• Understand what can regression be used for
• Learn ho to select variables for explanative models

If you wish to make an apple pie from scratch, you must first invent the universe.

• Carl Sagan

Mars, what are you doing?

Universe according to Ptolemy

Universe accordin to Copernicus

• Other differences include: choosing variable, evaluating model fit, choosing sample sizes and more…

• For more details, see: Shmueli, G. (2010). To Explain or To Predict? (SSRN Scholarly Paper ID 1351252). Social Science Research Network. https://doi.org/10.2139/ssrn.1351252

• Predictive models: Which people are going to vote?
• Explanative models: What is the effect of age on voter turnout?
• Descriptive models: What is the relationship between age and voter turnout?
• Inferential models: How many people are going to vote?

• Which model are you aiming for?

• We are going to be mainly interested in explanative models.

• A researcher is interested in the relationship between intelligence and work self-discipline among adults, but is short on funding.

• Their collegue suggests using university students as their sample.

• Is this a valid design decision?

• Goal of analysis matters

• Some fields can rely on randomization of treatment (e.g. drug testing). Social sciences generally can’t.

• Strong focus on theory, with help of Directed Acyclic Graphs.

DAG example

Does increasing knowledge about Covid raise the probability a person gets vaccinated?

Knowledge leads to behavior?

• What if we only have cross-sectional data?

• Should we control for:
  • Socio-economic status?
  • past hospitalization?
  • Percieved threat?

• Assume socio-econ. status raises knowledge about Covid and also raises vaccination probability.
• What does is it mean for the estimate of knowledge -> vaccination?

• Assume Covid knowledge lowers probability of hospitalization and at the same time, vaccination lowers probability of hospitalization.
• What does is it mean for the estimate of knowledge -> vaccination?

• Two 6 sided die, fair, independent.
• Can you tell outcome of the second dice based on outcome of the first one?

• Two 6 sided die, fair, independent.
• But this time, we know the total.

• Conditioning on / controlling for colliders creates artificial relationships.

• We should never condition on colliders.

• How could Covid knowledge influence vaccination probability?
• Perhaps by raising the perceived threat of health problems?
• Presence of mediators changes interpretation of regression coefficients!

3

• What if the relationships between Covid knowledge and vaccination probability changes based on where people live?
• Moderators are interactions. Without them, we get an average effect.

3

• A researcher is interested in the relationship between intelligence and work self-discipline among adults, but is short on funding.

• Their collegue suggests using university students as their sample.

• Is this a valid design decision?

• While drawing DAGs can be easily done by hand, R can make them pretty
• It can also tell you what variables to control for, assuming your DAG is correct.

• We need to packages to work with DAGS in ggplot2 framework:

install.packages("dagitty") # for drawing DAGs in R
install.packages("ggdag") # For making them in ggplot2

dagify(y ~ x + z + q ,
       x ~ z,
       q ~ x,
       w ~ y + x) %>% 
  ggdag() +
  theme_void() # to get rid of the backround

• Same result as previously, more control over the looks

dagify(y ~ x + z + q ,
       x ~ z,
       q ~ x,
       w ~ y + x) %>% 
  ggplot(aes(x = x, xend = xend, y = y, yend = yend)) +
  geom_dag_edges() +
  geom_dag_point() +
  geom_text(aes(label = name), color = "white") +
  theme_void()

dagify(y ~ x + z + q ,
       x ~ z,
       q ~ x,
       w ~ y + x,
       labels = c(y = "Vaccination\nProbability", x = "Covid\nKnowledge",
                  z = "Soc-econ. status", q = "Perceived threat", w = "Hospitalization"),
       coords = list(x = c(y = 2, x = 1, z = 1.5, w = 1.5, q = 1.5),
                     y = c(y = 1, x = 1, z = 1.15, w = 0.85, q = 0.94))) %>% 
  ggplot(aes(x = x, xend = xend, y = y, yend = yend)) +
  geom_dag_edges() +
  geom_dag_point() +
  geom_text(aes(label = label), color = "red") +
  theme_void()

our_dag <- dagify(y ~ x + z + q ,
                  x ~ z,
                  q ~ x,
                  w ~ y + x,
                  exposure = "x",
                  outcome = "y")

ggdag_adjustment_set(our_dag, shadow = T) + theme_void() # red ones are confounders

our_dag <- dagify(y ~ x + z + q ,
                  x ~ z,
                  q ~ x,
                  w ~ y + x,
                  exposure = "x",
                  outcome = "y")

ggdag_collider(our_dag) + theme_void()