When analysing the quantitative multivariate models of relationships between the type of coalition formed and sets of independent variables, I have not tried to assess
strength of influence of the independent variables on the dependent variable, only the direction. When logistic regression is applied as the tool of the analyses, an implicit assumption is that the effect of each independent variable, measured as its effect on the probability of the dependent variable having a certain outcome, varies with differing combinations of values for the other independent variables (Sørensen 1989:79). This assumption seems reasonable in the context of local politics, where a bundle of local factors apparently have influence on the coalitions formed. This is why I found it more interesting to merely observe the direction of influence of each of the independent variables on the dependent variable. Logistic regression is quite a «robust» tool, the direction of the estimated influence has a higher probability of remaining constant, despite changes in the values of the other independent variables.
Looking at table 7.2 as a whole, we observe that the signs for all the coefficients, with the exception of INCOME, remain unchanged in all the models applied. Two variables have a negative influence on the probability that oversized coalitions will be formed:
CENTRAL and FEMALE. The more central the geographical location of a municipality, the lower the probability of an oversized coalition being formed; and the larger percentage of female representatives in the municipal council, the less chance of observing that an oversized coalition is formed. Three variables have a positive influence on the probability of oversized coalitions being formed: ONEPARTY, BLOCKBOU/NOBLOCK and EU. The probability of oversized coalitions being formed increases if a majority of the municipality’s inhabitants voted «Yes» in the EU-referendum. It also increases if one party controls a majority of the representatives in the municipal council, or if there is a bourgeois controlled majority, seen in relation to municipal councils where no block holds a majority. The latter result indicates that, when bargaining across borders between blocks is necessary to form a winning
coalition, the climate hardens, and the formation of minimal coalitions becomes more likely.
The other variables tested in the models do not appear to have any significant
influence on the coalition formation. The models perform in a similar way when the goodness-of-fit-statistics are studied. For all models, a null hypothesis stating that all the coefficients except for β0 are 0 is rejected on a 1% significance level. Thus, the analyses show that variables other than just locally-based ones exist which influence municipal coalition formation. A reasonable interpretation could be that the results indicate a tradition of consensus-building but with a few exceptions due to the assumed influence of some kind of modernity and block-influence.
Secondly, the models make correct predictions regarding the size of about 66% of the mayoral coalitions observed. This implies an improvement of about 6% compared with the univariate frequency distribution when trying to predict whether a coalition will be minimal or oversized. This also implies, however, that much remains to be explained concerning municipal coalition formation.
8 Multivariate analysis: committee coalitions
In this chapter, I use the technique of logistic regression to analyse models that try to predict the size of the committee coalitions formed. I apply the same method and use the same models as for mayoral coalitions in the previous chapter, to see whether the independent variables affect the dependent variable differently when this is
operationalised as committee coalitions. The concept of committee coalitions has been defined and discussed earlier; the operationalisations are not changed. For a
description of the models and their independent variables, see chapter 7.
The models employed to estimate the probability that a committee coalition will be oversized, are the following:
Model 1: L = β0+ β1SIZE + D1CENTRAL(1) + D2CENTRAL(2) + D4CENTRAL(4) + D5CENTRAL(5) + D6CENTRAL(6) + D7CENTRAL(7) + β2INCOME + β3ONEPARTY + D8BLOCKSOS + D9BLOCKBOU + β4EU + β5
HH-INDEX + β6FEMALE,
Model 2: L = β0+ β1SIZE + D1CENTRAL(1) + D2CENTRAL(2) + D4CENTRAL(4) + D5CENTRAL(5) + D6CENTRAL(6) + D7CENTRAL(7) + β2INCOME + β3ONEPARTY + β5NOBLOCK + β6EU + β7HH-INDEX + β8FEMALE,
Model 3: L = β0+ β1SIZE + β2CENTRAL + β3INCOME + β4ONEPARTY +
D1BLOCKSOS + D2BLOCKBOU + β5EU + β6HH-INDEX + β7FEMALE,
Model 4 L = β0+ β1SIZE + β2CENTRAL + β3INCOME + β4ONEPARTY + β5NOBLOCK
+ β6EU + β7HH-INDEX + β8FEMALE,
where, for all models, D denotes the coefficient associated with each of the dummy variables; andL P COALTYPE
P COALTYPE
= =
− =
æ èç
ö
ln ( ) ø÷
( )
1
1 1 .
Chapter 7 contains a discussion on whether the regression assumptions are met or not.
The general principles on which the models are based are presented there.
