inv.prior.cov {BFI} | R Documentation |
Creates an inverse covariance matrix for a Gaussian prior
Description
inv.prior.cov
builds a diagonal inverse covariance matrix for the Gaussian prior distribution based on the design matrix of covariates, that takes into account the number of regression parameters in case of categorical covariates. In case of a linear model, it also includes a row and column for the variance of the measurement errors.
Usage
inv.prior.cov(X, lambda = 1, L = 2, family = gaussian, intercept = TRUE,
stratified = FALSE, strat_par = NULL, center_spec = NULL)
Arguments
X |
design matrix of dimension |
lambda |
the vector used as the diagonal of the (inverse covariance) matrix that will be created by |
L |
the number of centers. This argument is used only when |
family |
a description of the error distribution and link function used to specify the model. This can be a character string naming a family function or the result of a call to a family function (see |
intercept |
logical flag for having an intercept. By changing the |
stratified |
logical flag for performing the stratified analysis. If |
strat_par |
a one- or two-element integer vector for indicating the stratification parameter(s). The values |
center_spec |
a vector of |
Details
inv.prior.cov
creates a diagonal matrix with the vector lambda
as its diagonal. The argument stratified = TRUE
should only be used to construct a matrix for the prior density in case of stratification in the fictive combined data. Never be used for the construction of the matrix for analysis in the centers.
When stratified = FALSE
, the length of the vector lambda
depends on the covariate matrix X
, family
, and whether an “intercept” is included in the model. For example, if the design matrix X
has p
columns with continuous or dichotomous covariates, family = gaussian
, and intercept = TRUE
, then lambda
should have p+2
elements. In this case, if in X
there is a categorical covariate with q>2
categories, then the length of lambda
increases with q-2
. All values of lambda should be non-negative as they represent the inverse of the variance of the Gaussian prior.
Note that, if all values in the vector lambda
equal, one value is enough to be given as entry.
If lambda
is a scalar, the function inv.prior.cov
sets each value at the diagonal equal to lambda
. In the linear regression model the last parameter is assumed to be the inverse of the variance of the prior distribution for the measurement error. If lambda
is two dimensional, the first value is used for the prior of the regression parameters and the second for the inverse of the variance of the prior distribution for the measurement error.
If stratified = TRUE
the length of the vector lambda
should be equal to the number of parameters in the combined model.
If intercept = FALSE
, for the binomial
family the stratified analysis is not possible therefore stratified
can not be TRUE
.
If stratified = FALSE
, both strat_par
and center_spec
must be NULL
(the defaults), while if stratified = TRUE
only one of the two must be NULL
.
The output of inv.prior.cov()
can be used in the main functions MAP.estimation()
and bfi()
.
Value
inv.prior.cov
returns a diagonal matrix. The dimension of the matrix depends on the number of columns of X
, type of the covariates (continuous/dichotomous or categorical), family
, and intercept
.
Author(s)
Hassan Pazira
Maintainer: Hassan Pazira hassan.pazira@radboudumc.nl
References
Jonker M.A., Pazira H. and Coolen A.C.C. (2024). Bayesian federated inference for estimating statistical models based on non-shared multicenter data sets, Statistics in Medicine, 1-18. <https://doi.org/10.1002/sim.10072>
See Also
Examples
#----------------
# Data Simulation
#----------------
X <- data.frame(x1=rnorm(50), # standard normal variable
x2=sample(0:2, 50, replace=TRUE), # categorical variable
x3=sample(0:1, 50, replace=TRUE)) # dichotomous variable
X$x2 <- as.factor(X$x2)
X$x3 <- as.factor(X$x3)
#---------------------
# Load the BFI package
#---------------------
library(BFI)
# The (inverse) variance value (lambda=0.05) is assumed to be
# the same for Gaussian prior of all parameters (for non-stratified)
#-------------------------------------------------
# Inverse Covariance Matrix for the Gaussian prior
#-------------------------------------------------
# y ~ Binomial with 'intercept'
inv.prior.cov(X, lambda=0.05, family=binomial) # returns a 5-by-5 matrix
# y ~ Binomial without 'intercept'
inv.prior.cov(X, lambda=0.05, family="binomial", intercept = FALSE) # a 4-by-4 matrix
# y ~ Gaussian with 'intercept'
inv.prior.cov(X, lambda=0.05, family=gaussian) # returns a 6-by-6 matrix
#--------------------
# Stratified analysis
#--------------------
# y ~ Binomial when 'intercept' varies across 3 centers:
inv.prior.cov(X, lambda=c(.2, 1), family=binomial, stratified=TRUE, strat_par = 1, L = 3)
# y ~ Gaussian when 'intercept' and 'sigma2' vary across 2 centers; y ~ Gaussian
inv.prior.cov(X, lambda=c(1, 2, 3), family=gaussian, stratified=TRUE, strat_par = c(1, 2))
# y ~ Gaussian when 'sigma2' varies across 2 centers (with 'intercept')
inv.prior.cov(X, lambda=c(1, 2, 3), family=gaussian, stratified=TRUE, strat_par = 2)
# y ~ Gaussian when 'sigma2' varies across 2 centers (without 'intercept')
inv.prior.cov(X, lambda=c(2, 3), family=gaussian, intercept = FALSE, stratified=TRUE,
strat_par = 2)
#--------------------------
# Center specific covariate
#--------------------------
# center specific covariate has K=2 categories across 4 centers; y ~ Binomial
inv.prior.cov(X, lambda=c(0.1:2), family=binomial, stratified=TRUE,
center_spec = c("Iran","Netherlands","Netherlands","Iran"), L=4)
# center specific covariate has K=3 categories across 5 centers; y ~ Gaussian
inv.prior.cov(X, lambda=c(0.5:3), family=gaussian, stratified=TRUE,
center_spec = c("Medium","Big","Small","Big","Small"), L=5)
# center specific covariate has K=4 categories across 5 centers; y ~ Gaussian
inv.prior.cov(X, lambda=1, family=gaussian, stratified=TRUE, center_spec = c(3,1:4), L=5)