# coefbounds: Coefficient bounds for linear models In brentonk/coefbounds: Nonparametric Bounds for Regression with Interval-Censored Outcomes

## Description

Estimates the projections of the identification region along each coefficient dimension for a linear or logistic regression model with interval-censored outcomes (Beresteanu and Molinari 2008, Corollary 4.5). If requested, uses a nonparametric bootstrap to estimate critical values for hypothesis tests about these projections (Beresteanu and Molinari 2008, Algorithm 4.2).

## Usage

 ```1 2 3``` ```coefbounds(formula, data, subset, na.action, model = c("linear", "logit"), boot = 100, cluster_id = NULL, maxit = 10, remove_collinear = TRUE, return_boot_est = FALSE) ```

## Arguments

 `formula` Model formula of the form `yl + yu ~ x1 + x2 + ...`, where `yl` is the lower bound on the response, `yu` is the upper bound, and `x1 + x2 + ...` are the covariates. For instrumental variables estimation, use a formula like ```yl + yu ~ x1 + x2 + ... | z1 + z2 + ...```, as in `ivreg` in the AER package. IV estimates not available for logit models. `data, subset, na.action` As in `lm` `model` `"linear"` for linear regression (default), `"logit"` for logistic regression. `boot` Number of bootstrap iterations used to estimate the critical values for inference. `cluster_id` Vector of cluster IDs for cluster bootstrap. If `NULL` (the default), an ordinary bootstrap is used. `maxit` Maximum number of iterations for the approximation in logistic regression models. Ignored when `model = "linear"`. `remove_collinear` How to treat boostrap iterations in which the design matrix is rank-deficient. If `TRUE` (the default), a warning is issued and the bad iterations are removed. If `FALSE`, the function fails with an error when a rank-deficient design matrix is encountered. `return_boot_est` Whether to include the bootstrap estimates of the coefficient bounds in the returned object.

## Details

In the linear case, implements largely the same functionality as `oneDproj` and `CI1D` in Beresteanu et al.'s (2010) Stata program.

## Value

A list of class `"coefbounds"` containing:

`coefficients`

Matrix containing the sample estimates of the coefficient bounds.

`dist`

List of matrices containing the bootstrap Hausdorff distances (undirected and directed) used for inference.

`boot_est`

(if requested) List of matrices of bootstrap estimates of the coefficient bounds.

`nobs`

Number of observations used in fitting.

`call`

Original function call.

`model`

Model used.

Brenton Kenkel

## References

Arie Beresteanu and Francesca Molinari. 2008. "Asymptotic Properties for a Class of Partially Identified Models." Econometrica 76 (4): 763–814.

Arie Beresteanu, Francesca Molinari and Darcy Steeg Morris. 2010. "Asymptotics for Partially Identified Models in Stata." https://molinari.economics.cornell.edu/programs.html

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## Simulate data set.seed(18) x1 <- rnorm(50) x2 <- rnorm(50) y <- 1 - x1 + x2 + rnorm(50) yl <- floor(y) yu <- ceiling(y) ## Fit model without covariates fit_mean <- coefbounds(yl + yu ~ 1, boot = 0) all.equal(coef(fit_mean)[1, "lower"], mean(yl)) all.equal(coef(fit_mean)[1, "upper"], mean(yu)) ## Fit model with covariates fit_full <- coefbounds(yl + yu ~ x1 + x2, boot = 10) coef(fit_full) ```

brentonk/coefbounds documentation built on May 11, 2017, 4:47 p.m.