binary_iv_designer {DesignLibrary} | R Documentation |

Builds a design with one instrument, one binary explanatory variable, and one outcome.

```
binary_iv_designer(
N = 100,
type_probs = c(1/3, 1/3, 1/3, 0),
assignment_probs = c(0.5, 0.5, 0.5, 0.5),
a_Y = 1,
b_Y = 0,
d_Y = 0,
outcome_sd = 1,
a = c(1, 0, 0, 0) * a_Y,
b = rep(b_Y, 4),
d = rep(d_Y, 4),
args_to_fix = NULL
)
```

`N` |
An integer. Sample size. |

`type_probs` |
A vector of four numbers in [0,1]. Probability of each complier type (always-taker, never-taker, complier, defier). |

`assignment_probs` |
A vector of four numbers in [0,1]. Probability of assignment to encouragement (Z) for each complier type (always-taker, never-taker, complier, defier). Under random assignment these are normally identical since complier status is not known to researchers in advance. |

`a_Y` |
A real number. Constant in Y equation. Assumed constant across types. Overridden by |

`b_Y` |
A real number. Effect of X on Y equation. Assumed constant across types. Overridden by |

`d_Y` |
A real number. Effect of Z on Y. Assumed constant across types. Overridden by |

`outcome_sd` |
A real number. The standard deviation of the outcome. |

`a` |
A vector of four numbers. Constant in Y equation for each complier type (always-taker, never-taker, complier, defier). |

`b` |
A vector of four numbers. Slope on X in Y equation for each complier type (always-taker, never-taker, complier, defier). |

`d` |
A vector of four numbers. Slope on Z in Y equation for each complier type (non zero implies violation of exclusion restriction). |

`args_to_fix` |
A character vector. Names of arguments to be args_to_fix in design. |

A researcher is interested in the effect of binary X on outcome Y. The relationship is confounded because units that are more likely to be assigned to X=1 have higher Y outcomes. A potential instrument Z is examined, which plausibly causes X. The instrument can be used to assess the effect of X on Y for units whose value of X depends on Z if Z does not negatively affect X for some cases, affects X positively for some, and affects Y only through X.

See vignette online for more details on estimands.

A simple instrumental variables design with binary instrument, treatment, and outcome variables.

```
# Generate a simple iv design: iv identifies late not ate
binary_iv_design_1 <- binary_iv_designer(N = 1000, b = c(.1, .2, .3, .4))
## Not run:
diagnose_design(binary_iv_design_1)
## End(Not run)
# Generates a simple iv design with violation of monotonicity
binary_iv_design_2 <- binary_iv_designer(type_probs = c(.1,.1,.6, .2), b_Y = .5)
## Not run:
diagnose_design(binary_iv_design_2)
## End(Not run)
# Generates a simple iv design with violation of exclusion restriction
binary_iv_design_3 <- binary_iv_designer(d_Y = .5, b_Y = .5)
## Not run:
diagnose_design(binary_iv_design_3)
## End(Not run)
# Generates a simple iv design with violation of randomization
binary_iv_design_4 <- binary_iv_designer(N = 1000, assignment_probs = c(.2, .3, .7, .5), b_Y = .5)
## Not run:
diagnose_design(binary_iv_design_4)
## End(Not run)
# Generates a simple iv design with violation of first stage
binary_iv_design_5 <- binary_iv_designer(type_probs = c(.5,.5, 0, 0), b_Y = .5)
## Not run:
diagnose_design(binary_iv_design_5)
## End(Not run)
```

[Package *DesignLibrary* version 0.1.10 Index]