# Calculating metrics of missing variables when using sum contrast

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

``````