A clustering view on ESS measures of political interest: An EM-MML approach Cláudia Silvestre Margarida Cardoso Mário Figueiredo Escola Superior de Comunicação Social - IPL BRU_UNIDE, ISCTE-IUL Instituto de Telecomunicações, Inst. Sup. Técnico Portugal
Objective Model Finite Mixture Models Selection Criterion Minimum Message Length Outline Algorithm EM-MML Results Conclusions
Clustering the regions in the European Social Survey based on attitudes towards politics Voted last national election ( Yes; No; Not eligible) Contacted politician or government official in last 12 months Objective Worked in political party or action group in last 12 months Worked in another organisation or association in last 12 months Worn or displayed campaign badge/sticker in last 12 months (Y/N) Signed petition in last 12 months Taken part in lawful public demonstration in last 12 months Boycotted certain products last in 12 months Feel closer to a particular party than all other parties
𝐿 𝑔 𝑧 𝑗 | 𝜄 = 𝛽 𝑙 𝑔 𝑧 𝑗 | 𝜄 𝑙 𝑙 =1 K is the number of segments Model: 𝑧 𝑗 is regarded as “incomplete data”, the Finite Mixture allocation to segments ( 𝑨 𝑗 ) being missing Models Complete data: 𝑧 𝑗 , 𝑨 𝑗
The log of complete likelihood Model: Finite Mixture 𝑔 𝑧 𝑗, 𝑨 𝑗 𝜄 𝑨 𝑗 𝛽 𝑔 𝑧 𝑗 𝜄 Models 𝑗 uknown
How to select the number of segments? Information criteria such as BIC, AIC, CAIC, AIC3 or ICL can be used … We adopt Minimum Message Length criterion embedded in the model estimation (Figueiredo and Selection Jain, 2002), which: Criterion Provides estimates of all the model parameters including the number of segments Is less sensitive to initialization than EM Avoids the boundary of the parameters space
Shannon’s Information Theory: optimally transmitting a random variable Y with probability 𝑔 𝑧 requires about − 2 𝑔 𝑧 bits of information. Selection to encode 𝑧 : 𝑧 𝜄 − 2 𝑔 𝑧, 𝜄 Criterion: MML to encode 𝑧 and 𝜄 the total message length is: 𝑧, 𝜄 𝑧 𝜄 + 𝜄
EM is a popular algorithm for finding ML parameter estimates, when unobserved (missing) data is considered in the model. Algorithm: EM-MML The EM-MML A mixture of multinomials is adopted and the MML estimates are obtained via an EM-type algorithm.
Categorical variables: 𝑍 𝑍 , … , 𝑍 𝑗 , … 𝑍 𝑍 𝑗 𝑍 𝑗 , … , 𝑍 𝑗𝐸 where variable 𝑒 ( 𝑒 1 … 𝐸 ) has 𝐷 𝑒 categories Algorithm: EM-MML 𝜄 𝜄 , … , 𝜄 , 𝛽 , … , 𝛽 , 𝛽 are the clusters’ weights or mixing probabilities 𝜄 the multinomials ’ parameters
𝑗 log 𝑔 𝑧 𝜄 log 𝑔 𝑧 𝑗 𝜄 Mixture of multinomials: Algorithm: EM-MML 𝐸 𝐷 𝑒 𝑧 𝑗𝑒𝑑 𝜄 𝑒𝑑 𝑔 𝑧 𝑗 𝜄 𝛽 𝑜! 𝑧 𝑗𝑒𝑑 ! 𝑒 𝑑
