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everyone!

I am trying to analyze my non-normally distributed outcome data from a psychological behavioural experiment. I have tried some commonly used transformation functions to covert them into normally distribution, but all failed, so I hope to ask for help about the non-parametric alternatives to 3-way repeated measure ANOVA.

There were three factors (independent variables=IV) in my design, and all were categorical variables: IV A was a between-subject factor and had three levels (low, middle, high), IV B was a within-subject factor and had two levels (low, high), IV C was also a within-subject factor and had two levels(short, long). I hope to conduct a 3-way repeated measure ANOVA to investigate the main and interaction effects of the three factors on the outcomes(dependent variables). The dependent variables were continuous scale variables.

I prefer the SPSS software, MATLAB and R. Could anyone please provide any suggestions for my problems? Thank you!

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Consider using a longitudinal proportional odds ordinal logistic regression model. You can make the ordinary model longitudinal in multiple ways, including a Markov model and a random effects model. The latter is less likely to fit the needed correlation patterns if you have serial correlation instead of compound symmetry. All this is best done with Bayesian modeling as illustrated here but you can also use frequentist models. R has the richest environment for semiparametric (ordinal) models. See for example the VGAM, ordinal, and mixor package in addition to univariate ordinal models in the rms package's lrm and orm function, the latter for continuous Y, efficiently handling 1000s of distinct Y levels.

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  • $\begingroup$ Hi, Frank! Thanks for your suggestion and help. Sorry, the longitudinal proportional odds ordinal logistic regression model is quite novel to me. Are the Markov model, the random effects model and the Bayesian modeling all for the longitudinal proportional odds ordinal logistic regression model? Could you please provide more suggestions for books or files that I could refer to learn more about this model?Thank you! $\endgroup$
    – user322715
    Commented May 26, 2021 at 2:25
  • $\begingroup$ See multiple reports related to this at hbiostat.org/proj/covid19 and also the vignette at hbiostat.org/R/rmsb $\endgroup$ Commented May 26, 2021 at 15:05

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