The true data-generating mechanism for the simulated data is Y = 4Z-0.8X1- 3X2 + 6X4 + Xs + error. d.) Note that the outcome of interest Y is a function of Xs, and thus balance on X5 is critical for valid causal inference. If units are matched or partitioned into subgroups according to their true propensity scores, are these subgroups expected to be balanced, on average, in terms of X5? Why or why not? Choose the best answer. Yes, because Xs is unrelated to the true propensities. Yes, because the outcome Y is still a function of X5 No, because it is impossible to know if the subgroups are balanced in terms of Xs No, because Xs is independent of all other covariates No, because X5 is not a confounding variable Now fit a single propensity score model that is overspecified: use all five covariates as well as Interactions between x3 and each of the other four covariates to predict the propensities. Again, use the fitted model to predict point estimates of the propensity scores for each observation, and compare your estímates to the true propensities. e.) What is the standard deviation of the prediction errors e (X) - ê (X) for the propensities predicted by this overspecified propensity model? Choose the closest answer. 0.005 0.03 0.09 0.90 11.5
The true data-generating mechanism for the simulated data is Y = 4Z-0.8X1- 3X2 + 6X4 + Xs + error. d.) Note that the outcome of interest Y is a function of Xs, and thus balance on X5 is critical for valid causal inference. If units are matched or partitioned into subgroups according to their true propensity scores, are these subgroups expected to be balanced, on average, in terms of X5? Why or why not? Choose the best answer. Yes, because Xs is unrelated to the true propensities. Yes, because the outcome Y is still a function of X5 No, because it is impossible to know if the subgroups are balanced in terms of Xs No, because Xs is independent of all other covariates No, because X5 is not a confounding variable Now fit a single propensity score model that is overspecified: use all five covariates as well as Interactions between x3 and each of the other four covariates to predict the propensities. Again, use the fitted model to predict point estimates of the propensity scores for each observation, and compare your estímates to the true propensities. e.) What is the standard deviation of the prediction errors e (X) - ê (X) for the propensities predicted by this overspecified propensity model? Choose the closest answer. 0.005 0.03 0.09 0.90 11.5
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
3
Transcribed Image Text:The true data-generating mechanism for the simulated data is
Y = 4Z – 0.8X1 - 3X2 + 6X4 + Xs + error.
d.) Note that the outcome of interest Y is a function of Xs, and thus balance on Xg is critical for
valid causal inference. If units are matched or partitioned into subgroups according to their true
propensity scores, are these subgroups expected to be balanced, on average, in terms of X5? Why
or why not? Choose the best answer.
Yes, because X5 is unrelated to the true propensities.
Yes, because the outcome Y is still a function of X5
No, because it is impossible to know if the subgroups are balanced in terms of X5
No, because Xs is independent of all other covariates
No, because Xs is not a confounding variable
Now fit a single propensity score model that is overspecified: use all five covariates as well as
Interactions between x3 and each of the other four covariates to predict the propensities. Again,
use the fitted model to predict point estimates of the propensity scores for each observation, and
compare your estimates to the true propensities.
e.) What is the standard deviation of the prediction errorse (X) - ê (X) for the propensities
predicted by this overspecified propensity model? Choose the ciosest answer.
0.005
0.03
0.09
0.90
11.5
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman