BIFIEsurvey (version 3.5-19)

BIFIE.linreg: Linear Regression

Description

Computes linear regression.

Usage

BIFIE.linreg(BIFIEobj, dep=NULL, pre=NULL, formula=NULL,
    group=NULL, group_values=NULL, se=TRUE)
# S3 method for BIFIE.linreg
summary(object,digits=4,...)
# S3 method for BIFIE.linreg
coef(object,...)
# S3 method for BIFIE.linreg
vcov(object,...)

Value

A list with following entries

stat

Data frame with unstandardized and standardized regression coefficients, residual standard deviation and \(R^2\)

output

Extensive output with all replicated statistics

...

More values

Arguments

BIFIEobj

Object of class BIFIEdata

dep

String for the dependent variable in the regression model

pre

Vector of predictor variables. If the intercept should be included, then use the variable one for specifying it (see Examples).

formula

An R formula object which can be applied instead of providing dep and pre. Note that there is additional computation time needed for model matrix creation.

group

Optional grouping variable(s)

group_values

Optional vector of grouping values. This can be omitted and grouping values will be determined automatically.

se

Optional logical indicating whether statistical inference based on replication should be employed.

object

Object of class BIFIE.linreg

digits

Number of digits for rounding output

...

Further arguments to be passed

See Also

Alternative implementations: survey::svyglm, intsvy::timss.reg, intsvy::timss.reg.pv, stats::lm

See BIFIE.logistreg for logistic regression.

Examples

#############################################################################
# EXAMPLE 1: Imputed TIMSS dataset
#############################################################################

data(data.timss1)
data(data.timssrep)

# create BIFIE.dat object
bdat <- BIFIEsurvey::BIFIE.data( data.list=data.timss1, wgt=data.timss1[[1]]$TOTWGT,
             wgtrep=data.timssrep[, -1 ] )

#**** Model 1: Linear regression for mathematics score
mod1 <- BIFIEsurvey::BIFIE.linreg( bdat, dep="ASMMAT", pre=c("one","books","migrant"),
              group="female" )
summary(mod1)

if (FALSE) {
# same model but specified with R formulas
mod1a <- BIFIEsurvey::BIFIE.linreg( bdat, formula=ASMMAT ~ books + migrant,
               group="female", group_values=0:1 )
summary(mod1a)

# compare result with lm function and first imputed dataset
dat1 <- data.timss1[[1]]
mod1b <- stats::lm( ASMMAT ~ 0 + as.factor(female) + as.factor(female):books +
                              as.factor(female):migrant,
                         data=dat1,  weights=dat1$TOTWGT )
summary(mod1b)

#**** Model 2: Like Model 1, but books is now treated as a factor
mod2 <- BIFIEsurvey::BIFIE.linreg( bdat, formula=ASMMAT ~ as.factor(books) + migrant)
summary(mod2)

#############################################################################
# EXAMPLE 2: PISA data | Nonlinear regression models
#############################################################################

data(data.pisaNLD)
data <- data.pisaNLD

#--- Create BIFIEdata object immediately using BIFIE.data.jack function
bdat <- BIFIEsurvey::BIFIE.data.jack( data.pisaNLD, jktype="RW_PISA", cdata=TRUE)
summary(bdat)

#****************************************************
#*** Model 1: linear regression
mod1 <- BIFIEsurvey::BIFIE.linreg( bdat, formula=MATH ~ HISEI )
summary(mod1)

#****************************************************
#*** Model 2: Cubic regression
mod2 <- BIFIEsurvey::BIFIE.linreg( bdat, formula=MATH ~ HISEI + I(HISEI^2) + I(HISEI^3) )
summary(mod2)

#****************************************************
#*** Model 3: B-spline regression

# test with design of HISEI values
dfr <- data.frame("HISEI"=16:90 )
des <- stats::model.frame( ~ splines::bs( HISEI, df=5 ), dfr )
des <- des$splines
plot( dfr$HISEI, des[,1], type="l", pch=1, lwd=2, ylim=c(0,1) )
for (vv in 2:ncol(des) ){
    lines( dfr$HISEI, des[,vv], lty=vv, col=vv, lwd=2)
}

# apply B-spline regression in BIFIEsurvey::BIFIE.linreg
mod3 <- BIFIEsurvey::BIFIE.linreg( bdat, formula=MATH ~ splines::bs(HISEI,df=5) )
summary(mod3)

#*** include transformed HISEI values for B-spline matrix in bdat
bdat2 <- BIFIEsurvey::BIFIE.data.transform( bdat, ~ 0 + splines::bs( HISEI, df=5 ))
bdat2$varnames[ bdat2$varsindex.added ] <- paste0("HISEI_bsdes",
            seq( 1, length( bdat2$varsindex.added ) ) )

#****************************************************
#*** Model 4: Nonparametric regression using BIFIE.by

?BIFIE.by

#---- (1) test function with one dataset
dat1 <- bdat$dat1
vars <- c("MATH", "HISEI")
X <- dat1[,vars]
w <- bdat$wgt
X <- as.data.frame(X)
# estimate model
mod <- stats::loess( MATH ~ HISEI, weights=w, data=X )

# predict HISEI values
hisei_val <- data.frame( "HISEI"=seq(16,90) )
y_pred <- stats::predict( mod, hisei_val )
graphics::plot( hisei_val$HISEI, y_pred, type="l")

#--- (2) define loess function
loess_fct <- function(X,w){
    X1 <- data.frame( X, w )
    colnames(X1) <- c( vars, "wgt")
    X1 <- stats::na.omit(X1)
#    mod <- stats::lm( MATH ~ HISEI, weights=X1$wgt, data=X1 )
    mod <- stats::loess( MATH ~ HISEI, weights=X1$wgt, data=X1 )
    y_pred <- stats::predict( mod, hisei_val )
    return(y_pred)
}

#--- (3) estimate model
mod4 <-  BIFIEsurvey::BIFIE.by( bdat, vars, userfct=loess_fct )
summary(mod4)

# plot linear function pointwise and confidence intervals
graphics::plot( hisei_val$HISEI, mod4$stat$est, type="l", lwd=2,
        xlab="HISEI", ylab="PVMATH", ylim=c(430,670) )
graphics::lines( hisei_val$HISEI, mod4$stat$est - 1.96* mod4$stat$SE, lty=3 )
graphics::lines( hisei_val$HISEI, mod4$stat$est + 1.96* mod4$stat$SE, lty=3 )
}