
Not applicable (R function)

### Response
Not specified in source.
```

--------------------------------

### Cross-Tabulate Instrument and Treatment in R

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

This R code generates a cross-tabulation of the instrument ('bishopcity') and the treatment ('libero_comune_allord') variables, showing their joint distribution.

```r
table(gsz$bishopcity, gsz$libero_comune_allord)
#>    
#>        0    1
#>   0 5173    5
#>   1  120   59
```

--------------------------------

### AR Test Results

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Shows results from the Anderson-Rubin (AR) test, including the F-statistic, p-value, and confidence interval based on Chernozhukov and Hansen (2008). Indicates if the confidence interval is bounded.

```R
g$AR
#> $Fstat
#>         F       df1       df2         p 
#>   48.4768    1.0000 4350.0000    0.0000 
#>
#> $ci.print
#> [1] "[-1.2626, -0.7073]"
#>
#> $ci
#> [1] -1.2626 -0.7073
#>
#> $bounded
#> [1] TRUE
```

--------------------------------

### First-Stage Correlation Coefficient (rho)

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Shows the Pearson correlation coefficient between the treatment variable and the predicted treatment from the first-stage regression, after partialling out covariates.

```R
g$rho
#> [1] 0.6455
```

--------------------------------

### Plot Coefficients and CIs

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Generates a coefficient plot for OLS and 2SLS estimates with various inferential methods. The plot displays the effective F-statistic, number of observations, and clusters. Base R plotting functions can be used for further customization.

```r
plot_coef(g)
```

```r
plot_coef(g, ols.methods = c("analy"), iv.methods = c("analy", "ar", "tf"),
  main = "Comparison between OLS and IV Estimates", ylab = "Estimates", 
  grid = FALSE, stats = FALSE, ylim = c(-2, 0.5))
```

--------------------------------

### plot_coef Function

Source: https://yiqingxu.org/packages/ivDiag/reference/plot_coef.html

Visualizes point estimates and confidence intervals of OLS and IV estimates. It takes the output from `ivDiag::ivDiag` and allows customization of displayed methods, plot titles, labels, grid, statistics, and y-axis limits.

```APIDOC
## plot_coef

### Description
Visualise point estimates and confidence intervals of OLS and IV estimates.

### Usage
```R
plot_coef(out, 
  ols.methods = c("analy","bootc","boott"),
  iv.methods = c("analy","bootc","boott","ar","tf"),
  main = NULL, ylab = "Coefficient", grid = TRUE,
  stats = TRUE, ylim = NULL)
```

### Arguments

* `out` (output from `ivDiag::ivDiag`): The primary input object containing the results from the `ivDiag` function.
* `ols.methods` (vector of strings, optional): Specifies which inferential methods for OLS to display. Defaults to `c("analy","bootc","boott")`.
* `iv.methods` (vector of strings, optional): Specifies which inferential methods for 2SLS to display. Defaults to `c("analy","bootc","boott","ar","tf")`.
* `main` (string, optional): The title of the plot.
* `ylab` (string, optional): The label for the y-axis. Defaults to "Coefficient".
* `grid` (logical, optional): A flag to indicate whether to display grid lines. Defaults to `TRUE`.
* `stats` (logical, optional): A flag to indicate whether to display statistics such as effective F, number of observations, and number of clusters. Defaults to `TRUE`.
* `ylim` (two-element vector, optional): Specifies the range for the y-axis.

### Value
A base R plot object.
```

--------------------------------

### plot_ltz Function

Source: https://yiqingxu.org/packages/ivDiag/reference/plot_ltz.html

Visualise approximate sampling distributions for scalar IV coefficient with local-to-zero adjustment.

```APIDOC
## plot_ltz(out = NULL, iv_est = NULL, ltz_est = NULL, prior = NULL, xlim = NULL)

### Description
Visualise approximate sampling distributions for scalar IV coefficient with local-to-zero adjustment.

### Arguments
- **out** (output from `ivDiag::ltz`) - NULL
- **iv_est** (a two-element vector of IV estimate and standard error) - NULL
- **ltz_est** (a two-element vector of local-to-zero estimate and standard error) - NULL
- **prior** (a two-element vector of prior mean and standard deviation) - NULL
- **xlim** (a two-element vector specifying the range of the x-axis) - NULL

### Value
A ggplot2 object.
```

--------------------------------

### eff_F()

Source: https://yiqingxu.org/packages/ivDiag/reference/index.html

Calculates the Effective F statistic.

