Fitting Hierarchical Generalized Linear Models with Bias Correction in Small Area Estimation

hglmbc is used to fit hierarchical generalized linear models using h-likelihood with bias correction in small area estimation (SAE) for exponential family distributions with normally distributed random effects.

hglmbc(
  data,
  mformula = NULL,
  dom = NULL,
  y.family = "binomial",
  rand.family = "gaussian",
  tol = 1e-05,
  ...
)

Arguments

data	a data frame.
mformula	an object of class myFormula: a symbolic description of the model to be fitted. The details of the mformula is given under details section.
dom	a domain/cluster/small area to specify the random effect. e.g. numeric zipcode, county, or state code, and also name of the county or name of the state.
y.family	a distribution from _exponential family_ to describe the error distribution. See "family".
rand.family	a discription of the distribution of random effects.
tol	predefined tolerance value. Default value is tol=1e-10.
...	other arguments, See details section.

Value

An object of class hglmbc consists of the hierarchical maximum likelihood estimates (HMLEs) of fixed effects, random effects, and variance parameters with other values,

est.beta

HMLE of fixed effects.

re

HMLE of the random effects.

var.par

HMLE of the dispersion parameter for the random effects.

fe.cov

the estimated variance-covariance matrix of the fixed effects.

fe.cov

the estimated vaiance-covaraince matrix of the random effects.

iter

number of iterations at convergence.

AICBIC

A list of likelihood values for model selection purposes,where AIC is the AIC value, BIC is the BIC value ("AIC"), hLik is the h-likelihood value.

summary

a summary object of the fitted model.

Details

A typical model has the form response ~ terms where the response is the (numeric) vector and terms is a series of terms which specifies a linear predictor for response. A terms are specified as a linear combination of predictors, in Small Area Estiamtion (SAE), it is a vector of fixed effects. e.g. y ~ x1 + x2 + as.factor(x3).

If a formula is not defined, the user can input the response variable, resp, a vector of fixed effects, such as fe.disc for categorical variables and fe.cont for continuous variables. If not, the user can define the resp, then, it will automatically select the fixed effects based on the variable types.

The hglmbc function also has the flexibility to use different reference category for factor variables. e.g. ref.group can be defined for each categorical variable. By default the reference group will be considered in alphebetical order or numerical order. In order to use a different reference group, ref.group needs to be defined. e.g. for categorical variables age (groups: 1, 2, 3), if the prefered reference group is 2, then set ref.group = "age2".

See also

family, DesignM

Examples

if (FALSE) {
# Using ever use of smoke data set. Discrete and continuous variables are defined.
data <- eversmoke
mformula <- "smoke_ever ~ as.factor(age) + as.factor(gender) + as.factor(race)
+ as.factor(year) + povt_rate"
dom <- "county"
y.family <- "binomial"
rand.family <- "gaussian"
hglmbc.fit <- hglmbc(data=eversmoke, mformula, dom = "county", y.family="binomial")

# mformula is not defined,
resp <- "smoke_ever"
dom <- "county"
catX <- c("year","gender","race","age")
contX <- "povt_rate"

hglmbc.fit <- hglmbc(data = eversmoke, resp, dom = "county",fe.disc = catX,
fe.cont = contX, y.family = "binomial")


# Poisson-Normal HGLM
N = 1000
p = 20
nVars = 5
x = matrix(rnorm(N * p), N, p)
beta = rnorm(nVars)
f = x[, seq(nVars)] %*% beta
mu = exp(f)
y = rpois(N, mu)

}