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I have problems about understanding the intuition and differences about when to apply fixed effects, hierarchical linear models (multilevel models) and hierarchical mixed models. I will try to explain my difficulties in understanding with following example I am currently working on.

I would like to analyze the influence of component characteristics to its performance during the product development process. Each component belongs to a subsystem and the subsystem belongs to a product. Thus, I have hierarchical data. The dependent variable is measured on all level. The independent variables are measured on all levels. I have this data for a couple of similar products with the same hierarchical structure resulting in panel data with repeated cross-sections.

Here are some examples of my variables.

Dependent variable:

  • Development performance

Independent variables:

  • Number of materials
  • Weight
  • Complexity
  • Prior experience
  • Novelty
  • Subsystem dummy (subsystem level)
  • Number of parts (subsystem level)
  • Budget (subsystem level)
  • Assigned engineers (subsystem level)
  • Product dummy (subsystem level)
  • Customer segment (product level)
  • Market (product level)
  • Price (product level)

This is what I understood so far.

Fixed effects:

  • With the help of fixed effects all time invariant effects will be absorbed, so the omitted variable bias is reduced.
  • In my case I would like to use component fixed effects and product fixed effects as I may have left out some variables on the component level and products also differ slightly.
  • Due to fixed effects I won’t be able to analyze interaction effects between individual and group level characteristics as group characteristics are absorbed. But this is not a problem as my questions are on the component level.
  • Constant factors like the hierarchical dummy variable drop out.

Hierarchical linear models (multilevel models)

  • Characteristics are analyzed on multiple levels simultaneously
  • I could use different types (Random intercepts, random slopes or random intercepts and slopes model)
  • Evaluation of interaction effects between individual and group level characteristics is possible.
  • But: Here I might get a problem with omitted variable bias

Hierarchical mixed models

  • Mixed models are characterized as containing both fixed and random effects.
  • The fixed effects are analogous to standard regression coefficients and are estimated directly.
  • Random effects may take the form of random intercepts or random coefficients.

So here are finally my questions

  1. Fixed effects model: How do I include independent variables from higher levels that are not time invariant? Each group data is allocated to the individual level??? Is this correct or does it violate the independence assumption.

  2. What is the intuition choosing between fixed effects, hierarchical linear models and mixed models? What conditions should be met?

  3. What problems (e.g. endogeneity or bias problem) does each model solve?

  4. Mixed models: What variables should I use as fixed and random effects?
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