Calculating metrics of missing variables when using sum contrast

General
1

Dear all,

I’m trying to model the effect of some variables on the response variable in speech-related data. I’m using sum contrast for ease on interpretability. However, there are some aspects of this kind of contrast that I’m not sure I have got them right.

For the fixed variable position, I have three levels position1, position2, and position3 and two are displayed in the summary. For the estimate of third level (position3), I would I just need to subtract the coefficients of both position1 and position2 from the grand intercept:
-0.03 − (-0.12) - (0.13) = -0.04.
This is for calculating the Estimate of the third level.

Q1- How about calculating Est.Error, l-95% CI, and u-95% CI for that level? Should I follow the same procedure and substract the corresponding metrics from grand/scaled intercept? (Note that all variables are standardized).

Q2- Since all variables are standardized, what is the technical name for calling the intercept in this case? I’m aware that I can’t use something like “grand scaled mean” due to the standardization process.

Q3- When it come to the interaction, target_vowel has three levels, voicing has two levels. How can I calculate just the Estimate for these predictors:
a- position3:voicing1

b- position3:voicing1:target_vowel3

Here is the model summary.

Population-Level Effects: 
                                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept                           -0.03      0.14    -0.32     0.25 1.00     5006     9931
position1                           -0.12      0.06    -0.23    -0.01 1.00    28940    26620
position2                            0.13      0.07    -0.00     0.27 1.00    22316    25610
voicing1                            -0.05      0.05    -0.15     0.06 1.00    23643    26165
target_vowel1                        0.27      0.07     0.14     0.40 1.00    22462    24704
target_vowel2                       -0.33      0.06    -0.45    -0.20 1.00    23523    26269
poa1                                -0.06      0.05    -0.15     0.04 1.00    31156    26651
poa2                                 0.05      0.06    -0.06     0.17 1.00    23050    25021
rep                                  0.04      0.03    -0.01     0.10 1.00    70989    25995
position1:voicing1                   0.00      0.06    -0.11     0.12 1.00    27836    25775
position2:voicing1                  -0.06      0.06    -0.18     0.05 1.00    27191    26318
position1:target_vowel1             -0.24      0.08    -0.39    -0.08 1.00    22941    23990
position2:target_vowel1              0.15      0.08    -0.00     0.30 1.00    24254    25518
position1:target_vowel2              0.28      0.08     0.12     0.43 1.00    23488    25444
position2:target_vowel2             -0.24      0.07    -0.38    -0.10 1.00    25248    24689
voicing1:target_vowel1              -0.28      0.07    -0.41    -0.15 1.00    23182    26245
voicing1:target_vowel2               0.28      0.06     0.16     0.41 1.00    24610    26218
position1:voicing1:target_vowel1     0.24      0.08     0.08     0.40 1.00    23393    23355
position2:voicing1:target_vowel1    -0.07      0.07    -0.21     0.08 1.00    24501    25509
position1:voicing1:target_vowel2    -0.15      0.08    -0.31    -0.00 1.00    22996    24711
position2:voicing1:target_vowel2     0.14      0.08    -0.01     0.29 1.00    24029    26580

Any advice is greatly appreciated?

2

Hi, @Dallak. Is there a Stan-related component to the question? Is the output you’re showing from a particular Stan-related package, for example?

3

Hi @Bob_Carpenter!
I guess this is not a stan particular question as it relates more to contrast-related question. I am happy to delete if it does not fit here.

4

No need to delete. It’s just not clear anyone will answer it. We’re mainly focused on Bayesian inference here, not calculating confidence intervals (assuming those were confidence intervals and not credible intervals—I just realized the brms labels the credible intervals “CI”).