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Regression reconsidered 5
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- 1Regression is descriptive (average value of Y, given the value(s) of X and summarises large datasets with potential issues outliers, nonlinearities and extrapolations with continuous covariates); predictive (predicting Y given specific realizations of X= x, paribus assumption: thes ystem will remain stable, i.e. structural relationship between Y and X is constant); causal (changes in Y follow changes in X, a priori, this interpretation is only adequate in an analysis of a randomized experiment)Assumptions: The independent variables are measured with no error.
•The predictors are linearly independent, i.e. it is not possible to express any predictor as a linear combination of the others (no multicollinearity).
•The errors are uncorrelated, that is, the variance–covariance matrix of the errors is diagonal and each non-zero element is the variance of the error (independence).
•The variance of the error is constant across observations (homoscedasticity).
•The mean of the response variable is a linear combination of the parameters and the predictor variables(linearity).
•The regression residuals are normally distributed (normality).
•The errors are uncorrelated to the regressors(orthogonality). - 2Omitted variable bias: is what the regression assumption that the covariates be unrelated to the error term implies and violations of this assumptions are usually conceptualized as a problem of omitted variable biasControlling via regression: problems occur if D is related to either baseline bias or differential treatment effect bias.
Selecting relevant confounders: D->Y and Y-> D produce the same covariance structure, i.e. they are observationally equivalent; so are X ->D ->Y and D ->X ->Y - 3X is a cause of Y when change in X produces change in Y; or (because some Xs don’t change) Ys tend to line up with fixed values of X; when Y starts after X ended; when X is relatively stable, and Y is volatileRegression pertains to all statistical control methods for causal inference
•Re (2), matching estimators non-parametrically balance X across D in order to make subjects under T and C state look similar
•Re (3), matching estimators throw away information from the joint distribution of Y and X that is unrelated to variation in D until the remaining distribution of X is equivalent for both T and C group - 4Regression models remain one of the most popular techniques for the evaluation of alternative explanations in social sciencesStrengths: computational simplicity, its multitude forms and the ease with which one can induce computer software to generate standard errors
Weaknesses: suppress attention towards potential heterogeneity of causal effects, exogeneity can befuddle researchers who otherwise grasp the conditions that undergrids matching.
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- Fichas sobre Regression reconsidered 5, creado por tri_nana el 01/07/2015.
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