# Investigating Number of Speeches in Parliament

Data Essay - Lecture Quantitative Methods - Fall Semester 2017

The purpose of this data essay is to examine whether different electoral regimes affect the participation of members of parliament (MP) in parliamentary debates. The task was to empirically test two hypotheses that claim opposing effects of ideological distance on the number of speeches delivered by MPs in proportional and majoritarian systems.

**Hypothesis 1** *In majoritarian systems, the larger the distance between an MP’s ideological position to the party, the more speeches the MP delivers in parliament.*
**Hypothesis 2** *In proportional systems, the larger the distance between MP’s ideological
position to the party, the fewer speeches the MP delivers in parliament.*

### Overview

- Setting up the Working Environment
- Getting a Feeling for the Data
- Basic and Extended Models
- Simulating the Differences between Countries
- Modelling the UK Case
- Modelling the German Case
- Simulating the Differences between Parties in Germany

```
rm(list = ls())
#setwd("C:/...") # be sure to set the right working directory
library(MASS)
library(foreign)
library(ggplot2)
library(hydroGOF)
library(stargazer)
```

```
Warning message:
"package 'ggplot2' was built under R version 3.4.2"Warning message:
"package 'hydroGOF' was built under R version 3.4.3"Loading required package: zoo
Warning message:
"package 'zoo' was built under R version 3.4.2"
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Please cite as:
Hlavac, Marek (2015). stargazer: Well-Formatted Regression and Summary Statistics Tables.
R package version 5.2. http://CRAN.R-project.org/package=stargazer
```

```
setwd("C:/Users/laris/Desktop/MMDS/Semester 2 - HWS2017/Multivariate Analyses/Data Essay")
```

The Dataset contains two data sets, one for Germany (2005-2009) and one for the UK (2001-2005). The data sets contain information on the number of legislative speeches for a subset of the MPs, 169 in the UK and 209 in Germany. Both data sets contain a measurement of each MP’s distance to the position of the party leaders. The data sets further include party affiliation and if the MP is one of the party leaders. In the German case the data set includes further variables on whether a candidate was elected via the party list or as a district candidate, committee assignments and where a MP is ideologically located in comparison to the governing coalition

```
# LOADING THE DATA AND GETTING A FEELING FOR IT
dta <- load("Dataessay.Rdata")
#summary(GERdata)
#summary(UKdata)
# RE-CODING SOME OF THE VARIABLES
GERdata$FDP <- ifelse(GERdata$party_affiliation == "FDP", 1, 0)
GERdata$CDU_CSU <- ifelse(GERdata$party_affiliation == "CDU/CSU", 1, 0)
GERdata$SPD <- ifelse(GERdata$party_affiliation == "SPD", 1, 0)
GERdata$Linke <- ifelse(GERdata$party_affiliation == "DIE LINKE.", 1, 0)
GERdata$ingov <- GERdata$SPD + GERdata$CDU_CSU
GERdata$list_candidate_new <- ifelse(GERdata$list_candidate == "District", 0, 1)
```

## Descriptive Statistics

The variable, which is going to be dependent in our models to test the given hypotheses, counts the number of speeches of selected members of parliaments (MP) during an election period. The data was collected for Germany and the United Kingdom. When we look at the distribution of this (obviously) count data (Figure 1), we see its fast falling curve and its long tail. This pattern is typical for a so called Poisson Distribution or a Negative Binomial Distribution (we will test later, what specific kind of distribution we find here).

```
#stargazer(GERdata)
#stargazer(UKdata)
hist(GERdata$number_speeches,
main = "Frequency of Number of Speeches (Count Data) \n
in Germany",
xlab = "Number of Speeches (counted per MP)")
hist(UKdata$number_speeches,
main = "Frequency of Number of Speeches (Count Data) \n
in the United Kingdom",
xlab = "Number of Speeches (counted per MP)")
#hist(GERdata$ideological_distance)
#hist(UKdata$ideological_distance)
```

In this figure we also see immediately the different ranges of number of speeches in Germany and the UK: While in Germany the parliament member with the highest number of speeches talked 68 times, in UK we observed a maximum number of 711 speeches (see also the Appendix Overview: Provided Variables for a more details). Therefore, and from now on, we will investigate the variable dependencies for both countries separately.

