
# hcinfer <img src="man/figures/logo.png" align="right" height="139" alt="hcinfer logo"/>

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`hcinfer` computes heteroskedasticity-consistent covariance estimators
and normal Wald inference for ordinary least squares models. The
currently implemented covariance matrix estimators are listed below.

## Implemented Estimators

The table below is generated by `hc_methods()` and lists the covariance
matrix estimators currently implemented in `hcinfer`.

| type | label | description | default_arguments |
|:---|:---|:---|:---|
| hc0 | HC0 | White heteroskedasticity-consistent estimator. | none |
| hc1 | HC1 | HC0 with degrees-of-freedom scaling. | none |
| hc2 | HC2 | Leverage-adjusted estimator with exponent 1. | none |
| hc3 | HC3 | Leverage-adjusted estimator with exponent 2. | none |
| hc4 | HC4 | Adaptive leverage correction by Cribari-Neto. | none |
| hc4m | HC4m | Modified HC4 correction by Cribari-Neto and da Silva. | none |
| hc5 | HC5 | High-leverage correction by Cribari-Neto, Souza, and Vasconcellos. | k = 0.7 |
| hc5m | HC5m | Modified HC5 correction by Li, Zhang, Zhang, and Wang. | k = 0.7, k1 = 1, k2 = 0, k3 = 1, gamma1 = 1, gamma2 = 1.5 |
| hcbeta | HCbeta | Beta-distribution leverage correction. | c1 = 7, c2 = 0.75, lower = 0.01, upper = 0.99 |

## Installation

``` r
# install.packages("hcinfer")

# Development version
remotes::install_github("prdm0/hcinfer")
```

## Basic Use

``` r
library(hcinfer)

schools <- PublicSchools
schools$income_scaled <- schools$income / 10000
schools$income_scaled_sq <- schools$income_scaled^2

fit <- lm(expenditure ~ income_scaled + income_scaled_sq, data = schools)

result <- hcinfer(fit)
```

The default estimator is HCbeta. Use `tests()` and `confint()` to
extract the main inferential quantities as tibbles.

``` r
tests(result)
#> # A tibble: 3 × 8
#>   term             estimate null_value std_error z_value p_value alpha reject
#>   <chr>               <dbl>      <dbl>     <dbl>   <dbl>   <dbl> <dbl> <lgl>
#> 1 (Intercept)          833.          0      851.   0.979   0.328  0.05 FALSE
#> 2 income_scaled      -1834.          0     2309.  -0.794   0.427  0.05 FALSE
#> 3 income_scaled_sq    1587.          0     1547.   1.03    0.305  0.05 FALSE
confint(result)
#> # A tibble: 3 × 4
#>   term             conf_low conf_high level
#>   <chr>               <dbl>     <dbl> <dbl>
#> 1 (Intercept)         -834.     2500.  0.95
#> 2 income_scaled      -6359.     2691.  0.95
#> 3 income_scaled_sq   -1446.     4620.  0.95
```

## Confidence Intervals

The `plot()` method displays the robust confidence intervals and marks
the null value used in the tests.

``` r
plot(result)
```

<img src="man/figures/README-unnamed-chunk-5-1.png" alt="Robust confidence intervals for the public-schools regression coefficients."  />

## Diagnostics

Use `vcov_hc()` when you only need the robust covariance matrix and its
diagnostics. The `plot()` method for this object shows leverage values
and HC adjustment factors.

``` r
cov_hcbeta <- vcov_hc(fit)
plot(cov_hcbeta)
```

<img src="man/figures/README-unnamed-chunk-6-1.png" alt="HCbeta adjustment factors plotted against leverage values for the public-schools regression."  />

## Main Functions

``` r
hc_methods()
coef(result)
vcov(result)
```

The most common workflow is:

``` r
fit <- lm(y ~ x1 + x2, data = data)
result <- hcinfer(fit, type = "hcbeta")

summary(result)
tests(result)
confint(result)
plot(result)
```

## Learn More

Start with `vignette("introduction", package = "hcinfer")` for a compact
overview of the package API.

## References

- White, H. (1980). A heteroskedasticity-consistent covariance matrix
  estimator and a direct test for heteroskedasticity. *Econometrica*,
  48(4), 817-838.
  [doi:10.2307/1912934](https://doi.org/10.2307/1912934).
- Hinkley, D. V. (1977). Jackknifing in unbalanced situations.
  *Technometrics*, 19(3), 285-292.
  [doi:10.1080/00401706.1977.10489550](https://doi.org/10.1080/00401706.1977.10489550).
- Horn, S. D., Horn, R. A., and Duncan, D. B. (1975). Estimating
  heteroscedastic variances in linear models. *Journal of the American
  Statistical Association*, 70(350), 380-385.
  [doi:10.1080/01621459.1975.10479877](https://doi.org/10.1080/01621459.1975.10479877).
- MacKinnon, J. G. and White, H. (1985). Some
  heteroskedasticity-consistent covariance matrix estimators with
  improved finite sample properties. *Journal of Econometrics*, 29(3),
  305-325.
  [doi:10.1016/0304-4076(85)90158-7](https://doi.org/10.1016/0304-4076(85)90158-7).
- Davidson, R. and MacKinnon, J. G. (1993). *Estimation and Inference in
  Econometrics*. Oxford University Press.
- Cribari-Neto, F. (2004). Asymptotic inference under heteroskedasticity
  of unknown form. *Computational Statistics and Data Analysis*, 45(2),
  215-233.
  [doi:10.1016/S0167-9473(02)00366-3](https://doi.org/10.1016/S0167-9473(02)00366-3).
- Cribari-Neto, F. and da Silva, W. B. (2011). A new
  heteroskedasticity-consistent covariance matrix estimator for the
  linear regression model. *AStA Advances in Statistical Analysis*,
  95(2), 129-146.
  [doi:10.1007/s10182-010-0141-2](https://doi.org/10.1007/s10182-010-0141-2).
- Cribari-Neto, F., Souza, T. C., and Vasconcellos, K. L. P. (2007).
  Inference under heteroskedasticity and leveraged data. *Communications
  in Statistics - Theory and Methods*, 36(10), 1877-1888.
  [doi:10.1080/03610920601126589](https://doi.org/10.1080/03610920601126589).
- Li, S., Zhang, N., Zhang, X., and Wang, G. (2016). A new
  heteroskedasticity-consistent covariance matrix estimator and
  inference under heteroskedasticity. *Journal of Statistical
  Computation and Simulation*, 87(1), 198-210.
  [doi:10.1080/00949655.2016.1198906](https://doi.org/10.1080/00949655.2016.1198906).
- Cunha, M. A., Cribari-Neto, F., and Marinho, P. R. D. (manuscript). A
  beta-based heteroskedasticity-consistent covariance matrix estimator.
