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Lecture 9 (Week 5, Monday)

Review

  • error = the difference between what your model predicts and what your actual scores are in the data
  • randomness = data generating process; the process that generates variation
  • variation in data, when put in a model, becomes error

Overview of Explanatory Models

Empty Model Gives Birth to Error

  • SS tells us how much total error
  • where exactly, does the empty model minimize error?
    • in the sample distribution
    • we don't know the error in the population distribution
    • error = residual = score - predicted

Explanatory Models Seek to Reduce Error

  • trying to reduce error in the outcome variable
  • if we add an explanatory variable, can we reduce error?
  • how should we interpret sum of squares from the empty model?
    • amount of unexplained variation in the outcome variable
    • in empty model, all the variation is unexplained

SS From Empty Model Quantifies Total Error

  • SS Total = total variation in outcome, adds up to 100%
  • by reducing model down, some of our variation has been explained

Two-Group Model - Specifying

  • total error is unchanged
  • reducing unexplained error increases explained error
  • data = group + error
  • how much is error reduced in the GROUP model vs. the EMPTY model?
  • empty model lets us partition each score into model (mean) + prediction
  • explanatory models let us reduce error
  • now we can partition each score into error from the model, and error reduced from the empty model

Fitting, Predict, Resid (Partitioning Scores)

Can Respect Improve Medical Adherence?

  • hypothesis: respectful instructions will create better medical adherence (especially in adolescents)
  • study procedure
    • taste instruction (spoon 1)
    • watch video instructions (respectful or not)
    • how much medicine did they eat? (spoon 2)
  • look at data fram Vegemite.brief
Vegemite.brief <- select(Yeager.Vegemite.Data, r.condition, spoon2.difference)
head(Vegemite.brief)
  • each row is a participant
  • what would a value of 0 on the outcome variable mean?
    • they didn't eat any of the vegemite
    • difference between what they were given and what they ate was 0

Explore the Distribution of the Outcome Variable

gf_histogram(~spoon2.difference, data=Vegemite.brief, fill="green") %>%
gf_facet_grid(respect.condition~.) %>%
gf_vline(xintercept=~mean, data=favstats(spoon2.difference~respect.condition, data=Vegemite.brief))
  • bimodal distribution, people either ate all of it or nearly none of it
  • what are the possible causes of the mean difference?
    • randomness
    • consequences of respect conditions