| Title: | Linear Regression Based on 'ILSE' for Missing Data |
|---|---|
| Description: | Linear regression when covariates include missing values by embedding the correlation information between covariates. Especially for block missing data, it works well. 'ILSE' conducts imputation and regression simultaneously and iteratively. More details can be referred to Huazhen Lin, Wei Liu and Wei Lan. (2021) <doi:10.1080/07350015.2019.1635486>. |
| Authors: | Wei Liu [aut, cre], Huazhen Lin [aut], Wei Lan [aut] |
| Maintainer: | Wei Liu <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1.7 |
| Built: | 2024-11-20 06:36:43 UTC |
| Source: | CRAN |
extracts model coefficients from object of class "ilse".
Coef(object)Coef(object)
object |
an object of class "ilse". |
Coefficients extracted from object.
coef, coefficient
# example one data(nhanes) NAlm2 <- ilse(age~., data=nhanes) Coef(NAlm2)# example one data(nhanes) NAlm2 <- ilse(age~., data=nhanes) Coef(NAlm2)
Generate two type of correlation matrix
cor.mat(p, rho, type='toeplitz')cor.mat(p, rho, type='toeplitz')
p |
a positive integer, the dimension of correlation matrix. |
rho |
a value between 0 and 1, a baseline vlaue of correlation coefficient. |
type |
a character, specify the type of correlation matrix and only include 'toeplitz' and 'identity' in current version. |
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.
return a correlation matrix with a type of specified structure.
nothing
Liu Wei
nothing.
cov2cor
cor.mat(5, 0.5) cor.mat(5, 0.5, type='identity')cor.mat(5, 0.5) cor.mat(5, 0.5, type='identity')
Generate two type of covariance matrix
cov.mat(sdvec,rho, type='toeplitz')cov.mat(sdvec,rho, type='toeplitz')
sdvec |
a positive vector, standard deviation of each random variable. |
rho |
a value between 0 and 1, a baseline vlaue of correlation coefficient. |
type |
a character, specify the type of correlation matrix and only include 'toeplitz' and 'identity' in current version. |
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.
return a covariance matrix with a type of specified structure.
nothing
Liu Wei
nothing.
cov2cor
cov.mat(rep(5,5), 0.5) cov.mat(c(2,4,3), 0.5, type='identity')cov.mat(rep(5,5), 0.5) cov.mat(c(2,4,3), 0.5, type='identity')
Estimate regression coefficients based on Full Information Maximum Likelihood Estimation, which can couple missing data, including response missing or covariates missing.
fimlreg(...) ## S3 method for class 'formula' fimlreg(formula, data=NULL, ...) ## S3 method for class 'numeric' fimlreg(Y, X, ...)fimlreg(...) ## S3 method for class 'formula' fimlreg(formula, data=NULL, ...) ## S3 method for class 'numeric' fimlreg(Y, X, ...)
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under 'Details'. |
Y |
a numeric vector, the reponse variable. |
X |
a numeric matrix that may include NAs, the covariate matrix. |
data |
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which clse is called. |
... |
Optional arguments. |
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.
Return a list including following components:
beta |
A named vector of coefficients |
formula |
The formula used |
data |
The raw data |
Liu Wei
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)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 when covariates include missing values embedding the correlation information between covariates by Iterative Least Square Estimation.
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, ...)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 passed to other methods. |
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under 'Details'. |
Y |
a numeric vector, the reponse variable. |
X |
a numeric matrix that may include NAs, the covariate matrix. |
data |
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which ilse is called. |
bw |
a positive value, specify the bandwidth in estimating missing values, default as NULL. When bw=NULL, it is automatically selected by empirical method. |
k.type |
an optional character string, specify the type of kernel used in iterative estimating algorithm and support 'epk', 'biweight', 'triangle', 'gaussian', 'triweight', 'tricube', 'cosine', 'uniform' in current version, defualt as 'gaussian'. |
method |
an optional character string, specify the iterative algorithm, support 'Par.cond' and 'Full.cond' in current version. |
max.iter |
an optional positive integer, the maximum iterative times, defualt as '20'. |
peps |
an optional positive value, tolerance vlaue of relative variation rate of estimated parametric vector, default as '1e-7'. |
feps |
an optional positive vlaue, tolerance vlaue of relative variation rate of objective function value, default as '1e-7'. |
arma |
an optional logical value, whether use armadillo and Rcpp to speed computation, default as TRUE |
verbose |
an optional logical value, indicate whether output the iterative information, default as 'TRUE'. |
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.
