boolprep: Specify Boolean Model
In boolean3: Boolean Binary Response Models

Description Usage Arguments Details Value Author(s) References See Also Examples

Construct a boolean object that can then be fit with boolean.

1 2	boolprep(..., data, subset, weights, na.action, offset, family = list(binomial(link = "logit")))

`...`	formula specification for boolean model. See the details and examples sections below.
`data`	`data.frame` containing the data to be used in the model.
`subset`	select subset of data. See `lm` for details.
`weights`	specify model weights (not implemented).
`na.action`	set `na.action`. See `lm` for details.
`offset`	specify an offset. Offsets are not implemented and this parameter is simply ignored.
`family`	a model `family` to use for estimation. This can be comprised of a list of link functions when the desire is to have model components with different links. `binomial` is the only family supported at this time. See `family` for more details.

boolprep sets up a boolean model object that can then be fit with boolean. A properly specified model (contained in ...) will contain at least three components. The first component must specify the boolean logic to be employed. For instance, the y ~ (a | b) formula would indicate a logical or between the a and b submodels, while y ~ (a & b) would indicate a logical and. y is the name of the response variable of interest. Logical operators can be nested; e.g., y ~ (a | (b & c)) is valid. The second and third components are submodels and are specified as usual: a ~ x1 + x2 and b ~ x3 + x4 + x5, where are the x-variables are covariates. a, b, and c are labels indicating the submodel position in the boolean specification.

boolprep returns a boolean-class object containing the model components needed to estimate a boolean model.

Jason W. Morgan (morgan.746@osu.edu)

Braumoeller, Bear F. (2003) “Causal Complexity and the Study of Politics.” Political Analysis 11(3): 209–233.

See boolean for model estimation.

## Generate some fake data
require(mvtnorm)
set.seed(12345)
N  <- 2000
Df <- cbind(1, rmvnorm(N, mean=rep(0, 5)))

## Set coefficients
beta.a <- c(-2.00, 0.33, 0.66, 1.00)
beta.b <- c(0.00, 1.50, -0.25)

## Generate path probabilities following a normal model.
y.a <- as.vector(pnorm(tcrossprod(beta.a, Df[, 1:4])))
y.b <- as.vector(pnorm(tcrossprod(beta.b, Df[, c(1, 5, 6)])))

## AND and OR-model
or <- function(x, y) { x + y - x * y }
and <- function(x, y) { x * y }
y.star.OR  <- or(y.a, y.b)
y.star.AND <- and(y.a, y.b)

## Observed responses
y.OR <- rbinom(N, 1, y.star.OR)
y.AND <- rbinom(N, 1, y.star.AND)

## Set up data.frame for estimation
Df <- cbind(1, Df)
Df <- as.data.frame(Df)
Df[,1] <- y.OR
Df[,2] <- y.AND
names(Df) <- c("y.OR", "y.AND", "x1", "x2", "x3", "x4", "x5")

## Before estimating, boolean models need to be specified using the
## boolprep function.

## OR model, specified to use a probit link for each causal path. This
## matches the data generating process above.
mod.OR <- boolprep(y.OR ~ (a | b), a ~ x1 + x2 + x3, b ~ x4 + x5,
                   data = Df, family=list(binomial("probit")))