18. Missing Data, Internal Validity, External Validity

Question 1

Effect of data missing at random on bias and other

Answer 1

• No concerns of bias
• Just a smaller sample –> increase s.e.
• OLS estimator is still unbiased

Question 2

Effect of data of missing based on a cutoff of the x value

Answer 2

• No Bias
• smaller sample –> higher s.e.e
• reduces var(x) –> higher s.e.

As the slope of the regression line is the same across the domain of all x, we just have a smaller domain but still the same slope

Question 3

Effect of data missing based on a cutoff of the y value

Answer 3

• Causes Bias

Error is represented by vertical distance between a point and the line.

small x values need a large positive error to meet threshold, thus as x increases, error term decreases on average –> omitted variable in ui that changes on avg. when x changes –> confounder

Question 3

how to test if MAR believable

Answer 3

look at summary statistics of other variables and compare those with missing andn non-missing

Question 4

What is ‘internal validity?

Answer 4

Estimate can be interpreted as a causal effect for the population that is used in the study

no issues (confounders, attenuation bias, bias due to y cutoffs, no simultanaeity/reverse causality, no bad control)

Question 5

External validity

Answer 5

estimate is represenative of the effect for another population

nearly always an assumption, checked by creating estimates in various settings and checking if effects are comparable

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Effect of data missing at random on bias and other

Answer 9

• No concerns of bias
• Just a smaller sample
• OLS estimator is still unbiased

Question 10

Effect of data of missing based on a cutoff of the x value

Answer 10

• No Bias

As the slope of the regression line is the same across the domain of all x, we just have a smaller domain but still the same slope

Question 11

Effect of data missing based on a cutoff of the y value

Answer 11

• Causes Bias

Error is represented by vertical distance between a point and the line.

small x values need a large positive error to meet threshold, thus as x increases, error term decreases on average –> omitted variable in ui that changes on avg. when x changes –> confounder

Question 12

What is ‘internal validity?

Answer 12

Estimate can be interpreted as a causal effect for the population that is used in the study

no issues (confounders, attenuation bias, bias due to y cutoffs, no simultanaeity/reverse causality, no bad control)

Question 13

External validity

Answer 13

estimate is represenative of the effect for another population

nearly always an assumption, checked by creating estimates in various settings and checking if effects are comparable

Question 14

What is standardising a variable?

Answer 14

standardising is a form of normalising where we

• u (mean)
• / (divide) by s.d.

useful for when units cannot be easily understood

Question 15

When standardiisng just x1, what is B1 interpreted as

Answer 15

𝛽1∗ is interpreted as “the average change in 𝑦 that is associated with 𝑥1 increasing by 1 standard deviation.”

Question 16

standardising just y, what is B1 interpreted as

Answer 16

𝛽1∗ is interpreted as “the average number of standard deviations that 𝑦 changes by that is associated with 𝑥1 increasing by 1.”

Question 17

standardising both x1 and y, what is B1 interpreted as?

Answer 17

“the average number of standard deviations that 𝑦 changes by that is associated with 𝑥1 increasing by 1 standard deviation.”

Question 18

Do we have to subtract the mean and dividie by the standard deviation

Answer 18

No for the interpretation it is sufficient to divide by the standard deviation