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:
beta |
a named vector of coefficients |
hX |
a imputed design matrix |
d.fn |
a nonnegative value, vlaue of relative variation rate of objective function value |
d.par |
a nonnegative value, relative variation rate of estimated parametric vector when algorithm stopped. |
iterations |
a positive integer, iterative times in total. |
residuals |
the residuals, that is response minus fitted values. |
fitted.values |
the fitted mean values. |
inargs |
a list including all input arguments. |
nothing
Wei Liu
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.
## 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)## 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)
Different type of kernel functions.
kern(u, type='epk')kern(u, type='epk')
u |
a numeric vector, evluated points in kernel funciton. |
type |
a optional character string, specify the type of used kernel functionand support 'epk', 'biweight', 'triangle', 'guassian', 'triweight', 'tricube', 'cosine', 'uniform' in current version, defualt as 'epk'. |
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.
Return a numeric vector with length equal to 'u'.
Liu Wei
KernSmooth package
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')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')
A small data set with missing values.
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).
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.
Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall. Table 6.14.
# example one data(nhanes) bw <- 1 ilse(age~., data=nhanes,bw=bw)# example one data(nhanes) bw <- 1 ilse(age~., data=nhanes,bw=bw)
print method for class "ilse" or class "fiml".
print(object) ## S3 method for class 'ilse' print(object) ## S3 method for class 'fiml' print(object)print(object) ## S3 method for class 'ilse' print(object) ## S3 method for class 'fiml' print(object)
object |
an object of class "ilse" or "fiml". |
For "ilse", print the basic information of ilse estimation and algorithm and return a list including
beta |
a named vector of coefficients |
Bmat |
a named matrix that summary the estimated beta in every iteration. |
residuals |
the residuals, that is response minus fitted values. |
fitted.values |
the fitted mean values. |
d.fn |
a nonnegative value, vlaue of relative variation rate of objective function value |
d.par |
a nonnegative value, relative variation rate of estimated parametric vector when algorithm stopped. |
K |
a positive integer, iterative times in total. |
For "fiml", print the basic information of fiml estimation and return a list including
beta |
A named vector of coefficients |
iterations |
A positive integer, iterative times in total. |
stop.code |
The stop code returned by nlm. |
print.lm
data(nhanes) NAlm1 <- ilse(age~., data=nhanes) a <- print(NAlm1) a fimllm <- fimlreg(age~., data=nhanes, iterlim= 40) b <- print(fimllm) bdata(nhanes) NAlm1 <- ilse(age~., data=nhanes) a <- print(NAlm1) a fimllm <- fimlreg(age~., data=nhanes, iterlim= 40) b <- print(fimllm) b
summary method for class "ilse" or "fiml".
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)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)
object |
an object of class "ilse". |
Nbt |
an positive integer, the repeated times of bootstrap to eatimate covariance matrix of regression coefficient. |
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.
summary.lm fitted.vlaues residuals
# example one data(nhanes) NAlm <- ilse(age~., data=nhanes) summary(NAlm, Nbt=5) fimllm <- fimlreg(age~., data=nhanes) summary(fimllm, Nbt = 5)# example one data(nhanes) NAlm <- ilse(age~., data=nhanes) summary(NAlm, Nbt=5) fimllm <- fimlreg(age~., data=nhanes) summary(fimllm, Nbt = 5)