## Model Selection

### Underlying Distribution

First, we will test whether the pattern in the count data shows a poisson or a negative binomial distribution. They differ in the value of α, what is 0 in the poisson distribution. This difference would affect our estimates, because they are based on the assumption of an underlying distribution. The result of the Likelihood-Ratio-Test between the poisson model and the respective negative binomial model shows, that we can at least at a 95%- confidence be sure to reject the H0 that α equals 0. The following models will therefore be build upon the assumption of an underlying negative binomial distribution.

```
# BASIC MODELS AND LIKELIHOOD-RATIO-TEST
# BASIC POISSON MODEL
m0a <- glm(number_speeches ~ ideological_distance,
data = GERdata, family = "poisson")
m0b <- glm(number_speeches ~ ideological_distance,
data = UKdata, family = "poisson")
# BASIC NEGATIVE BINOMIAL MODEL
m1a <- glm.nb(number_speeches ~ ideological_distance,
data=GERdata, control = glm.control(maxit=100))
m1b <- glm.nb(number_speeches ~ ideological_distance,
data=UKdata, control = glm.control(maxit=100))
```

```
# FUNCTION: LIKELIHOOD-RATIO-TEST
compute.lrt <- function(model.nb, model.po, sign.level){
L1 <- logLik(model.po)
L2 <- logLik(model.nb)
LRT <- -2*L1 + 2*L2
return(LRT > qchisq(sign.level, df = 1))
}
compute.lrt(m1a, m0a, 0.95) # TRUE --> negative binomial model is better!
```

TRUE

```
# EXPANDED MODELS
m2a <- glm.nb(number_speeches ~ party_leader +
ideological_distance,
data=GERdata,
control = glm.control(maxit=100))
m2b <- glm.nb(number_speeches ~ party_leader +
ideological_distance,
data=UKdata,
control = glm.control(maxit=100))
#stargazer(m1a, m1b, m2a, m2b)
```

```
anova(m1a, m2a)
anova(m1b, m2b)
newGER <- GERdata
newGER$m1a <- predict(m1a, newGER, type = "response")
newGER$m2a <- predict(m2a, newGER, type = "response")
rmse(newGER$m1a, GERdata$number_speeches)
rmse(newGER$m2a, GERdata$number_speeches)
newUK <- UKdata
newUK$m1b <- predict(m1b, newUK, type = "response")
newUK$m2b <- predict(m2b, newUK, type = "response")
rmse(newUK$m1b, UKdata$number_speeches)
rmse(newUK$m2b, UKdata$number_speeches)
```

Model | theta | Resid. df | 2 x log-lik. | Test | df | LR stat. | Pr(Chi) |
---|---|---|---|---|---|---|---|

ideological_distance | 1.542051 | 195 | -1546.604 | NA | NA | NA | |

party_leader + ideological_distance | 1.580399 | 194 | -1541.899 | 1 vs 2 | 1 | 4.705125 | 0.03007281 |

Model | theta | Resid. df | 2 x log-lik. | Test | df | LR stat. | Pr(Chi) |
---|---|---|---|---|---|---|---|

ideological_distance | 1.305019 | 151 | -1842.362 | NA | NA | NA | |

party_leader + ideological_distance | 1.312192 | 150 | -1841.409 | 1 vs 2 | 1 | 0.9527573 | 0.3290184 |

15.071932635599

14.8527808549615

129.867854313204

129.312636830255

In this basic model we can see that for Germany, the coefficient of ideological distance is negative (in accordance to our hypothesis 2) and the coefficient is significant on a 90% significance level. Looking at the UK we see a positive coefficient (as expected in hypothesis 1), but unfortunately the coefficient is not significant because the p-value is too high.

