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Last data update: 2014.03.03

R: Parameter estimation using MCLL

mcll_est

R Documentation

Parameter estimation using MCLL

Description

Parameter estimation using Monte Carlo local likelihood

Usage

mcll_est(data, prior.func, alp=0.7,
        method="BFGS",  lower = -Inf, upper = Inf,
        control=list(), use.locfit=TRUE,
        con.manual=list(method="BFGS", lower = -Inf, upper = Inf,
        control=list()) )

Arguments

`data`	posterior samples of model parameters. a `matrix` or `data.frame` of size m \times p (m: sample size, p: dimension of the parameters).
`prior.func`	a prior function. An argument should be a vector of parameter values and a return value should be the log prior density for those parameter values.
`alp`	a real value between 0 and 1. α takes a value between 0 and 1, which is the nearest neighbor bandwidth with the kth smallest distance d where k = lfloor n α floor and d(x, x_{i}) = \| x - x_{i} \| with the sample size n
`method`	an optimization method to be used in maximizing the approximation to the unnormalized log-likelihood. Options from `optim` are Nelder-Mead, BFGS, CG, L-BFGS-B, and SANN.
`lower, upper`	bounds on the variables for the L-BFGS-B method in `optim`.
`control`	a list of control parameters. See control options for `optim`.
`use.locfit`	logical. If TRUE, `locfit` is used to compute a local likelihood density estimate. If FALSE, a code from the `mcll` package is used. `locfit` is typically faster but sometimes fails for high-dimensional parameter spaces.
`con.manual`	a list. An optimization method for finding the polynomial coefficients, lower and upper bounds on the variables for the L-BFGS-B method, and a list of control parameters when `use.locfit` = FALSE. See control options for `optim`.

Details

Nested maximizations in Step 2 in the Monte Carlo local likelihood estimation. It makes use of the R package locfit and the R function optim. The posterior samples should be on the real line (e.g., variance parameters should be on the log-scale). The prior distributions (provided as a form of prior.func) should be the same as those used for obtaining the posterior samples of the model parameters. For details, see Section 2 in Jeon et al. (2012).

Value

mcll_est returns a list of the following components,

`par`	parameter estimates on the original scale.
`value`	value of the function corresponding to `par`. This is an unnormalized log-likelihood from the MCLL algorithm. One can use this to compute the Bayes factor. For details, see Appendix of Jeon et al. (2012).
`counts`	a two-element integer vector giving the number of calls to function and gradient, respectively.
`convergence`	an integer code. 0 indicates successful completion. For possible error codes, see the document for `optim`.
`message`	a character string giving any additional information returned by `optim`, or NULL.

Author(s)

Minjeong Jeon <jeon.117@osu.edu>

References

Jeon, M., Kaufman, C., and Rabe-Hesketh, S. (2014). Monte Carlo local likelihood for approximate MLE of complex models. Under revision.

Loader, C. (2012). locfit: Local regression, likelihood, and density estimation. Downloadable from http://cran.r-project.org/web/packages/locfit/index.html.

Examples

## example

# posterior samples
data(samp)

# prior function
prior.func <- function(vec.t) {
    sum(dnorm(vec.t, m= c(0,0,0,0, -0.9870405, -0.9870405) ,
                sd=c(100,100,100,100, 1/0.766672, 1/0.766672) , log=TRUE))
}

## parameter estimation
run1 <- system.time(
    result1 <- mcll_est(data=samp, prior.func= prior.func, alp=0.7,
        method = "BFGS", control= list(maxit=10000))
)

# result1$par
#            b0        b1         b2       b3       tau0     tau1
#[1,] 0.9275766 -2.871686 -0.6488625 3.589313 0.08118962 0.148478