In GAMLj3 add a note under the table when a variable is centered

[Mik]

Hello,

Since the coefficients change when a variable is centered in a regression model, I suggest that it would be useful to add a note under the coefficient table when this is the case.

I added an example in the attachment.

Regards,

Michael

[mcfanda@gmail.com]

Would you ask to add the same note to any software that centers categorical variable? Gamlj centers the continuous variables by default because when it does not matter results are the same of not centering, but when it metters (interactions, random intercepts, etc) results are what users expect (main effects, random means, etc)

The same is done for categorical variables. The aim is to convey the idea that in the linear models there is no difference between categorical variables and continuous variables, this difference has been perpetrated by software, but it has no statistical underpinning (Aiken, L. S. (1991). Multiple regression: Testing and interpreting interactions. sage.)

Nonetheless, one can remove centering in the Covariates Scaling panel.

[mcfanda@gmail.com]

However, what we can do is to add in the info table a reminder about the continuous variables scaling

[Mik]

Yes I would. Thank you for the Aiken (1991) reference. My point was not about the default option but to remind the user about the option that is selected. Without that information, there is no way to know in the output how the covariates were scaled (centered vs. original scores). For the sake of replication of the results, I think this is important. Many software have embedded default options that are not "visible". This might not be an issue for knowledgeable users, but it is always important for learners and when the goal is to teach about these techniques.

[Mik]

I would also add that mean centering predictors is not a necessity:

"First, mean centering X and M prior to computation of their product produces an estimate of the effect of X or M on Y that is conditioned on a value of M or X that will always be within the range of the data (i.e., at the sample mean), unlike when mean centering is not done. Thus, by mean centering, the consequences of the kind of misinterpretations we describe here will be much less severe when they occur. Second, in complex models with several interactions involving the same variable, multicollinearity can in rare circumstances produce computational difficulties in some statistical programs. Mean centering X and M prior to computing their product does indeed reduce this “nonessential” multicollinearity and thereby eases the computation problems that sometimes though rarely arise. In the majority of applications of moderated multiple regression in the field of communication, however, mean centering or standardization is a choice one can make, to do or not to do, rather than a requirement." (Hayes et al., 2012, p. 10).

Reference: Hayes, A. F., Glynn, C. J., & Huge, M. E. (2012). Cautions regarding the interpretation of regression coefficients and hypothesis tests in linear models with interactions. Communication Methods and Measures, 6(1), 1–11. DOI: 10.1080/19312458.2012.651415

[mcfanda@gmail.com]

Sure, in fact in gamlj one can center, standardize and not center (keep the original). They all produce correct results (actually the same model is produced), only with different interpretation of the coefficients. Centering guarantees that the interpretation of the coefficients is the one *most users* expect, but for users that know what they are doing, centering is surely not necessary.
However, in the next version a reminder of the centering will be in the "Info table" (not in every table because it clutters the tables a bit too much).

[mcfanda@gmail.com]

It's coming out like this. I hope it works

p1.png (25.91 KiB) Viewed 2586 times

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p3.png (26.68 KiB) Viewed 2586 times

when the IVs use the same method, it says

p2.png (24.56 KiB) Viewed 2586 times

[Mik]

This is perfect, thank you very much for being open to my suggestion.