Skip to content

Latest commit

 

History

History
93 lines (84 loc) · 4 KB

lecture10.md

File metadata and controls

93 lines (84 loc) · 4 KB

Lecture 10 (Week 5, Wednesday)

Adding an Explanatory Variable to the Model

  • which diagram shows error from the empty model; which the two-group model?
  • explanatory models seek to reduce error
    • partition variation into explained and unexplained (error)
  • what is sum of squares?
    • statistic, not a parameter
    • anything you can calculate based on your data is a statistic
    • parameter is unknown because we don't know about the population

Vegemite.brief (continued)

  • spoon2. difference by Respect
    • respect, or random?
    • does Respect explain some of the variation? the means are different
    • what are the possible causes of this mean difference?

Shuffle Exercise: Exploring the Random DGP

  • shuffle the Respect variable
  • make a new variable based on the variable respect.condition
Vegemite.brief$respect.shuffle <- shuffle(Vegemite.brief$respect)
str(Vegemite.brief)

tally(~respect.condition, data=Vegemite.brief)

tally(~respect.shuffle, data=Vegemite.brief)
  • outputs are the same because we've just shuffled the people within the two categories
head(select(Vegemite.brief, respect.condition, respect.shuffle, spoon2.difference))

Vegemite.brief$respect.shuffle <- shuffle(Vegemite.brief$respect)
gf_histogram(~spoon2.difference, data=Vegemite.brief, fill="orange") %>%
gf_facet_grid(respect.shuffle~.) %>%
gf_vline(xintercept=~mean, data=favstats(spoon2.difference~respect.shuffle, data=Vegemite.brief))

  • the mean difference changes every time you run it

  • completely random pairings of conditions, so the results are varying randomly

  • gives us the context for judging how likely the results we got are random

  • what are the possible causes of the mean difference in this shuffled distribution?

    • these are not the results of our study
    • the only possible cause is randomness
    • we simulated the data generating process; we know it's random
    • eventually, if we run this enough times, we will produce results that look like the actual results we got

  • the mean of spoon2.difference does not change

  • the fact that we have to run this so many times suggests that our results are not only due to random chance

DATA = MODEL + ERROR

  • vegemite eaten = respect + error
    • GLM notation: Yi = b0 + b1Xi + ei
    • b0 = mean of group 1
    • b1 = increment you need to add to group 1 to get the mean of group 2
  • vegemite eaten = mean + error
    • GLM notation: Yi = b0 + ei
    • null model

Using Vegemite.brief data, fit and save two models of spoon2.difference: empty.model & respect.model.

empty.model <- lm(spoon2.difference ~ NULL, data=Vegemite.brief)
respect.model <- lm(spoon2.difference ~ respect.condition, data=Vegemite.brief)
empty.model
respect.model

Using the Model to Make Predictions

  • Yi = 0.138 + 0.088 * Respecti + ei
  • Y-hati = 0.138 + 0.088 * Respecti
    • no error term because this is just a prediction
    • we don't know the error to predict

As the researcher, which parameter are we most interested in?

  • β0 in the empty model, β0 in the two-group model, or β1 in the two-group model?
    • both β0 and β1 in the two-group model

Save the predicted & residual scores from the two models into the Vegemite.brief data frame.

Predicted and Residuals from the Empty Model

Vegemite.brief$empty.predict <- predict(empty.model)
Vegemite.brief$empty.resid <- resid(empty.model)
head(select(Vegemite.brief, respect.condition, spoon2.difference, empty.predict, empty.resid))

Predicted and Residuals from the Two-Group (Respect) Model

Vegemite.brief$respect.predict <- predict(respect.model)
Vegemite.brief$respect.resid <- resid(respect.model)
head(select(Vegemite.brief, respect.condition, spoon2.difference, respect.predict, respect.resid))
  • the comparison between the two models will tell us how much error was reduced