```APIDOC
## eff_F()

### Description
Effective F statistic calculation.

### Method
Not applicable (R function)

### Endpoint
Not applicable (R function)

### Parameters
Not specified in source.

### Request Example
Not applicable (R function)

### Response
Not specified in source.
```

--------------------------------

### ltz Function

Source: https://yiqingxu.org/packages/ivDiag/reference/ltz.html

Estimates Local-to-Zero IV coefficients and SEs for a single instrument.

```APIDOC
## ltz

### Description
Estimates Local-to-Zero IV coefficients and SEs for a single instrument.

### Usage
```R
ltz(data, Y, D, Z, controls, FE = NULL, cl = NULL, weights = NULL, prior, prec = 4)
```

### Arguments

* `data` (dataframe): The name of the dataframe containing the data.
* `Y` (string): The outcome variable.
* `D` (string): The treatment variable.
* `Z` (vector of strings): The instrumental variables.
* `controls` (vector of strings): The control variables.
* `FE` (vector of strings, optional): The fixed effects variables.
* `cl` (string, optional): The clustering variable.
* `weights` (string, optional): The variable that stores weights.
* `prior` (numeric vector): Prior mean and standard deviation of the direct effect of instrument on outcome.
* `prec` (numeric): Precision of results (defaults to 4).

### Value

* `iv` (list): Results from a 2SLS regression.
* `ltz` (list): Results after local-to-zero adjustment.
* `prior` (list): Prior mean and standard deviation.

### Examples

```R
data(ivDiag)
controls <- c('altitudine', 'escursione', 'costal', 'nearsea', 'population', 
    'pop2', 'gini_land', 'gini_income')
ltz_out <- ltz(data = gsz, Y = "totassoc_p", D = "libero_comune_allnord", 
    Z = "bishopcity", controls = controls, weights = "population", 
    prior = c(0.178, 0.137))
plot_ltz(ltz_out)

library(testthat)
test_that("Check local-to-zero adjustment", {
  expect_equal(as.numeric(ltz_out$ltz[1]), 3.6088)
})
```
```

--------------------------------

### Define IV Variables and Controls in R

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

This R code defines the outcome, treatment, instrument, and control variables for an IV analysis, consistent with the original paper's methodology.

```r
Y <- "totassoc_p"
D <- "libero_comune_allord"
Z <- "bishopcity"
weights <- "population"
controls <- c('altitudine', 'escursione', 'costal', 'nearsea', 
              'population', 'pop2', 'gini_land', 'gini_income')
```

--------------------------------

### Perform Valid t-Ratio Procedure

Source: https://yiqingxu.org/packages/ivDiag/reference/tF.html

Use this function to calculate valid t-ratios when performing instrumental variable analysis. Ensure you have the 2SLS coefficient, its standard error, and the first-stage F statistic.

```r
tf.out <- tF(coef = -0.9835, se = 0.1540, Fstat = 8598)
```

--------------------------------

### tF Procedure Results

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Provides results from the tF procedure (Lee et al., 2022), including the critical value for the t-test adjusted by the effective F-statistic, and confidence intervals.

```R
g$tF
#>         F        cF      Coef        SE         t    CI2.5%   CI97.5%   p-value 
#> 8598.3264    1.9600   -0.9835    0.1424   -6.9071   -1.2626   -0.7044    0.0000
```

--------------------------------

### Estimate Local-to-Zero IV Coefficients

Source: https://yiqingxu.org/packages/ivDiag/reference/ltz.html

Use the `ltz` function to estimate Local-to-Zero Instrumental Variable coefficients and standard errors for a single instrument. Ensure the 'ivDiag' package is loaded and data is prepared.

```R
data(ivDiag)
controls <- c('altitudine', 'escursione', 'costal', 'nearsea', 'population', 
    'pop2', 'gini_land', 'gini_income')
ltz_out <- ltz(data = gsz, Y = "totassoc_p", D = "libero_comune_allnord", 
    Z = "bishopcity", controls = controls, weights = "population", 
    prior = c(0.178, 0.137))
plot_ltz(ltz_out)
```

--------------------------------

### Apply ivDiag and Plot Coefficients

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Applies the `ivDiag` function to estimate OLS and 2SLS coefficients and plots the results. Ensure the necessary data and variables are correctly specified.

```r
g <- ivDiag(data = gsz, Y = Y, D = D, Z = Z, 
            controls = controls, 
            weights = weights)
g
```

```r
plot_coef(g)
```

--------------------------------

### Perform tF Procedure

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Applies the tF procedure for testing instrumental variables. This function requires the 2SLS coefficient, its standard error, and the first-stage F-statistic. It outputs various test statistics and p-values.

```r
tF(coef = -0.9835, se = 0.1540, Fstat = 8598)
```

--------------------------------

### Conduct AR Test

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Performs the AR test, which is important for checking for endogeneity in instrumental variable models. The function returns the F-statistic, confidence intervals, and boundedness information.

