# Unbalanced Longitudinal Multilevel Model Power Analysis

I am trying to conduct a power analysis on a multilevel longitudinal model (pre-existing household panel dataset) and am having trouble figuring out how to do it (or if it is even needed in the first place, however I am assuming that I will be asked the question by reviewers if I do not include it). I am using R for all analysis (lme4 package) and would therefore prefer an R solution if possible (but it doesn’t have to be).

Below is a summary of the model.

Outcome DV

• Job satisfaction measured over time (up to 10 time points)

Level 1 (within-person) variables:

• Time
• Personality trait 1
• Personality trait 2
• Personality trait 3
• Personality trait 4
• Personality trait 5
• Employment status (part-time or full-time, coded as 0 or 1)
• Monthly gross income

Level 2 (between-person) variables:

• Time (the between-person component of the level 1 variable)
• Personality trait 1 (the between-person component of the level 1 variable)
• Personality trait 2 (the between-person component of the level 1 variable)
• Personality trait 3 (the between-person component of the level 1 variable)
• Personality trait 4 (the between-person component of the level 1 variable)
• Personality trait 5 (the between-person component of the level 1 variable)
• Employment status (the between-person component of the level 1 variable)
• Monthly gross income (the between-person component of the level 1 variable)
• Gender
• Average age

Cross-level interaction:

• Time (level 1) x Personality Trait 1 (level 2)

The model has job satisfaction as its outcome variable where I am interested in modelling the growth in job satisfaction as a consequence of between-person (level 2) extraversion (hence the cross-level interaction). Individuals serve as the level two clusters (N = 7,275) and observations of time serve as the primary level one predictor (N = 23,974, unbalanced such that different individuals have different N observations). All other variables are covariates and for all time-varying covariates I have split them into their within-person and between-person components (hence the double-up at level 1 and level 2 for all variables but age and gender).

Any help would be appreciated.

• If you still want to do it, then given the complexity in your design I would say that the only viable approach is simulation. That is, you simulate, say $$B = 1000$$ datasets from your model based on the postulated design, you fit the model in each dataset and you perform the test of interest and keep the p-values. The proportion of times the p-value was significant at a give level will be your power.