1 Overview

This supplementary document complements the paper Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish.

Only relevant R code is shown in this document. The full code can be inspected on the OSF repository at https://osf.io/hy7nt/?view_only=d06775a2cb1d4786a0442b0f15d73296, in the file code/analysis.Rmd.

2 Atriculatory data processing

The figure below illustrates the PC1-PC2 rotation for all individual speakers.

This is Figure 1 from the paper, which illustrates the articulatory data processing, as well as vowel formants. See paper for details.

3 Descriptive statistics plots

4 Inferential statistics

## # R2 for Mixed Models
## 
##   Conditional R2: 0.830
##      Marginal R2: 0.772

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.828

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.832

## V1 = a:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.1947 0.0803 70.9 -2.426  0.0178 
## 
## V1 = e:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.3938 0.0721 46.9 -5.462  <.0001 
## 
## V1 = i:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.0232 0.0708 43.8 -0.328  0.7444 
## 
## V1 = o:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.4242 0.0750 54.8 -5.655  <.0001 
## 
## V1 = u:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.0926 0.0759 57.4 -1.219  0.2277 
## 
## V1 = ɨ:
##  contrast              estimate     SE   df t.ratio p.value
##  unstressed - stressed  -0.1340 0.0739 51.7 -1.813  0.0756 
## 
## Degrees-of-freedom method: kenward-roger

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.906

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.907

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.909

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.731

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.732

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.732

## # R2 for Mixed Models
## 
##   Conditional R2: 0.896
##      Marginal R2: 0.721

## # R2 for Mixed Models
## 
##   Conditional R2: 0.895
##      Marginal R2: 0.721

## # R2 for Mixed Models
## 
##   Conditional R2: 0.896
##      Marginal R2: 0.721

5 Model summaries

6 Further exploratory analyses

## # R2 for Mixed Models
## 
##   Conditional R2: 0.781
##      Marginal R2: 0.718

## # R2 for Mixed Models
## 
##   Conditional R2: 0.798
##      Marginal R2: 0.732

## # R2 for Mixed Models
## 
##   Conditional R2: 0.808
##      Marginal R2: 0.743

## # R2 for Mixed Models
## 
##   Conditional R2: 0.904
##      Marginal R2: 0.818

## # R2 for Mixed Models
## 
##   Conditional R2: 0.904
##      Marginal R2: 0.819

## # R2 for Mixed Models
## 
##   Conditional R2: 0.909
##      Marginal R2: 0.826

## # R2 for Mixed Models
## 
##   Conditional R2: 0.749
##      Marginal R2: 0.642

## # R2 for Mixed Models
## 
##   Conditional R2: 0.749
##      Marginal R2: 0.642

## # R2 for Mixed Models
## 
##   Conditional R2: 0.751
##      Marginal R2: 0.642

## # R2 for Mixed Models
## 
##   Conditional R2: 0.914
##      Marginal R2: 0.720

## # R2 for Mixed Models
## 
##   Conditional R2: 0.914
##      Marginal R2: 0.720

## # R2 for Mixed Models
## 
##   Conditional R2: 0.915
##      Marginal R2: 0.720

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.719

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.719

## Random effect variances not available. Returned R2 does not account for random effects.

## # R2 for Mixed Models
## 
##   Conditional R2: NA
##      Marginal R2: 0.720

## Linear mixed model fit by REML ['lmerModLmerTest']
## Formula: z1 ~ (1 + duration | speaker) + (1 | frame) + V1 * duration
##    Data: midpoint_rotated_4PCs
## REML criterion at convergence: 1507.675
## Random effects:
##  Groups   Name        Std.Dev.  Corr 
##  frame    (Intercept) 0.1850794      
##  speaker  (Intercept) 0.0725332      
##           duration    0.0009817 -1.00
##  Residual             0.3918978      
## Number of obs: 1440, groups:  frame, 12; speaker, 10
## Fixed Effects:
##  (Intercept)           V1e           V1i           V1o           V1u  
##   -0.0071179    -0.3859335    -0.8904109    -0.1072723    -0.2021698  
##          V1ɨ      duration  V1e:duration  V1i:duration  V1o:duration  
##   -0.1597102     0.0113978    -0.0066102    -0.0117384    -0.0006565  
## V1u:duration  V1ɨ:duration  
##   -0.0127163    -0.0115170

## # R2 for Mixed Models
## 
##   Conditional R2: 0.905
##      Marginal R2: 0.753

## # R2 for Mixed Models
## 
##   Conditional R2: 0.905
##      Marginal R2: 0.753

## # R2 for Mixed Models
## 
##   Conditional R2: 0.905
##      Marginal R2: 0.752

## Linear mixed model fit by REML ['lmerModLmerTest']
## Formula: z2 ~ (1 + duration | speaker) + (1 | frame) + V1 * duration
##    Data: midpoint_rotated_4PCs
## REML criterion at convergence: 629.3296
## Random effects:
##  Groups   Name        Std.Dev. Corr 
##  frame    (Intercept) 0.374359      
##  speaker  (Intercept) 0.174768      
##           duration    0.002869 -1.00
##  Residual             0.284728      
## Number of obs: 1440, groups:  frame, 12; speaker, 10
## Fixed Effects:
##  (Intercept)           V1e           V1i           V1o           V1u  
##   -0.1968455     0.6291168     1.3587379    -0.3125603    -0.5222861  
##          V1ɨ      duration  V1e:duration  V1i:duration  V1o:duration  
##    0.2731720    -0.0015114     0.0008838     0.0060753    -0.0040087  
## V1u:duration  V1ɨ:duration  
##   -0.0018357     0.0047848

7 Session info

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.1.0 (2021-05-18)
##  os       macOS Big Sur 10.16         
##  system   x86_64, darwin17.0          
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_GB.UTF-8                 
##  tz       Europe/Berlin               
##  date     2021-06-11                  
## 
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