In a next step we want to expand this basic model with the remaining comparable variable party leader. It makes sense to include this variable, because a party leader may have a higher number of speeches in parliament, and simultaneously a very low ideological distance (measured to his/her own position, obviously). As we can see in Table 1, the variable ideological distance remains significant for Germany, and also the variable party leader has some impact on the number of speeches. The comparison of the AIC as well as the RMSE support the impression, that the Expanded Model works better for the German data. For the United Kingdom it seems that this additional variable has no additional impact, because it is not significant. This is also supported by the AIC values, because it rises from the Basic Model to the Expanded Model.

## Simulating the Differences between Countries

```
# SIMULATING THE DIFFERENCE BETWEEN THE SYSTEMS
gamma.hat.uk1 <- coef(m2b)
V.hat.uk1 <- vcov(m2b)
S.uk1 <- mvrnorm(1000, gamma.hat.uk1, V.hat.uk1)
gamma.hat.ger1 <- coef(m2a)
V.hat.ger1 <- vcov(m2a)
S.ger1 <- mvrnorm(1000, gamma.hat.ger1, V.hat.ger1)
# SCENARIOS: HIGHEST AND LOWEST VALUE OF IDEOLOGICAL DISTANCE,
# SIMULATE THE VALUES FOR EACH COUNTRY SEPARATELY
germin.ideo.scen <- cbind(1, 0, min(GERdata$ideological_distance, na.rm=TRUE))
germax.ideo.scen <- cbind(1, 0, max(GERdata$ideological_distance, na.rm=TRUE))
ukmin.ideo.scen <- cbind(1, 0, min(UKdata$ideological_distance, na.rm=TRUE))
ukmax.ideo.scen <- cbind(1, 0, max(UKdata$ideological_distance, na.rm=TRUE))
Xbeta.germin <- S.ger1 %*% t(germin.ideo.scen)
Xbeta.germax <- S.ger1 %*% t(germax.ideo.scen)
Xbeta.ukmin <- S.uk1 %*% t(ukmin.ideo.scen)
Xbeta.ukmax <- S.uk1 %*% t(ukmax.ideo.scen)
lambda.germin <- exp(Xbeta.germin)
lambda.germax <- exp(Xbeta.germax)
lambda.ukmin <- exp(Xbeta.ukmin)
lambda.ukmax <- exp(Xbeta.ukmax)
theta.ger <- m2a$theta
theta.uk <- m2b$theta
exp.germin <- sapply(lambda.germin,
function(x) mean(rnbinom(100, size = theta.ger, mu = x)))
exp.germax <- sapply(lambda.germax,
function(x) mean(rnbinom(100, size = theta.ger, mu = x)))
exp.ukmin <- sapply(lambda.ukmin,
function(x) mean(rnbinom(100, size = theta.uk, mu = x)))
exp.ukmax <- sapply(lambda.ukmax,
function(x) mean(rnbinom(100, size = theta.uk, mu = x)))
exp.ger <- c(exp.germin, exp.germax)
exp.uk <- c(exp.ukmin, exp.ukmax)
df.ger <- data.frame(exp.ger)
df.uk <- data.frame(exp.uk)
df.ger$id <- c(rep("min", 1000), rep("max", 1000))
df.uk$id <- c(rep("min", 1000), rep("max", 1000))
ggplot(df.ger, aes(x = exp.ger, fill = id)) +
geom_density(alpha = 0.4) +
guides(fill = guide_legend(title = "")) +
xlab("Expected Speeches") +
ylab("Density") +
ggtitle("Simulating German Number of Speeches") +
theme_bw()
ggplot(df.uk, aes(x = exp.uk, fill = id)) +
geom_density(alpha = 0.4) +
guides(fill = guide_legend(title = "")) +
xlab("Expected Speeches") +
ylab("Density") +
ggtitle("Simulating British Number of Speeches") +
theme_bw()
```

Figure 2 used the Expanded Models from table 1 to simulate outcomes with interesting variable values. For each of the two countries we used the highest and the lowest value for ideological distance and defined the variable party leader equals 0, because it was the most common value for this variable. The resulting outcomes are shown in red for the highest value and in blue for the lowest value.