Assuming that: The segments have independent priors … independent from the mixing probabilities A noninformative Jeffreys prior for 𝜄 Algorithm: 𝑧, 𝜄 𝑧 𝜄 + 𝜄 EM-MML 𝑁 𝑜 𝛽 12 + 𝑙 𝑨 𝑁 + 1 𝑜 + 𝑙 𝑨 − log 𝑔 𝑧 𝜄 2 12 2 ,𝛽 𝑙 >0 𝑁 is the number of parameters specifying each segment 𝑙 𝑨 is the number of segments with non-zero probability
E-step 𝐹 𝑎 𝑗 𝑧 𝑗 ; 𝑄 𝑎 𝑗 1 𝑧 𝑗 ; 𝜄 𝑢 𝜄 𝑢 𝛽 𝑢 𝑔 𝑧 𝑗 ; 𝑢 𝜄 Algorithm: EM-MML 𝛽 𝑢 𝑔 𝑧 𝑗 ; 𝑢 𝜄 where 𝑧 𝑗𝑒𝑑 𝐸 𝐷 𝑒 𝑢 𝜄 𝑒𝑑 𝑢 𝑔 𝑧 𝑗 ; 𝜄 𝑜! 𝑧 𝑗𝑒𝑑 ! 𝑒 𝑑
M-step Update the estimates of mixing probabilities 𝑢+ 𝛽 − 𝑁 𝑄 𝑎 𝑗 1 𝑧 𝑗 ; 𝜄 𝑢 𝑛𝑏𝑦 0, 𝑗 2 − 𝑁 Algorithm: 𝑄 𝑎 𝑗 1 𝑧 𝑗 ; 𝑛𝑏𝑦 0, 𝑗 𝜄 𝑢 2 EM-MML Update the estimates of multinomial parameters 𝑄 𝑎 𝑗 1 𝑧 𝑗 ; 𝜄 𝑢 𝑗 𝑧 𝑗𝑒𝑑 𝑢+ 𝜄 𝑒𝑑 𝑄 𝑎 𝑗 1 𝑧 𝑗 ; 𝑜! 𝑗 𝜄 𝑢
compute 𝑗 , 𝜄 (𝑢) 𝑄 𝑎 𝑗 1 𝑍 𝛽 Algorithm: = 0 𝛽 EM-MML K:=K -1 > 0 compute 𝜄
The clustering of Regions in the European Social Survey based on attitudes towards Results politics, using EM-MML, yields 2 clusters
BIC; CAIC; ICL AIC; AIC3 EM-MML 2012 7 7 2 Number of clusters 0.213 0.191 0.361 Silhouette index 83.327 74.977 190.825 Calinski-Harabasz Computation time Results: 109 109 2 (seconds) cohesion-separation 2014 7 8 2 Number of clusters stability 0.152 0.164 0.367 Silhouette index computationtime 80.766 78.477 189.552 Calinski-Harabasz Computation time 91 91 2 (seconds) 2012 0.377 0.499 0.707 Adjusted Rand vs Normalized 2014 mutual 0.523 0.591 0.598 information
number of regions number of regions 160 160 147 140 140 126 120 120 114 100 100 93 Results: 80 80 round 6 vs round 7 60 60 40 40 20 20 0 0 ESS6 CLU 1 ESS6 CLU 2 ESS7 CLU 1 ESS7 CLU 2
80% 76% 70% Regions in cluster 2 share a 65% more active role in politics 57% 60% (Yes %) 50% 40% 37% 32% 28% 26% 30% 16% 20% 12% 13% 9% 10% 9% 9% 8% 10% 5% 6% 6% 4% 2% 0% Contacted Worked in Worked in Worn or Signed Taken part in Boycotted Feel closer to a Voted last Not eligible to politician or political party another displayed petition last 12 lawful public certain particular national vote government or action organisation or campaign months demonstration products last party than all election official last 12 group last 12 association badge/sticker last 12 months 12 months other parties months months last 12 months last 12 months ESS6 CLU 1 ESS6 CLU 2
80% 73% 70% 65% Regions in cluster 1 share a 58% 60% more passive role in politics (Yes %) 50% 41% 40% 34% 28% 30% 25% 18% 20% 13% 12% 12% 8% 10% 9% 7% 6% 10% 5% 5% 3% 5% 0% Contacted Worked in Worked in Worn or Signed Taken part in Boycotted Feel closer to a Voted last Not eligible to politician or political party another displayed petition last 12 lawful public certain particular national vote government or action organisation or campaign months demonstration products last party than all election official last 12 group last 12 association badge/sticker last 12 months 12 months other parties months months last 12 months last 12 months ESS7 CLU 1 ESS7 CLU 2
