boolean {boolean}R Documentation

Partial-Observability Logit or Probit Models for Testing Boolean Hypotheses

Description

Boolean logit and probit are a family of partial-observability n-variate models designed to permit researchers to model causal complexity, or multiple causal "paths" to a given outcome (e.g., a situation in which either a or b will produce y, one in which (a or b) and c produce y, and so forth).

Usage

boolean(structure, method, maxoptions = "", optimizer="nlm",
        safety=1, bootstrap=FALSE, bootsize=100)

Arguments

structure Structure of equation to be estimated, in standard y ~ f(x) form, using & to represent the Boolean operator "and" and | to represent the Boolean operator "or." (Note that the syntax requires that constants be entered explicitly; see the entry for boolprep for details.) Be sure to enter the correct functional form and balance parentheses; if in doubt, or just for convenience, use the boolprep command to prepare structure prior to estimation.
method Either "logit" or "probit".
maxoptions Maximization options (see nlm or optim for details).
optimizer Either "nlm" or "optim".
safety Number of search attempts. The likelihood functions implied by Boolean procedures can become quite convoluted; in such cases, multiple searches from different starting points can be run. Works only when using nlm.
bootstrap If TRUE, bootstraps standard errors.
bootsize Number of iterations if bootstrap=TRUE.

Details

Boolean permits estimation of Boolean logit and probit equations (see Braumoeller 2003 for derivation). Boolean logit and probit model situations in which any number of antecedent conditions (a, b, c, ...) occur with probabilities that can be modeled using standard logit or probit curves, and the antecedent conditions combine in a manner described by Boolean logic to produce the dependent variable. For example, theory might suggest that a binary dependent variable y occurs only when conditions a and b are present, that the probability of a's occurrence is influenced by variables x1...x4, and that the probability of b's occurrence is influenced by variables x5...x8. Alternately, theory might suggest that y occurs if (a and b) or (c and d) are present (in other words, that a-d are INUS conditions; see Mackie 1965), and that the probability of the occurrence of each antecedent condition is influenced by some vector of independent variables. Boolean logit and probit are designed for use in such situations.

Value

Returns an object of class booltest, with slots @Calculus, @LogLik, @Variables, @Coefficients, @StandardErrors, @Iterations, @Hessian, @Gradient, @Zscore, @Probz, @Conf95lo, @Conf95hi, @pstructure, and @method (note that some slots may be left empty if the relevant information is not furnished by the maximizer).

Note

Examining profile likelihoods with boolprof is highly recommended. Boolean logit and probit are partial observability models, which are generically starved for information; as a result, maximum likelihood estimation can encounter problems with plateaus in likelihood functions even with very large n.

Author(s)

Bear F. Braumoeller, Harvard University, bfbraum@fas.harvard.edu
Jacob Kline, Harvard University, jkline@fas.harvard.edu

References

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

Mackie, J. L. (1965) "Causes and Conditions." American Philosophical Quarterly 2(4): 245-264.

See Also

boolprep to prepare structure of equation, boolfirst to graph first differences after estimation, and boolprof to produce profile likelihoods after estimation.

Examples

library("boolean")
set.seed(50)
x1<-rnorm(1000)
x2<-rnorm(1000)
x3<-rnorm(1000)
x4<-rnorm(1000)
x5<-rnorm(1000)
x6<-rnorm(1000)
e1<-rnorm(1000)/3
e2<-rnorm(1000)/3
e3<-rnorm(1000)/3
y<-1-(1-pnorm(-2+0.33*x1+0.66*x2+1*x3+e1)*1-(pnorm(1+1.5*x4-0.25*x5+e2)*pnorm(1+0.2*x6+e3)))
y <- y>runif(1000)
answer <- boolean(y ~( ((cons+x1+x2+x3)|((cons+x4+x5)&(cons+x6))) ), method="probit")

## Examine coefficients, standard errors, etc.
summary(answer)

## Examine "summary" output plus Hessian, gradient, etc.
show(answer)

## Plot first differences for model
plot(answer)

## Plot profiles
plot(answer, panel="boolprof")

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