By comparing this two figures, we see that the order of the two curves is swapped. This supports the impression we had from the coefficients from table 1, that the hypotheses are supported, at least in their general direction. But we can also see in this comparison, that the curves of the UK overlap more than for Germany, which is another indicator that the impact of ideological distance may be more meaningful for Germany than for the UK.

## Deeper Modelling

### United Kingdom

For the United Kingdom there is only one variable left that could be used for further model building. When we add this variable to the already expanded model (see Appendix United Kingdom: Further Models for detailed results), we observe that ideological distance is now significant, too, and also AIC and RMSE are reduced in comparison to the Expanded Model in table 1. When we exclude now the not significant variable party leader we remain with the (in this comparison) best model for predicting the number of speeches in the British parliament.

```
# MODELLING THE UK CASE
# MODEL 3: FULL MODEL
m3b <- glm.nb(number_speeches ~ party_leader +
ideological_distance +
conservative_MP,
data=UKdata,
control = glm.control(maxit=100))
# MODEL 4: REDUCED (BEST) MODEL
m4b <- glm.nb(number_speeches ~ ideological_distance +
conservative_MP,
data=UKdata,
control = glm.control(maxit=100))
anova(m4b, m3b)
newUK$m3b <- predict(m3b, newUK, type = "response")
rmse(newUK$m3b, UKdata$number_speeches)
newUK$m4b <- predict(m4b, newUK, type = "response")
rmse(newUK$m4b, UKdata$number_speeches)
#stargazer(m3b, m4b)
m3b
```

```
Error in glm.nb(number_speeches ~ party_leader + ideological_distance + : konnte Funktion "glm.nb" nicht finden
Traceback:
```

### Germany

For Germany our possibilities to build further models are greater. Appendix Germany: Further Models shows an overview over the different calculated models. Model 3 was calculated with all the available variables except for the party dummies and showed immediately an improvement as well for the AIC as for the RMSE, this measurement dropped by roughly 2.5 points. But in this model, compared to the previous one from table 1, party leader lost its significance. Ideological distance remained significant at an 0.1-level, while the new variables number of committee memberships and whether the speaker was member of a governing party are significant at a 0.01-level. This could support the suspicion that there is a general “engagement” level underlying, affecting both the number of speeches and the number of committee memberships in a positive manner. The coefficient calculated whether the MP is member of a governing party shows a negative sign, so it seems that the “smaller” parties (because we have a coalition between the two biggest parties at this point in time) are over-proportionally represented in speeches.

The fourth model adds the party dummy variables to the previosly described model, but this step worsens both the AIC and the RMSE. No party dummy is significant (CDU/CSU was excluded, because there would be a perfect collinearity with “member of government party” together with the SPD dummy). This can be seen also in the fact, that the signs and significance levels of the coefficients of the other variables stay the same and the coefficients only change slightly.

In a fifth model we want to summarize only those variables that were found to be significant. Indeed, this model is the best of the models we calculated so far, measured by the RMSE as well as by the AIC. There would have been a model with an even lower RMSE (when excluding ideological distance), but this would increase the AIC a lot.

The last model, model 6 respectively, was only build to be a good foundation for the later on simulation of party differences, therefore, besides the party dummies, only the previous significant variables were included, except for member of governing party, because this would lead to redundancy with the party dummies of SPD and CDU/CSU. This model is not as good as the best model (compared by AIC and RMSE), but it is interesting that SPD and CDU/CSU become significant on a 0.01-level, when the member of governing party variable was removed.

