Lab 8: Transformations

Princeton University

Author

Jason Geller, Ph.D.(he/him)

Published

November 30, 2023

Introduction to dataset

We will be analyzing data from the following paper:

Winter, B., Perlman, M., Perry, L. K., & Lupyan, G. (2017). Which words are most iconic? Iconicity in English sensory words. Interaction Studies, 18(3), 433-454.(file:///Users/jasongeller/Downloads/interactionStudies_WinterEtAl2017.pdf)

For this study, Winter et al. collected iconicity ratings from 2,500 native American English speakers for 3,000 words. Participants were asked to rate each word for whether “it sounds like what it means” or “it sounds like the opposite of what it means” on a scale from -5.0 to +5.0. Here, we will be looking at each word’s average iconicity score, and we want to look at what words are most iconic.

Analysis 1: Centering a predictor

Let’s load the data into R


    

  

  

  





A quick explanation of some of the columns.


    

  • Word = the word (should be unique words)
    • 

  • SER = sensory experience ratings from Juhasz & Jap (2013)
    • 

  • imageability = imageability ratings from Cortese & Fugett (2004)
    • 

  • Concreteness = concreteness ratings from Brysbaert et al. (2014)
    • 

  • Systematicity = systematicity ratings from Monaghan et al. (2014)
    • 

  • frequency = frequency of words from SUBTLEX (Brysbaert & New, 2009)
    • 





Check whether there are any duplicate words in the dataset (get_dupes from Janitor package is good one to use)





  
  

    

    

      

    

  

  

  





    

  • If so, which ones are they? Get rid of those:
    

      

    • tuxedo and yacht
      • 

    • 




  
  

    

    

      

    

  

  

  







Get rid of NAs in the model





  
  

    

    

      

    

  

  

  







Fit a model regressing iconicity onto the predictor SER (sensory experience ratings):





  
  

    

    

      

    

  

  

  







Check model:





  
  

    

    

      

    

  

  

  







Create a centered predictor:





  
  

    

    

      

    

  

  

  







Create a centered lm model:





  
  

    

    

      

    

  

  

  







Check both model outputs





  
  

    

    

      

    

  

  

  






  
  

    

    

      

    

  

  

  







Any differences between the two?




    

  • Nope. Only the intercept is different.
    • 





Write up the interpretation of the centered model (interecpt and slope)




    

  • \(b_0\): The mean value of iconicity when SER is at it’s mean
    • 

  • \(b_1\): As SER increases, iconicity increases, \(b\) = 0.184, SE = 0.024, t=7.54, p < .001. That is, SER scores are associated increased rating of iconicity.
    • 







Analysis 2: Log-transforming a predictor




Create a ggplot2 density graph of the frequency predictor:





  
  

    

    

      

    

  

  

  







Check the same frequency predictor on a log scale:





  
  

    

    

      

    

  

  

  







Use mutate() to log transform the frequency predictor:





  
  

    

    

      

    

  

  

  







Fit two models, one regressing iconicity onto raw frequency, and one regressing it onto log frequency:





  
  

    

    

      

    

  

  

  







Compare model summaries with glance()





  
  

    

    

      

    

  

  

  







use the anova fucntion to statistically compare both models





  
  

    

    

      

    

  

  

  







Which one fits the data better?




    

  • The model with frequency logged fitted the data better
    • 





Write up the interpretation for the better fitting model





  
  

    

    

      

    

  

  

  





    

  • \(b_0\): the expected value of Y when frequency is at 0.
    • 

  • \(b_1\): A 1% increase in log frequency results in a -0.13/100 decrease in iconicity scores, b=-0.13, SE = 0.02, t = -7.36, p < .001.
    • 







Analysis 4: Multiple predictors


    

  • For the main analysis presented in Winter et al. (2017), they regressed iconicity simultaneously onto SER, concreteness, imageability, systematicity and log frequency.
    • 





fit that model





  
  

    

    

      

    

  

  

  







Check how the concreteness predictor behaves if imageability is not in the model:





  
  

    

    

      

    

  

  

  







What do you notice?




    

  • Concreteness is significant when imagabiity is not included.
    • 





Check correlation between concreteness and imageability





  
  

    

    

      

    

  

  

  







Is it high?




    

  • The correlation is high.
    • 





Check multicollinearity of the main with all the variables in the model





  
  

    

    

      

    

  

  

  





    

  • None of the VIFs > 10
    • 



There’s a lot of talk about different thresholds, with some saying >10 is worrisome, others saying >4 worrisome.


The model in the paper did not go with concreteness because they didn’t think it was sufficiently distinct from imageability, also on a theoretical level.






Analysis 5: Standardizing predictors


    

  • What predictors have the biggest influence on iconicity ratings?
    • 



The problem is that the slopes are unstandardized, which makes them difficult to compare. Remember that each coefficient is given as a rate of how much iconicity has to change “per one unit of that variable”. The problem is that “one unit” has very different meanings for the different variables.




Look at the range of SER and systematicity values





  
  

    

    

      

    

  

  

  





    

  • Whereas the SER variable ranges from 1 to about 5.2, the systematicity variable has a really narrow range. A one unit (=1.0) change is a massive jump for a variable with this metric.
    • 





Standardize each predictor in the model without concreatness





  
  

    

    

      

    

  

  

  







Then we re-fit the model with the standardized predictors.





  
  

    

    

      

    

  

  

  







Rank order the coefficients minus the intercept:





  
  

    

    

      

    

  

  

  







Which one has the biggest influence?




    

  • SER does
    • 





Write-up this model (focusing on the coeffiencets)




    

  • For each one standard deviation increase in ‘Imageability_z’, iconicity is expected to decrease by 0.367 units
    • 

  • A one standard deviation increase in the logarithm of frequency is associated with a decrease of about 0.117 units in iconicity
    • 

  • For each one standard deviation increase in ‘Systematicity_z’, iconicity increases by approximately 0.045 units
    • 

  • For each one standard deviation increase in ‘SER_z’, iconicity is expected to increase by about 0.417 units
    • 







Polynomial Regression




Load in data from https://osf.io/kzm7b





  
  

    

    

      

    

  

  

  







Subset the data so we only have a column for Fear Piggy and Enjoy Piggy





  
  

    

    

      

    

  

  

  







Create a plot visualizing the realtionship between the two variables





  
  

    

    

      

    

  

  

  







Do you think a linear model is a good fit to this data? Add a linear line to the data.





  
  

    

    

      

    

  

  

  





    

  • No. It does not fit the data very well.
    • 





Use mutate() to add a quadratic X term





  
  

    

    

      

    

  

  

  







Now fit a polynomial regression that includes a quadratic term





  
  

    

    

      

    

  

  

  







The coefficient for the squared term is negative. What does this mean?




    

  • It means the shape is inverted U–it incrases up to a certain point and decreases
    • 





Add a quadratic line to the scatter plot from above





  
  

    

    

      

    

  

  

  







Does a model with a quadrtic term fit the data better than a linear one? Test this.





  
  

    

    

      

    

  

  

  





    

  • It does not.
    • 













Note







While we do not find a significant quadratic relationship in this analysis, the paper does. This is because they looked at several scares and used a different model. Nonetheless, hopefully you better understand how to test non-linear relationships in a regression context