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?