All in all, the best model for Germany achieves a Root-Mean-Squared-Error of roughly 12. This value indicates that we are able to predict the number of speeches a MP does during the observed period with an average error of +- 12. Compared to the range of values the dependent variable can have, this number is quite high. Therefore I would expect that there is still a better model for this data.

```
# MODELLING THE GERMAN CASE
# MODEL 3: EXPANDED MODEL
m3a <- glm.nb(number_speeches ~ party_leader +
ideological_distance +
list_candidate_new +
committee +
caolMPoutside +
ingov,
data = GERdata,
control = glm.control(maxit = 100))
anova(m2a, m3a)
newGER$m3a <- predict(m3a, newGER, type = "response")
rmse(newGER$m3a, GERdata$number_speeches)
# MODEL 4: FULL MODEL
m4a <- glm.nb(number_speeches ~ party_leader +
ideological_distance +
list_candidate_new +
committee +
caolMPoutside +
ingov +
FDP +
SPD +
Linke,
data = GERdata,
control = glm.control(maxit = 100))
anova(m3a, m4a)
newGER$m4a <- predict(m4a, newGER, type = "response")
rmse(newGER$m4a, GERdata$number_speeches)
# MODEL 5: BEST MODEL
m5a <- glm.nb(number_speeches ~ ideological_distance +
committee +
ingov,
data = GERdata,
control = glm.control(maxit = 100))
anova(m5a, m4a)
newGER$m5a <- predict(m5a, newGER, type = "response")
rmse(newGER$m5a, GERdata$number_speeches)
# MODEL 6: PARTY MODEL (FOR SIMULATIONS)
m6a <- glm.nb(number_speeches ~ ideological_distance +
committee +
FDP +
CDU_CSU +
Linke +
SPD,
data = GERdata,
control = glm.control(maxit = 100))
newGER$m6a <- predict(m6a, newGER, type = "response")
rmse(newGER$m6a, GERdata$number_speeches)
#stargazer(m3a, m4a, m5a, m6a)
```

Model | theta | Resid. df | 2 x log-lik. | Test | df | LR stat. | Pr(Chi) |
---|---|---|---|---|---|---|---|

party_leader + ideological_distance | 1.580399 | 194 | -1541.899 | NA | NA | NA | |

party_leader + ideological_distance + list_candidate_new + committee + caolMPoutside + ingov | 2.455717 | 190 | -1463.705 | 1 vs 2 | 4 | 78.194 | 4.440892e-16 |

12.3182518934873

Model | theta | Resid. df | 2 x log-lik. | Test | df | LR stat. | Pr(Chi) |
---|---|---|---|---|---|---|---|

party_leader + ideological_distance + list_candidate_new + committee + caolMPoutside + ingov | 2.455717 | 190 | -1463.705 | NA | NA | NA | |

party_leader + ideological_distance + list_candidate_new + committee + caolMPoutside + ingov + FDP + SPD + Linke | 2.483081 | 187 | -1461.958 | 1 vs 2 | 3 | 1.746746 | 0.6265917 |

12.3262798051617

Model | theta | Resid. df | 2 x log-lik. | Test | df | LR stat. | Pr(Chi) |
---|---|---|---|---|---|---|---|

ideological_distance + committee + ingov | 2.403064 | 193 | -1467.611 | NA | NA | NA | |

party_leader + ideological_distance + list_candidate_new + committee + caolMPoutside + ingov + FDP + SPD + Linke | 2.483081 | 187 | -1461.958 | 1 vs 2 | 6 | 5.652997 | 0.4631611 |

12.0748504936798

12.0986683850752

## First Differences for Germany

```
# SIMULATION FOR FIRST DIFFERENCES
quants.mean.fun <- function(x){
c(quants = quantile(x, probs=c(0.025,0.5,0.975), mean = mean(x)))
}
gamma.hat.ger2 <- coef(m3a)
V.hat.ger2 <- vcov(m3a)
S.ger2 <- mvrnorm(1000, gamma.hat.ger2, V.hat.ger2)
```

To support the results interpreted from the regression table, we applied some simulation to have a look at the expected values of number of speeches in different scenarios. These scenarios were built based on Model 3 and took the median values of the variables, except for those the first difference was calculated on.

