33. Mimbuild Bollen

Category: Latent Structure / MIM Construction
Type: BlockSpec-based MIM builder (Bollen-style)

MimbuildBollen constructs a measurement–intermediate–measurement (MIM) model from a set of pure clusters produced by TSC, FOFC, FTFC, GFFC, or BPC. It uses BlockSpec constraints in the spirit of Bollen & Pearl’s measurement-model construction rules.

This algorithm is the standard way in Tetrad to convert latent clusters into a full latent-variable graph.

33.1. Purpose

Use MimbuildBollen when:

  • you have clusters of indicators (latent measurement blocks),

  • you want a latent-variable model (not just clusters),

  • you prefer a principled, SEM-style construction with interpretable loadings,

  • and you want consistency with the classic SEM literature (Bollen 1989).

33.2. How It Works (Conceptual)

  1. Input a set of clusters identified by a latent clustering algorithm.

  2. Create one latent variable for each cluster.

  3. Connect each latent to its observed indicators with directed edges.

  4. Apply BlockSpec constraints:

    • loadings within a block follow SEM identifiability conventions,

    • cross-cluster loadings are suppressed,

    • latent–latent covariances or edges are included according to the BlockSpec.

  5. Output a complete MIM model with latent variables in place.

MimbuildBollen creates a measurement model only; it does not infer causal relations among the latent variables themselves.

33.3. Strengths

  • Produces measurement models compatible with SEM literature.

  • Provides identifiability through BlockSpec.

  • Works directly with clusters from TSC/FOFC/etc.

33.4. Limitations

  • Requires pure clusters—impure indicators violate Bollen-style assumptions.

  • Does not infer the causal structure among the latent variables. (Use Blocks-Test-TS + PC/BOSS/FGES/etc. for that.)

33.5. Relation to Other Latent Tools

Tool

Relationship

MimbuildPca

Alternative construction using PCA instead of BlockSpec.

FactorAnalysis

Traditional factor model; does not use clusters.

Latent Clusters

Supplies the pure clusters for MimbuildBollen.

33.6. References

  • Bollen, K. A. (1989). Structural Equations with Latent Variables.

33.7. Summary

  • Mimbuild-Bollen converts latent clusters into a full measurement–intermediate–measurement (MIM) model using SEM-style BlockSpec rules. It produces interpretable latent variables with clean indicator structure and standard identifiability constraints, making it ideal when you need a principled measurement model consistent with Bollen’s SEM framework. It builds the latent blocks but does not estimate causal relations among the latent variables themselves.