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 X5 is unrelated to the true propensities. Yes, because the outcome Y is still a function of Xs No, because it is impossible to know if the subgroups are balanced in terms of X5 No, because X5 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 estimates 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 X5 is unrelated to the true propensities. Yes, because the outcome Y is still a function of Xs No, because it is impossible to know if the subgroups are balanced in terms of X5 No, because X5 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 estimates 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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text:The true data-generating mechanism for the simulated data is
Y = 4Z – 0.8X1 - 3X2 + 6X4 +X5 + error.
d.) Note that the outcome of interest Y is a function of X5, 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 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 X5 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 estimates 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
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