As we can see (in table 2) our results from the coefficient interpretation were supported. The only First Difference with substantial meaning is whether the MP is member of a governing party or not, because the confidence interval does not include 0. But when we look at the size of the difference, it means 1 speech more or less per election period.

```
# scenario: (y/n) party leader, median distance, median list,
# media committees, median outside, median ingov
scenario.lead <- cbind(1, 1, 0.1253, 1, 3, 0, 1)
scenario.notl <- cbind(1, 0, 0.1253, 1, 3, 0, 1)
X.lead <- as.matrix(rbind(scenario.lead, scenario.notl))
lead.combined <- S.ger2 %*% t(X.lead)
fd.lead <- lead.combined[,1] - lead.combined[,2]
quants.fd.lead <- apply(as.matrix(fd.lead), 2, quants.mean.fun)
quants.fd.lead
hist(fd.lead, main = "First Differences between Partyleaders
and Non-Partyleaders" )
abline(v = quants.fd.lead, lty = 2)
```

quants.2.5% | -0.08922938 |
---|---|

quants.50% | 0.24013696 |

quants.97.5% | 0.56187497 |

```
# scenario: no party leader, median distance, (y/n) list candidate,
# media committees, median outside, median ingov
scenario.list <- cbind(1, 0, 0.1253, 1, 3, 0, 1)
scenario.dire <- cbind(1, 0, 0.1253, 0, 3, 0, 1)
X.list <- as.matrix(rbind(scenario.list, scenario.dire))
list.combined <- S.ger2 %*% t(X.list)
fd.list <- list.combined[,1] - list.combined[,2]
quants.fd.list <- apply(as.matrix(fd.list), 2, quants.mean.fun)
quants.fd.list
hist(fd.list, main = "First Differences between List Candidates and
Direct Mandates" )
abline(v = quants.fd.list, lty = 2)
```

quants.2.5% | -0.1183215 |
---|---|

quants.50% | 0.1222505 |

quants.97.5% | 0.3452989 |

```
# scenario: no party leader, median distance, median list,
# media committees, (y/n) outside, median inreg
scenario.inco <- cbind(1, 0, 0.1253, 1, 3, 0, 1)
scenario.outc <- cbind(1, 0, 0.1253, 1, 3, 1, 1)
X.inco <- as.matrix(rbind(scenario.inco, scenario.outc))
inco.combined <- S.ger2 %*% t(X.inco)
fd.inco <- inco.combined[,1] - inco.combined[,2]
quants.fd.inco <- apply(as.matrix(fd.inco), 2, quants.mean.fun)
quants.fd.inco
hist(fd.inco, main = "First Differences between Speekers \n within
the Coalition Interval and outside" )
abline(v = quants.fd.inco, lty = 2)
```

quants.2.5% | -0.41507740 |
---|---|

quants.50% | -0.15265534 |

quants.97.5% | 0.09423774 |

```
# scenario: no party leader, median distance, median list,
# media committees, median outside, (y/n) inreg
scenario.ingo <- cbind(1, 0, 0.1253, 1, 3, 0, 1)
scenario.outg <- cbind(1, 0, 0.1253, 1, 3, 0, 0)
X.ingo <- as.matrix(rbind(scenario.ingo, scenario.outg))
ingo.combined <- S.ger2 %*% t(X.ingo)
fd.ingo <- ingo.combined[,1] - ingo.combined[,2]
quants.fd.ingo <- apply(as.matrix(fd.ingo), 2, quants.mean.fun)
quants.fd.ingo
hist(fd.ingo, main = "First Differences between Speekers \n from
the Governing Parties and the Opposition" )
abline(v = quants.fd.ingo, lty = 2)
```