The data-sets used differ from that used for analysing mayoral coalitions. Appendix 3 contains simple, descriptive statistics for each of the variables based on total
committee coalitions and reduced committee coalitions, respectively. There is variation across every independent variable.
There must not be perfect or near perfect correlation between the independent variables. The correlations between all the variables are shown in tables 8.1 and 8.2.
The six dummy variables describing centrality are not included in the correlation matrix. They are adequately represented by CENTRAL. In neither table does
multicollinearity occur between the variables, there are no correlation values above 0,80, which is normally considered to be the limit for such a test. Hence, it is safe to proceed with the analysis.
Table 8.A Correlations between all the variables in the models applied in the quantitative multivariate analyses, treating total committee coalitions as dependent variable (Person correlation coefficients, r). N= 383
COAL
-TYPE
SIZE CENT
-RAL
INCOME ONE
-PARTY
BLOCK
-SOS
BLOCK
-BOU
NOBLOCK EU
HH-INDEX
FEMALE
COALTYPE 0.02 0.02 -0.02 0.07 -0.06 0.00 -0.06 0.04 -0.01 -0.01 SIZE 0.02 0.35* -0.28* -0.10*** -0.02 0.06 0.05 0.51* -0.22 0.12**
CENTRAL 0.02 0.35* -0.48* -0.08 -0.02 0.08 0.08 0.43* -0.25* 0.05 INCOME -0.02 -0.28* -0.48* 0.11** -0.04 -0.10** -0.16* -0.30* 0.29* -0.07 ONEPARTY 0.07 -0.10*** -0.08 0.11** 0.39* -0.35* -0.05 -0.02 0.64* -0.00 BLOCKSOS -0.06 -0.02 -0.02 -0.04 0.39* -60.8* 0.22* 0.05 0.36* 0.10***
BLOCKBOU 0.00 0.06 0.08 -0.10** -0.35* -60.8* 0.64* -0.02 -0.41* 0.00 NOBLOCK -0.06 0.05 0.08 -0.16* -0.05 0.22* 0.64* 0.03 -0.16* 0.09***
EU 0.04 0.51* 0.43* -0.30* -0.02 0.05 -0.02 0.03 -0.09*** 0.13*
HH-INDEX -0.01 -0.22* -0.25* 0.29* 0.64* 0.36* -0.41* -0.16* -0.09*** 0.05 FEMALE -0.01 0.12** 0.05 -0.07 -0.00 0.10*** 0.00 0.09*** 0.13* 0.05
* Significant on 1%-level (two-tailed test)
** Significant on 5%-level (two-tailed test)
*** Significant on 10%-level (two-tailed test)
Table 8.B Correlations between all the variables in the models applied in the quantitative multivariate analyses, treating reduced committee coalitions as dependent variable (Person correlation coefficients, r). N= 408
COAL
-TYPE
SIZE CENT
-RAL
INCOME ONE
-PARTY
BLOCK
-SOS
BLOCK
-BOU
NOBLOCK EU
HH-INDEX
FEMALE
COALTYPE 0.10*** 0.08*** -0.07 0.09*** 0.07 -0.14* -0.09*** 0.15* 0.01 0.04 SIZE 0.10*** 0.35* -0.29* -0.10** -0.03 0.07 0.05 0.51* -0.21* 0.12**
CENTRAL 0.08*** 0.35* -0.49* -0.11** -0.05 0.09*** 0.07 0.44* -0.26* 0.0 INCOME -0.07 -0.29* -0.49* 0.14* -0.02 -0.12** -0.17* -0.30* 0.36* -0.07 ONEPARTY 0.09*** -0.10** -0.11** 0.14* 0.41* -0.35* -0.03 -0.04 0.64* -0.01 BLOCKSOS 0.07 -0.03 -0.05 -0.02 0.41* -0.62* 0.24* 0.02 0.34* 0.10**
BLOCKBOU -0.14* 0.07 0.09*** -0.12** -0.35* -0.62* 0.62* -0.00 -0.41* -0.02 NOBLOCK -0.09*** 0.05 0.07 -0.17* -0.03 0.24* 0.62* 0.02 -0.16* 0.08 EU 0.15* 0.51* 0.44* -0.30* -0.04 0.02 -0.00 0.02 -0.10*** 0.13**
HH-INDEX 0.01 -0.21* -0.26* 0.36* 0.64* 0.34* -0.41* -0.16* -0.10*** 0.05 FEMALE 0.04 0.12** 0.04 -0.07 -0.01 0.10** -0.02 -0.08 0.13** 0.05
* Significant on 1%-level (two-tailed test)
** Significant on 5%-level (two-tailed test)
*** Significant on 10%-level (two-tailed test)