With your DV I recommend using limited dependent variable regression (limdep). This was in the econometrics literature originally. Good luck, David Booth

Hi David,

Thanks for your thoughts. Limited dependent variable regression is a new phrase to me. It looks like I may benefit from considering truncated limited regression. I will look into that.

I did originally consider a more traditional logistic limited model, where the data is recategorized in binary manner. For this data set, the upper and lower asymptotes are never reached (on average) within a reasonable number of Trials (the repeated measure), so linear predictions of duration or percent correct response make nearly the same predictions as a logistic regression of a binary reclassification of the data. I feel like neither is truly an accurate representation of behavior, because I do have a truncated, but continuous DV, so for the moment I sided with the linear approach as this seems to be more convenient for readers in my field. I'm going to look into the truncated limited regression that your suggestion lead me to, perhaps I can find something better. The pairwise comparison issue still remains, but I'm happy for your suggestion on the DV, this was something else I considered a lot. Thanks.

I think the function/package/procedure for pairwise comparisons in all of R, SPSS, and SAS is emmeans. Some used to be lsmeans. This should be available for the model you are using. I'm not sure what's available in Python .

Hi,

A repeated measures ANOVA *is* a regression analysis. Roughly speaking, in statistical software packages the ANOVA application is just a convenient way to specify linear contrasts on the variables to get the cell means you want and the right error term for within subjects variables like Trial. If you run your model as a regression analysis, then you are on your own to write your linear contrasts, e.g.,

group 1 mean = b0 + b1*X1 + b2*X2 + ....+ b15*X15

group 2 mean

etc.

(you have 7 variables representing the 8 groups, 1 variable for Trial, and seven more variables to represent the group x trial interaction for a total of 15 predictor variables).

One argument for using ANOVA is that it saves you time and reduces the chance for user error in specifying your contrasts and correct error terms. As pointed out by another poster, this is lsmeans in SAS and emmeans in SPSS.

See this StackExchange discussion for more and a reference to a Gelman paper on the topic:

https://stats.stackexchange.com/questions/175246/why-is-anova-equivalent-to-linear-regression

Hope this helps,

Scot

Hi all, I am aware of the relationship between ANOVA and regression, but most of the time I find that regression is easier to interpret in the context of my work. This data set might be the exception, as I have more categorical variables than I normally work with. I did find some ways to analyze interactions in emmeans and similar functions that I was not expecting, so this was helpful too.

I have also found some discussion on creating z scores representing the difference between two regression coefficients. For a discussion see:

https://stats.stackexchange.com/questions/93540/testing-equality-of-coefficients-from-two-different-regressions

This, along with a Bonferroni or other familywise error rate correction may also be a good way to add some post hoc analysis to a regression analysis.

Thanks for all your thoughts.