quants.2.5% | -1.1553990 |
---|---|

quants.50% | -0.8804044 |

quants.97.5% | -0.6083633 |

## Differences between German Parties

Because it was quite surprising that the parties didn’t show any difference in the number of speeches, we simulated this difference, too, to get a better feeling of the data. In the figure below we see clearly the difference between government and opposition parties. This difference may result out of the unusual predominant size of the government (which controlled nearly 70% of the parliament seats [1]).

```
# SIMULATING OTHER QUANTITIES OF INTEREST
gamma.hat.ger3 <- coef(m6a)
V.hat.ger3 <- vcov(m6a)
S.ger3 <- mvrnorm(1000, gamma.hat.ger3, V.hat.ger3)
# SCENARIOS: TAKE MEDIAN EXCEPT FOR PARTY VALUES
scenario.FDP <- cbind(1, 0.1253, 3, 1, 0, 0, 0)
scenario.CDU <- cbind(1, 0.1253, 3, 0, 1, 0, 0)
scenario.LIN <- cbind(1, 0.1253, 3, 0, 0, 1, 0)
scenario.SPD <- cbind(1, 0.1253, 3, 0, 0, 0, 1)
scenario.GRU <- cbind(1, 0.1253, 3, 0, 0, 0, 0)
XbetaFDP <- S.ger3 %*% t(scenario.FDP)
XbetaCDU <- S.ger3 %*% t(scenario.CDU)
XbetaLIN <- S.ger3 %*% t(scenario.LIN)
XbetaSPD <- S.ger3 %*% t(scenario.SPD)
XbetaGRU <- S.ger3 %*% t(scenario.GRU)
lambdaFDP <- exp(XbetaFDP)
lambdaCDU <- exp(XbetaCDU)
lambdaLIN <- exp(XbetaLIN)
lambdaSPD <- exp(XbetaSPD)
lambdaGRU <- exp(XbetaGRU)
thetam6a <- m6a$theta
exp.FDP <- sapply(lambdaFDP,
function(x) mean(rnbinom(1000, size = thetam6a, mu = x)))
exp.CDU <- sapply(lambdaCDU,
function(x) mean(rnbinom(1000, size = thetam6a, mu = x)))
exp.LIN <- sapply(lambdaLIN,
function(x) mean(rnbinom(1000, size = thetam6a, mu = x)))
exp.SPD <- sapply(lambdaSPD,
function(x) mean(rnbinom(1000, size = thetam6a, mu = x)))
exp.GRU <- sapply(lambdaGRU,
function(x) mean(rnbinom(1000, size = thetam6a, mu = x)))
exp.values <- c(exp.FDP, exp.CDU, exp.LIN, exp.SPD, exp.GRU)
df.parties <- data.frame(exp.values)
df.parties$id <- c(rep("FDP", 1000),
rep("CDU/CSU", 1000),
rep("LINKE", 1000),
rep("SPD", 1000),
rep("GRUENE", 1000))
ggplot(df.parties, aes(x = exp.values, fill = id)) +
geom_density(alpha = 0.4) +
guides(fill = guide_legend(title = "")) +
xlab("Expected Speeches") +
ylab("Density") +
ggtitle("Simulated expected Number of Speeches, separated
by Party Affiliation") +
theme_bw()
```

## Conclusion

All in all we can say, that we can support both hypotheses at least in the direction they stated above. The strength may be worth to be discussed, as well as the importance of other variables, which were not available for the computation of models in this case.

It would be interesting, for example, if the appeared difference in government and opposition parties for Germany is also found for the UK, but unfortunately there was no separation between the Labour and the Liberal party. We saw for the German case, that this difference is highly significant, so maybe we could observe this in other countries as well.

Besides that there is still much work to do when we look at the sizes of effects (for example in table 2) or the size of the RMSE, which is still quite high compared to the range of actual values.

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