BandwidthGridSearch: Bandwidth grid search
In henrykye/semiBRM: Semiparametric Binary Response Models in R

Description Usage Arguments Details Value Examples

This performs grid search to find the best bandwidth for the fitted semiparametric binary response model.

BandwidthGridSearch(
  fit,
  criterion = "McF.R2",
  n.bandwidth = 50,
  bandwidth = NULL
)

`fit`	a fitted 'semiBRM' object.
`criterion`	a character indicating the criterion to be used for evaluation. It can be one in c("McF.R2", "accuracy", "precision") (see Details).
`n.bandwidth`	an integer of the number of bandwidths to be searched.
`bandwidth`	a vector of bandwidths to be evaluated.

Evaluation is based on in-sample semiparametric conditional probability Pr(Y=1|X), which is obtained from the leave-one-out version of the Gaussian Nadaraya-Watson estimator.

This function first randomly generates n.bandwidth candidates from a uniform distribution with range [h0/3, 3*h0], where h0 is the Silverman's rule of thumb bandwidth, h0 = sd(v)*1.06*N^(-1/5). Then, it computes 'performance' according to the given criterion over the candidates and picks up the 'best' one.

criterion = "McF.R2" employs the McFadden’s pseudo R-squared for assessment.

For criterion = "accuracy" or criterion = "precision", the function first predicts binary response using the semiparametric conditional probability, assigning 1 if the probability is greater than or equal to 0.5 and 0 otherwise. Then, it calculates the confusion matrix and predictive accuracy or precision. In turn, the maximizer of the predictive accuracy or precision becomes the best bandwidth.

a list with bandwidth.best: the best bandwidth found, criterion.value: its criterion value, criterion: the choice of criterion, and bandwith: the scoreboard for candidates.

# data generating process
N <- 500L
X1 <- rnorm(N)
X2 <- (X1 + 2*rnorm(N))/sqrt(5) + 1
X3 <- rnorm(N)^2/sqrt(2)
X <- cbind(X1, X2, X3)
beta <- c(2, 2, -1, -1)
V <- as.vector(cbind(X, 1)%*%beta)
Y <- ifelse(V >= rnorm(N), 1L, 0L)

# parameter estimation
qmle <- semiBRM(x = X, y = Y, control = list(iterlim=50))

# bandwidth search
h1 <- BandwidthGridSearch(qmle)
h2 <- BandwidthGridSearch(qmle, criterion = "accuracy", bandwidth = h1$bandwidth[,1L])
h3 <- BandwidthGridSearch(qmle, criterion = "precision", bandwidth = h1$bandwidth[,1L])