Hello Mario,

This is an excellent question that gets at a common and important challenge in quantitative political science and survey research. Your thinking is spot-on: direct mean comparisons are problematic with unequal sample sizes and heterogeneous variances, and standard ANOVA with Tukey's HSD is not appropriate when the assumption of homogeneity of variance is violated.

You have several good options. Let's break them down, from direct answers to your questions to a recommended workflow.

1. Answering Your Direct Question: Post-Hoc Tests for Unequal Variances

Is there other post hoc that do clusters like HSD but doesnt assume equality of variance?

Yes. The most common and well-regarded post-hoc test for this situation is the Games-Howell post-hoc test.

• What it is: The Games-Howell test is essentially a t-test between all pairs of groups that does not assume equal variances (it uses the Welch-Satterthwaite degrees of freedom correction) and is robust to unequal sample sizes.

• How it helps: It will give you a matrix of p-values for all pairwise comparisons (e.g., Party A vs. Party B, Party A vs. Party C, etc.). You can then manually "cluster" parties by identifying groups of parties that are not statistically different from each other.

• Limitation: While this solves the statistical assumption problem, it's a somewhat indirect way to cluster. You are inferring clusters from pairwise non-significance, which can sometimes be ambiguous. A true clustering method is often more direct and powerful for your goal of "mapping the parties."

2. Recommended Approach: Cluster Analysis

You are correct to consider cluster analysis, as this is precisely what the method is designed for: grouping objects (in your case, political parties) based on their similarity across one or more variables (ideological scores). I would recommend Hierarchical Agglomerative Clustering.

Here is a step-by-step workflow:

Step 1: Data Aggregation (The Crucial Step)

First, you need to move your unit of analysis from the individual partisan to the political party. This resolves your unequal sample size and variance issues at the source.

• For each ideological item or scale in your questionnaire, calculate an aggregate statistic for each party. The mean is standard. However, if your Likert data is skewed or you're worried about outliers, the median can be a more robust choice.

• Your resulting dataset should have parties as rows and the mean/median ideological scores as columns.

Step 2: Standardization (Optional but Recommended)

If your ideological scales have different ranges (e.g., one is 1-5, another is 1-10), you should standardize them. Convert each column to Z-scores (mean of 0, standard deviation of 1). This ensures that no single ideological dimension with a larger scale disproportionately influences the clustering.

Step 3: Perform Hierarchical Cluster Analysis

This method builds a tree-like structure (a dendrogram) that shows how parties are progressively merged based on similarity.

• Distance Metric: Use Euclidean Distance (or Squared Euclidean Distance). This is the standard "as the crow flies" distance between your parties in the multi-dimensional ideological space you've created.

• Linkage Method: This determines how the distance between clusters is calculated. Ward's Method is often an excellent starting point because it aims to create compact, well-separated clusters by minimizing the total within-cluster variance. Other common methods include "Complete Linkage" or "Average Linkage."

Step 4: Interpret the Dendrogram and Determine Clusters

The output will be a dendrogram. You read it from the bottom up. Parties that merge low on the tree are very similar; groups that merge high on the tree are very different. You decide on the final number of clusters by "cutting" the tree at a certain height. This visual representation is extremely powerful for mapping the ideological space.

JASP has a module for Exploratory Factor Analysis and a separate one for Cluster Analysis under the Machine Learning menu that can perform this procedure.

3. Answering Your Second Question: Multilevel Modeling

Or maybe is it better to just load them as level 2 factor in a multilevel model in hypothesis testing?

This is a very sophisticated and excellent idea, representing a more advanced alternative to simple aggregation.

• How it Works: You can run a random-intercepts multilevel model where individual ideological score is the outcome, with partisans (Level 1) nested within parties (Level 2). The model would look like this: Ideological_Score ~ 1 + (1 | Party).

• What it Gives You: This model does two things:

• It directly answers the hypothesis-testing question: "Is there significant variance in ideology between parties?" (by checking the variance of the random intercept).

• It produces Best Linear Unbiased Predictors (BLUPs) for each party. These BLUPs are essentially "shrunken" means. They are party-level estimates of ideology that have been adjusted for the reliability of each party's sample size (estimates from parties with small n are "shrunken" back toward the grand mean).

• How to Use it for Clustering: You can then take these highly robust BLUPs and use them as the input for your hierarchical cluster analysis (in Step 1 above, use the BLUPs instead of the simple means). This is arguably the most statistically sound way to derive the party-level scores for clustering.

Summary and Recommended Workflow

Option A (Straightforward and Robust):

• Aggregate: Calculate the mean (or median) ideological score for each party.

• Cluster: Perform a Hierarchical Cluster Analysis on the aggregated data (using Ward's method and Euclidean distance).

• Interpret: Use the resulting dendrogram to visually map the parties and decide on the number of clusters.

• Validate (Optional): Once you've assigned each party to a cluster, you can run a one-way ANOVA (using your final cluster assignments as the independent variable) with a Games-Howell post-hoc test to confirm that your derived clusters are, in fact, statistically distinct from one another on the key ideological dimensions.

Option B (Advanced and Methodologically Superior):

• Model: Run a multilevel model with partisans nested in parties.

• Extract: Save the random intercepts (BLUPs) for each party.

• Cluster: Use these BLUPs as the input for your Hierarchical Cluster Analysis. This approach elegantly handles the unequal sample sizes by incorporating their reliability directly into the party-level estimates.

Both approaches are valid, but Option B is more defensible from a purely methodological standpoint. Given your familiarity with these concepts, it may be the ideal route.

Good luck with your analysis! This sounds like a fascinating project.

Dear Mario,

I hope you are doing well.

Have you tested with Clara (Clustering Large Application)? I never used JASP for this kind of analysis, but I am sure that R run it.

Here some references: https://rpubs.com/Tanmay007/cluster_analysis

Best,

Amalia

The question is not very clear to me. It appears that you want to classify a group of individuals.

Any classification involves examining (A) similarity of members within a group and (B) dissimilarity between groups or ratio of A and B, showing efficiency of classification in terms of low value of within-group variance and high value of between-group variance

I prefer using Davies-Bouldin Index (DBI). For details please see Davies, D and Bouldin, W. (1979): A cluster separation measure, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1 (2), 224 – 227