% \VignetteIndexEntry{Duration of Unemployment - Different Codings of Covariables}
%\VignetteEngine{knitr::knitr}
%\VignetteEncoding{UTF-8}

\documentclass[a4paper]{article}

\title{Duration of Unemployment - Different Codings of Covariables}

\begin{document}

\maketitle

<<echo=FALSE,eval=FALSE>>=
options(width=80)
@

The  unemployment data represent a contingency table with rows refering to gender and columns to duration of unemployment.

<<eval=FALSE>>=
unemployment <- matrix(c(403, 238, 167, 175), nrow=2, ncol=2)
rownames(unemployment) <- c("male","female")
colnames(unemployment) <- c("<6 month",">6 month")
unemployment
rowSums(unemployment)
@
Calculation of odds and log-odds.
<<eval=FALSE>>=
( odds_m <- 403/167 )
( odds_w <- 238/175 )
( log_odds_m <- log(403/167) )
( log_odds_w <- log(238/175) )
@
For the fitting of a logit-model an alternative  dataset is generated.
First  (0-1)-coding is considered
<<eval=FALSE>>=
gender <- c(rep(1, 403+167), rep(0,238+175))
unemp <- c(rep(1, 403), rep(0, 167), rep(1, 238), rep(0, 175))
@
For control, one can compute the crosstabulation of the generated data.
<<eval=FALSE>>=
table(gender, unemp)
@
Fit of a logit model.
<<eval=FALSE>>=
bin <- glm(unemp ~ gender, family=binomial)
summary(bin)
bin$coef
exp(bin$coef)
@ 
Now a dataset in effect-coding is created.
<<eval=FALSE>>=
gender_effect <- c(rep(1, 403+167), rep(-1,238+175))
@
For control, one can compute the crosstabulation of the generated data.
<<eval=FALSE>>=
table(gender_effect, unemp)
@
Fit a logit model.
<<eval=FALSE>>=
bin_effect <- glm(unemp ~ gender_effect, family=binomial)
summary(bin_effect)
bin_effect$coef
exp(bin_effect$coef)
@

Now we consider  education level as explanatory variable.
<<eval=FALSE>>=
unemp_level <- matrix(c(202, 307, 87, 45,
                        96, 162, 66, 18), nrow=4, ncol=2)
colnames(unemp_level) <- c("Short term","Long term")
unemp_level
rowSums(unemp_level)
@
For the fitting of a logit-model a new dataset is generated.
First (0-1)-coding is considered.
<<eval=FALSE>>=
level <- factor(c(rep(1, 202+96), rep(2,307+162), rep(3,87+66), rep(4,45+18))) 
unemp_l <-  c(rep(1, 202), rep(0, 96), rep(1, 307), rep(0, 162),
            rep(1, 87), rep(0, 66), rep(1, 45), rep(0, 18))
@
For control, one can compute the crosstabulation of the generated data.
<<eval=FALSE>>=
table(level, unemp_l)
@
Fit a logit model on the data. 
Define the variable level as a factor with the reference category 4. 
<<eval=FALSE>>=
level <- relevel(level, ref=4)
bin_l <- glm(unemp_l ~ level, family=binomial)
summary(bin_l)
@

Now additionally quasi--variances can be computed. Therefore the function "qvcalc" from the "qvcalc"--library is used.

<<results='markup',eval=FALSE>>=
library(qvcalc)
qv<-qvcalc(bin_l,"level")
summary(qv)
plot(qv)
@

<<echo=FALSE,results='hide',eval=FALSE>>=
rm(unemployment)
@
\end{document}