```r
AR_test(data = rueda, Y = Y, D = D, Z = Z, controls = controls, cl = cl, 
        FE = NULL, weights = NULL)
```

--------------------------------

### Perform Anderson Rubin Test

Source: https://yiqingxu.org/packages/ivDiag/reference/AR_test.html

Use AR_test to perform the Anderson Rubin test. Specify the data, outcome variable, treatment variable, instrumental variables, and control variables. Confidence interval calculation can be disabled.

```R
data(ivDiag)
AR.out <- AR_test(data = rueda, Y = "e_vote_buying", D = "lm_pob_mesa", 
    Z = "lz_pob_mesa_f", controls = c("lpopulation", "lpotencial"),
    cl = "muni_code", CI = FALSE)
```

--------------------------------

### Perform LTZ Adjustment

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Applies the LTZ adjustment to IV estimates using a specified prior mean and standard deviation derived from a ZFS test. This function refines the 2SLS estimates by incorporating prior information.

```r
ltz_out <- ltz(data = gsz, Y = Y, D = D, Z = Z, 
    controls = controls, weights = weights, 
    prior = c(0.178, 0.137))
ltz_out
```

--------------------------------

### Compute Effective F Statistic

Source: https://yiqingxu.org/packages/ivDiag/reference/eff_F.html

Use this function to compute the effective F statistic. Ensure the data, outcome, treatment, and instrumental variables are correctly specified. Optional arguments include controls, fixed effects, clustering, and weights.

```R
effF <- eff_F(data = rueda, Y = "e_vote_buying", D = "lm_pob_mesa", 
    Z = "lz_pob_mesa_f", controls = c("lpopulation", "lpotencial"), 
    cl = "muni_code")
```

```R
library(testthat)
test_that("Check effective F", {
  expect_equal(floor(as.numeric(effF)), 8598)
})
```

--------------------------------

### AR_test Function

Source: https://yiqingxu.org/packages/ivDiag/reference/AR_test.html

The AR_test function performs the Anderson Rubin test for instrumental variables, offering robustness to weak instruments. It takes a dataframe and specifies variables for the outcome, treatment, instruments, controls, and optional fixed effects, clustering, and weights.

```APIDOC
## AR_test Function

### Description
Performs the Anderson Rubin test, which is robust to weak instruments.

### Usage
```R
AR_test(data, Y, D, Z, controls, FE = NULL, cl = NULL, weights = NULL, 
  prec = 4, CI = TRUE, alpha = 0.05, parallel = NULL, cores = NULL)
```

### Arguments

*   **data** (dataframe): The name of the dataframe containing the data.
*   **Y** (string): The name of the outcome variable.
*   **D** (string): The name of the treatment variable.
*   **Z** (vector of strings): The names of the instrumental variables.
*   **controls** (vector of strings): The names of the control variables.
*   **FE** (vector of strings, optional): The names of the fixed effects variables.
*   **cl** (string, optional): The name of the clustering variable.
*   **weights** (string, optional): The name of the variable that stores weights.
*   **prec** (numeric): Precision of results (default is 4).
*   **CI** (logical): A flag controlling whether to calculate the confidence interval using the inversion method (default is TRUE).
*   **alpha** (numeric): The level of statistical significance (default is 0.05).
*   **parallel** (logical, optional): A flag controlling parallel computing.
*   **cores** (numeric, optional): Setting the number of cores for parallel computing.

### Value

*   **Fstat** (numeric): The F statistic, degrees of freedom, and p-value.
*   **ci.print** (numeric): The confidence interval calculated via inversion (printed version).
*   **ci** (numeric): The confidence interval calculated via inversion (numeric version).
*   **bounded** (logical): Indicates if the confidence interval is bounded.

### Examples

```R
data(ivDiag)
AR.out <- AR_test(data = rueda, Y = "e_vote_buying", D = "lm_pob_mesa", 
    Z = "lz_pob_mesa_f", controls = c("lpopulation", "lpotencial"),
    cl = "muni_code", CI = FALSE)
library(testthat)

test_that("Check AR results", {
  expect_equal(as.numeric(AR.out$Fstat[1]), 50.5097)
})
```
```

--------------------------------

### ivDiag Function

Source: https://yiqingxu.org/packages/ivDiag/reference/ivDiag.html

Conducts various estimation and diagnostic procedures for instrumental variable designs.

