This app helps you to plan a study with the optimal number of persons (n) and time Points (t) for maximal power given your budget
Simply follow Steps (1), (2) and (3)

(1) Study Design

First, indicate key features of your planned study.


Persons N

Time Points T


(2) Model Characteristics

Second, indicate the model class that you plan to analyse the data with and the names of the manifest processes that you plan to investigate.


Please indicate at least one process name. Seperate multiple names with comma. The number of processes for a given model is inferred from the number of names. It is displayed right to the input field.



The example path diagram below helps you select a model class and set model parameters. It shows your currently selected model class and the non-zero model parameters of the defaults of the app.
(3) Model Parameters

Third, set model parameters and choose target parameters for which you want to maximize the joint power.

  • Set the model parameters in the matrices.
    (Note that variance parameters must be larger than zero)

  • Choose the target parameters from the drop-down menu.


    • Autoregressive and Cross-Lagged Effects (AR & CL)

    Specfiy AR effects in the diagonal; CL effects in the off-diagonal. For the direction of CL effects: columns → rows

    Dynamic Residuals (RES)

    Variances and Covariances

    Please only fill in covariances in lower triangular matrix.

    Unique Residuals (UNIQ)

    Variances and Covariances

    Please only fill in covariances in lower triangular matrix.

    Random Intercepts (I)

    Variances and Covariances

    Please only fill in covariances in lower triangular matrix.

    Random Slopes (S)

    Variances and Covariances

    Please only fill in covariances in lower triangular matrix.

    Covariances of Random Intercepts and Random Slopes (IS)


    Constant Accumulating Factor (A)

    Variances and Covariances

    Changing Accumulating Factor (B)

    Variances and Covariances

    Covariance of Accumulating Factors (AB)


    Results

    Finally, have a look at the results.
    Note that the results change immediately when you change any input.


    Optimal Number of Units for Maximal Power
     for which the power of the likelihood-ratio tests of the target parameters is maximal



    Maximum Power for All Target Parameters
     for all target parameters based on the optimal n and t solution

    Technical Details

    Here you have some further options.

  • Change precision of the optimizer.
    (“Precision” is a user-friendly term for what the argument pop.size of the genoud optimizer from the package rgenoud adjusts, see Mebane and Sekhon, 2011.)

  • Disallow logging of your results.
    (This helps us improving this app!)

  • Get technical information on your last results.


    • Run Time (in sec):
    Number of Iterations:

    Log Run Time (in sec):
    Log ID:
    Log Status:
    App Version:


    References
    Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. P. P. (2015). A critique of the cross-lagged panel model. Psychological Methods, 20, 102–116. https://doi.org/10.1037/a0038889

    Mebane, W. R., & Sekhon, J. S. (2011). Genetic optimization using derivatives: The rgenoud package for R. Journal of Statistical Software, 42. https://doi.org/10.18637/jss.v042.i11

    Usami, S., Murayama, K., & Hamaker, E. L. (2019). A unified framework of longitudinal models to examine reciprocal relations. Psychological Methods, 24, 637–657. https://doi.org/10.1037/met0000210

    If you use the app for publications, please cite the corresponding article:


    Ipsum, L. (2023). Lorem Ipsum Lorem Ipsum. https://shiny.psychologie.hu-berlin.de/optdynmo/