Regions in cluster 2 are clearly more interested in politics ( as expected…) 42% 45% 45% 41% 40% 40% 36% 37% 32% 35% 35% 30% 29% 30% 30% 30% 27% 26% 25% 25% 20% 20% 15% 14% Results 12% 15% 12% 15% 8% 10% 10% 7% 5% 5% 0% 0% How How How How interested interested interested interested in politics - in politics - in politics - in politics - very not at all very not at all interested interested interested interested ESS6 CLU 1 ESS6 CLU 2 ESS7 CLU 1 ESS7 CLU 2
Most respondents in Cluster 1 do not trust politicians… 25% 21% 20% 19% 15% 15% 13% 13% 14% 13% 13% Results 11% 11% 11% 10% 9% 10% 7% 5% 5% 5% 4% 2% 1% 0% 1% 0% 0% Trust in politicians - Not at all Trust in politicians - Completely ESS6 CLU 1 ESS6 CLU 2
…or political parties 25% 20% 20% 20% 15% 14% 14% 15% 14% 13% 13% Results 12% 11% 11% 10% 10% 9% 7% 5% 4% 5% 4% 2% 1% 0% 1% 0% 0% Trust in political parties - Not at all Trust in political parties - Completely ESS6 CLU 1 ESS6 CLU 2
Regions in cluster 2 share a more positive view of other people 25% ESS6 and ESS7 results being very similar 21% 21% 20% 18% 15% 15% 13% 12% 12% 12% 11% 11% 10% 10% 9% 9% 5% 5% 5% 4% 3% 3% 2% 2% 2% 2% 0% Mostly Most of the looking out time people for helpful themselves ESS6 CLU 1 ESS6 CLU 2
0% Slovenia 5,7% All regions in 10% Sweden 0,0% Sweden, Norway, Portugal 0% 9,8% Finland, Denmark 0% Poland 8,7% 9% Norway 0,0% and Germany belong 9% Netherlands 1,2% to cluster 2 0% Lithuania 9,6% 0% Israel 11,4% 3% Ireland 9,4% 0% Hungary 9,2% 4% United Kingdom 6,8% 8% France 1,9% Finland 12% 0,0% 10% Spain 0,5% 0% Estonia 10,9% 9% Denmark 0,0% 16% Germany 0,0% 0% Czech Republic 9,2% 6% Switzerland 1,8% 5% Belgium 3,9% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% ESS6 CLU 2 ESS6 CLU 1
All regions in Sweden, 0% Slovenia 7,4% Norway, Finland, 8% Sweden 0,0% 1% Portugal Denmark and Germany 5,8% 0% Poland 9,8% belong Norway 7% 0,0% to cluster 2 8% Netherlands 0,4% 0% Lithuania 13,6% 25 regions change to 0% Israel 15,5% cluster 2 , e.g. 4% Ireland 9,5% 0% Lisbon (in Portugal ) Hungary 10,3% 10% United Kingdom 0,4% Jihoceský kraj (in 9% France 0,0% Czech Republic) 10% Finland 0,0% 8% Spain 0,4% 4 regions change to Estonia 0% 12,4% cluster 1 : 7% Denmark 0,0% Prov. West-Vlaanderen 14% Germany 0,0% (in Belgium ), 1% Czech Republic 12,2% Principado de Asturias, 7% Switzerland 0,0% 6% La Rioja Belgium 2,3% (in Spain) and 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% ESS7 CLU 2 ESS7 CLU 1 Drenthe (in Netherlands)
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