Summary of BFI fits

Summary method for an object with class 'bfi' created by the MAP.estimation and bfi functions.

Usage

# S3 method for class 'bfi'
summary(object,
        cur_mat = FALSE,
        digits = max(3, getOption("digits") - 3),
        ...)

# S3 method for class 'summary.bfi'
print(x,
        digits = x$summary_digits,
        cur_mat = x$summary_cur_mat,
        ...)

Arguments

object

A fitted object of class "bfi".

x

An object of class "summary.bfi" returned by summary.bfi().

cur_mat

Logical; if TRUE, the minus curvature matrix is also printed when the summary object is displayed. The matrix remains available in A_hat regardless of this option. Default is FALSE for summary.bfi().

digits

Number of digits used to format the printed results.

...

Additional arguments, currently unused.

Details

summary.bfi() prepares a structured summary of results returned by MAP.estimation() or bfi().

The resulting object can be stored without producing printed output. When displayed, print.summary.bfi() prints the model family, link function or baseline hazard, parameter estimates, posterior standard deviations, and 95% credible intervals.

For local models, the log-posterior value and convergence status are also displayed.

The minus curvature matrix is retained in A_hat. When cur_mat = TRUE is supplied to summary.bfi(), this matrix is also printed when the summary object is displayed.

The print method returns the summary object invisibly.

Value

summary.bfi returns an object of class "summary.bfi", containing the components described below. print.summary.bfi() displays the summary and returns the supplied object invisibly.

theta_hat

the component from object. The last element of this vector is the estimate of the dispersion parameter (sigma2) if family = "gaussian". See the MAP.estimation and bfi functions.

A_hat

the component from object. See the MAP.estimation and bfi functions.

sd

the posterior standard deviations corresponding to the reported parameter estimates. For Gaussian models with center-specific residual variances, the standard deviations corresponding to sigma2 are transformed from the \(\log(\sigma^2)\) scale to the original \(\sigma^2\) scale using the delta method. See the MAP.estimation and bfi functions.

Lambda

the component from object. See the MAP.estimation function.

formula

the component from object. See the MAP.estimation function.

n

the component from object. See the MAP.estimation function.

np

the component from object. See the MAP.estimation function.

family

the component from object. See the MAP.estimation function.

intercept

the component from object. See the MAP.estimation function.

convergence

the component from object. See the MAP.estimation function.

control

the component from object. See the MAP.estimation function.

stratified

the component from object. See the bfi function.

estimate

the estimated regression coefficients. For gaussian models the common dispersion parameter is excluded, but center-specific residual variances obtained with strat_par = 2 or strat_par = c(1, 2) are included.

logLikPost

the value of the log-likelihood posterior density evaluated at estimates (theta_hat).

link

the link function only for GLMs, not for the survival family. By default the gaussian family with identity link function and the binomial family with logit link function are used.

dispersion

the estimated residual variance sigma2 for Gaussian models with a common residual variance. For Gaussian models with center-specific residual variances, this component is NULL. For the binomial family, the dispersion parameter is fixed at 1. For the survival family, this component is NULL.

CI

a 95% credible interval for the parameters. For center-specific residual variances the interval is computed on the \(\log(\sigma^2)\) scale and back-transformed, so it is always positive and not symmetric around the estimate. The standard deviation printed for these parameters is obtained by the delta method on the \(\sigma^2\) scale.

coef_table

A matrix containing the reported parameter estimates, posterior standard deviations, and 95% credible interval limits.

summary_digits

The number of digits selected for printing the summary.

summary_cur_mat

A logical value indicating whether the curvature matrix should be displayed when the summary is printed.

Author

Hassan Pazira
Maintainer: Hassan Pazira h.pazira@arq.org

See also

MAP.estimation and bfi

Examples

#-------------
# y ~ Gaussian
#-------------
# model assumption:
theta <- c(1, 2, 3, 4, 1.5)  # coefficients and sigma2 = 1.5

#----------------
# Data Simulation
#----------------
n      <- 40
X      <- data.frame(x1=rnorm(n),                     # continuous variable
                     x2=sample(1:3, n, replace=TRUE)) # categorical variable
Xx2_1  <- ifelse(X$x2 == '2', 1, 0)
Xx2_2  <- ifelse(X$x2 == '3', 1, 0)
X$x2   <- as.factor(X$x2)
eta    <- theta[1] + theta[2] * X$x1 + theta[3] * Xx2_1 + theta[4] * Xx2_2
mu     <- gaussian()$linkinv(eta)
y      <- rnorm(n, mu, sd = sqrt(theta[5]))

#----------------
# MAP estimations
#----------------
Lambda <- inv.prior.cov(X, lambda = c(0.1, 0.5), family = "gaussian")
fit    <- MAP.estimation(y, X, family = "gaussian", Lambda)
class(fit)
#> [1] "bfi_local" "bfi"      

#-------------------------
# Summary of MAP estimates
#-------------------------
summary(fit)
#> 
#> Summary of the local model:
#> 
#>    Formula: y ~ x1 + x2 
#>     Family: ‘gaussian’ 
#>       Link: ‘identity’
#> 
#> Coefficients:
#> 
#>             Estimate Std.Dev CI 2.5% CI 97.5%
#> (Intercept)   0.5084  0.3086 -0.0964   1.1131
#> x1            1.7132  0.1985  1.3241   2.1024
#> x22           3.9894  0.4696  3.0691   4.9098
#> x23           4.6264  0.4396  3.7648   5.4879
#> 
#> Dispersion parameter (sigma2):  1.434 
#>             log Lik Posterior:  -29.44 
#>                   Convergence:  0 
sumfit <- summary(fit, cur_mat = TRUE)
sumfit$estimate
#> (Intercept)          x1         x22         x23 
#>   0.5083817   1.7132473   3.9894438   4.6263612 
sumfit$logLikPost
#> [1] -29.44136
sumfit$dispersion
#>  sigma2 
#> 1.43356 
sumfit$CI
#>                   2.5 %   97.5 %
#> (Intercept) -0.09636638 1.113130
#> x1           1.32412402 2.102371
#> x22          3.06910368 4.909784
#> x23          3.76478601 5.487936
class(sumfit)
#> [1] "summary.bfi"