```APIDOC
## ivDiag Function

### Description
Conducts various estimation and diagnostic procedures for instrumental variable designs in one shot.

### Usage
```R
ivDiag(data, Y, D, Z, controls = NULL, FE = NULL, cl = NULL, weights = NULL,
  bootstrap = TRUE, run.AR = TRUE,
  nboots = 1000, parallel = TRUE, cores = NULL, 
  seed = 94305, prec = 4, debug = FALSE)
```

### Arguments

* **data** (dataframe): Name of a dataframe.
* **Y** (string): A string indicating the outcome variable.
* **D** (string): A string indicating the treatment variable.
* **Z** (vector of strings): A vector of strings indicating the instrumental variables.
* **controls** (vector of strings, optional): A vector of strings indicating the control variables.
* **FE** (vector of strings, optional): A vector of strings indicating the fixed effects variables.
* **cl** (string, optional): A string indicating the clustering variable.
* **weights** (string, optional): A string indicating the variable that stores weights.
* **bootstrap** (boolean): Whether to turn on bootstrap (TRUE by default).
* **run.AR** (boolean): Whether to run AR test (TRUE by default).
* **nboots** (numeric): A numeric value indicating the number of bootstrap runs.
* **parallel** (logical): A logical flag controlling parallel computing.
* **cores** (numeric, optional): Setting the number of cores.
* **seed** (numeric): Setting seed.
* **prec** (numeric): Precision of CI in string (4 by default).
* **debug** (boolean): For debugging purposes.

### Value

* **est_ols** (results): Results from an OLS regression.
* **est_2sls** (results): Results from a 2SLS regression.
* **AR** (results): Results from an Anderson-Rubin test.
* **F_stat** (results): Various F statistics.
* **rho** (numeric): Pearson correlation coefficient between the treatment and predicted treatment from the first stage regression (all covariates are partialled out).
* **tF** (results): Results from the tF procedure based on Lee et al. (2022).
* **est_rf** (results): Results from the first stage regression.
* **est_fs** (results): Results from the reduced form regression.
* **p_iv** (numeric): The number of instruments.
* **N** (numeric): The number of observations.
* **N_cl** (numeric): The number of clusters.
* **df** (numeric): The degree of freedom left from the 2SLS regression.
* **nvalues** (list): The unique values the outcome Y, the treatment D, and each instrument in Z in the 2SLS regression.

### Examples

```R
data(ivDiag)
g <- ivDiag(data = rueda, Y = "e_vote_buying", D = "lm_pob_mesa", 
    Z = "lz_pob_mesa_f", controls = c("lpopulation", "lpotencial"), 
    cl = "muni_code", bootstrap = FALSE, run.AR = FALSE)
plot_coef(g)

library(testthat)    
test_that("Check ivDiag output", {
  expect_equal(as.numeric(g$est_2sls[1,1]), -0.9835)
})
```
```

--------------------------------

### Conduct Effective F-statistic Test

Source: https://yiqingxu.org/packages/ivDiag/articles/iv_tutorial.html

Calculates the effective F-statistic for instrumental variable regression. This test is crucial for assessing the strength of instruments. Ensure the correct data and variable names are provided.

```r
eff_F(data = rueda, Y = Y, D = D, Z = Z, controls = controls, cl = cl, 
      FE = NULL, weights = NULL)
```

--------------------------------

### eff_F Function

Source: https://yiqingxu.org/packages/ivDiag/reference/eff_F.html

Computes the effective F statistic. This function is used to diagnose potential issues with weak instruments in instrumental variable regression.

```APIDOC
## eff_F Function

### Description
Computes the effective F statistic.

### Usage
```R
eff_F(data, Y, D, Z, controls = NULL, FE = NULL, cl = NULL, 
  weights = NULL, prec = 4)
```

### Arguments

* `data` (dataframe): The name of the dataframe containing the data.
* `Y` (string): The name of the outcome variable.
* `D` (string): The name of the treatment variable.
* `Z` (vector of strings): The names of the instrumental variables.
* `controls` (vector of strings, optional): The names of the control variables.
* `FE` (vector of strings, optional): The names of the fixed effects variables.
* `cl` (string, optional): The name of the clustering variable.
* `weights` (string, optional): The name of the variable that stores weights.
* `prec` (numeric): The precision of the results (defaults to 4).

### Value
Returns the effective F statistic.

### See Also
`ivDiag`

### References
Olea, José Luis Montiel, and Carolin Pflueger. 2013. "A Robust Test for Weak Instruments." Journal of Business & Economic Statistics 31 (3): 358–69.

### Examples
```R
# Example usage of eff_F
effF <- eff_F(data = rueda, Y = "e_vote_buying", D = "lm_pob_mesa", 
    Z = "lz_pob_mesa_f", controls = c("lpopulation", "lpotencial"), 
    cl = "muni_code")

# Test the result
library(testthat)
test_that("Check effective F", {
  expect_equal(floor(as.numeric(effF)), 8598)
})
```
```
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