Extracts Regression Coefficients

Description

extracts model coefficients from object of class "ilse".

Usage

  Coef(object)

Arguments

Value

Coefficients extracted from object.

See Also

coef, coefficient

Examples

# example one
data(nhanes)
NAlm2 <- ilse(age~., data=nhanes)
Coef(NAlm2)

Generate Two Type of Correlation Matrix

Description

Generate two type of correlation matrix

Usage

  cor.mat(p, rho, type='toeplitz')

Arguments

Details

The argument rho specify the size of correlation coeffient. As for argument type, if type='toeplitz', sigma_ij=rho^|i-j|; if type ='identity', sigma_ij=rho when i!=j and sigma_ij=1 when i=j.

Value

return a correlation matrix with a type of specified structure.

Note

nothing

Author(s)

Liu Wei

References

nothing.

See Also

cov2cor

Examples

  cor.mat(5, 0.5)
  cor.mat(5, 0.5, type='identity')

Generate Two Type of Covariance Matrix

Description

Generate two type of covariance matrix

Usage

  cov.mat(sdvec,rho, type='toeplitz')

Arguments

Details

The argument rho specify the size of correlation coeffient. As for argument type, if type='toeplitz', sigma_ij=rho^|i-j|; if type ='identity', sigma_ij=rho when i!=j and sigma_ij=1 when i=j.

Value

return a covariance matrix with a type of specified structure.

Note

nothing

Author(s)

Liu Wei

References

nothing.

See Also

cov2cor

Examples

  cov.mat(rep(5,5), 0.5)
  cov.mat(c(2,4,3), 0.5, type='identity')

Full Information Maximum Likelihood Linear Regression

Description

Estimate regression coefficients based on Full Information Maximum Likelihood Estimation, which can couple missing data, including response missing or covariates missing.

Usage

  fimlreg(...)

  ## S3 method for class 'formula'
fimlreg(formula, data=NULL, ...)
  ## S3 method for class 'numeric'
fimlreg(Y, X, ...)

Arguments

Details

Note that arguments ... of stats::nlm are the parameters of algorithm, see the details in help file of "nlm". "fimlreg" can cople with any type of missing data.

Value

Return a list including following components:

Author(s)

Liu Wei

See Also

ilse

Examples

data(nhanes)
## example one: include missing value
fiml1 <- fimlreg(age~., data=nhanes)
print(fiml1)
# example two: No missing vlaue
## example two: No missing value
n <- 100
group <- rnorm(n, sd=4)
weight <- 3.2*group + 1.5 + rnorm(n, sd=0.1)
fimllm <- fimlreg(weight~group, data=data.frame(weight=weight, group=group))
print(fimllm)

Linear Regression by Iterative Least Square Estimation

Description

Linear regression when covariates include missing values embedding the correlation information between covariates by Iterative Least Square Estimation.

Usage

  ilse(...)
  ## S3 method for class 'formula'
ilse(formula, data=NULL, bw=NULL,  k.type=NULL,  method="Par.cond", ...)
  ## S3 method for class 'numeric'
ilse(Y, X,bw=NULL, k.type=NULL, method="Par.cond", max.iter=20,
  peps=1e-5, feps = 1e-7, arma=TRUE, verbose=FALSE, ...)

Arguments

Details

Models for ilse are specified symbolically. A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed. A specification of the form first:second indicates the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second.

Value

ilse returns an object of class "ilse".

The functions summary and anova are used to obtain and print a summary and analysis of variance table of the results. The generic accessor functions coefficients, effects, fitted.values and residuals extract various useful features of the value returned by lm.

An object of class "ilse" is a list containing at least the following components:

Note

nothing

Author(s)

Wei Liu

References

Huazhen Lin, Wei Liu, & Wei Lan (2021). Regression Analysis with individual-specific patterns of missing covariates. Journal of Business & Economic Statistics, 39(1), 179-188.

See Also

lm

Examples

## exmaple one: include missing value
data(nhanes)
NAlm1 <- ilse(age~., data=nhanes,bw=1,
   method = 'Par.cond', k.type='gaussian', verbose = TRUE)
print(NAlm1)
NAlm2 <- ilse(age~., data=nhanes, method = 'Full.cond')
print(NAlm2)
## example two: No missing value
n <- 100
group <- rnorm(n, sd=4)
weight <- 3.2*group + 1.5 + rnorm(n, sd=0.1)
NAlm3 <- ilse(weight~group, data=data.frame(weight=weight, group=group),
   intercept = FALSE)
print(NAlm3)

Kernel Function

Description

Different type of kernel functions.

Usage

  kern(u, type='epk')

Arguments

Details

Note that K(u_i)=K(X_i-x_0) where u = (X_1-x_0, ..., X_n-x_0) and K_h(u_i)=1/h*K((X_i-x_0)/h) where h is bandwidth.

Value

Return a numeric vector with length equal to 'u'.

Author(s)

Liu Wei

See Also

KernSmooth package

Examples

library(graphics)
u <- seq(-1,1,by=0.01)
(Ku <- kern(u))
plot(u, Ku, type='l')
# guassian kernel
plot(u, kern(u, type='gaussian'), type ='l')
# cosine kernel
plot(u, Ku <- kern(u, type='cosine'), type ='l')

NHANES example - all variables numerical

Description

A small data set with missing values.

Format

A data frame with 25 observations on the following 4 variables. age: Age group (1=20-39, 2=40-59, 3=60+).

bmi: Body mass index (kg/m**2).

hyp: Hypertensive (1=no,2=yes).

chl: Total serum cholesterol (mg/dL).

Details

A small data set with all numerical variables. The data set nhanes2 is the same data set, but with age and hyp treated as factors.

Source

Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall. Table 6.14.

Examples

# example one
data(nhanes)
bw <- 1
ilse(age~., data=nhanes,bw=bw)

Print the Information of FIML or ILSE methods

Description

print method for class "ilse" or class "fiml".

Usage

  print(object)
  ## S3 method for class 'ilse'
print(object)

  ## S3 method for class 'fiml'
print(object)

Arguments

Value

For "ilse", print the basic information of ilse estimation and algorithm and return a list including

For "fiml", print the basic information of fiml estimation and return a list including

See Also

print.lm

Examples

data(nhanes)
NAlm1 <- ilse(age~., data=nhanes)
a <- print(NAlm1)
a

fimllm <- fimlreg(age~., data=nhanes, iterlim= 40)
b <- print(fimllm)
b

Summarizing the inference information for ILSE or FIML methods

Description

summary method for class "ilse" or "fiml".

Usage

  summary(object, Nbt=20)

  ## S3 method for class 'ilse'
summary(object, Nbt=20)

  ## S3 method for class 'fiml'
summary(object, Nbt=20)

  ##
  Fitted.values(object)
  ##
  Residuals(object)

Arguments

Value

The function summary.ilse computes and returns a named matrix of summary statistics of the fitted linear model given in object by ILSE or FIML methods. The function Fitted.values return a vector, fitted repsonse vlaues. The function Residuals return a vector, residuals.

See Also

summary.lm fitted.vlaues residuals

Examples

# example one
data(nhanes)
NAlm <- ilse(age~., data=nhanes)
summary(NAlm, Nbt=5)

fimllm <- fimlreg(age~., data=nhanes)
summary(fimllm, Nbt = 5)